Composite Sandwich Structures with Honeycomb Core

Clemson UniversityTigerPrints

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12-2012

Composite Sandwich Structures with HoneycombCore subjected to ImpactLei HeClemson University, [email protected]

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i

COMPOSITE SANDWICH STRUCTURES WITH HONEYCOMB CORE

SUBJECTED TO IMPACT

A Thesis

Presented to

the Graduate School of

Clemson University

In Partial Fulfillment

of the Requirements for the Degree

Master of Science

Mechanical Engineering

by

He Lei

December 2012

Accepted by:

Lonny.L.Thompson, Committee Chair

Gang Li

Mohammed Daqaq

ii

ABSTRACT

Composite sandwich structures constructed with honeycomb core can be an

effective means of absorbing impact in many engineer applications. Conventional

hexagonal honeycomb exhibit an effective positive Poisson’s ratio, are commonly

employed due to their lightweight and high axial stiffness properties. In contrast, auxetic

honeycombs offer high in-plane shear stiffness, and exhibit negative Poisson’s ratios with

lateral extension, instead of contraction, when stretched axially.

In this study, the dynamic response of an aluminum composite panel with a

honeycomb core constrained within two thin face sheets is investigated undergoing

impact with a rigid ball. The finite element models used to simulate impact of the rigid

ball with the honeycomb composite panel are solved using a nonlinear explicit dynamic

analysis procedure including large deformation in ABAQUS, a commercial software

package. This approach enables the cost-effective analysis, accurate estimation of the

impact, and further understanding of the parameters that influence the complex response.

The rebound velocity and kinetic energy time history of the rigid ball, together

with the kinetic and strain energies, and displacement and velocity for the elastic

structure during impact and after separation of the impacting bodies are presented to

show the effect of different velocity magnitudes of the impacting ball and comparisons

with regular and auxetic honeycomb cell geometries. Additionally, the effects of various

impacting velocities and honeycomb geometries are compared for impact in two

perpendicular in-plane directions, and from out-of-plane impact.

iii

Using the results of the incoming and rebound velocity of the ball, as well as the

velocity of the point of contact on the structure at separation, and effective coefficient of

restitution (COR) for the honeycomb sandwich structure is calculated and compared.

Other measures include the ratio of incoming to outgoing fall velocities and ratio of

incoming to outgoing kinetic energies.

Results show that the increase of the impacting velocity increases both the

kinetic energy and strain energy absorbed in the structure. Results also showed that for

both in-plane and out-of-plane impacts, the regular honeycomb structure absorbed more

energy compared to the auxetic structure. In addition, according to the results of the

COR, impact with the auxetic model shows higher elastic rebound than the regular

model.

iv

TABLE OF CONTENTS

Page

TITLE PAGE .................................................................................................................... i

ABSTRACT ..................................................................................................................... ii

LIST OF TABLES .......................................................................................................... iv

LIST OF FIGURES ......................................................................................................... #

CHAPTER

I. INTRODUCTION ......................................................................................... 1

II. MOMENTUM AND IMPACT THEORY .................................................... 6

III. MATERIAL AND GEOMETRY PROPERTIES ......................................... 9

Material Properties ................................................................................... 9

Modeling of the Sandwich Panel ............................................................ 12

IV. FINITE ELEMENT MODELS .................................................................... 18

Finite Element Models ........................................................................... 18

Constraints ............................................................................................. 21

Boundary Conditions ............................................................................. 22

Predefined Fields ................................................................................... 24

V. RESULTS AND DISCUSSION .................................................................. 25

Impact Behavior of Sandwich Panels .................................................... 25

Results of In-Plane Impact from X1 direction ....................................... 25

Results of In-Plane Impact from X2 direction ....................................... 45

Results of Out-of-Plane Impact .............................................................. 64

v

Table of Contents (Continued)

Page

VI. CONCLUSION AND FUTURE WORK .................................................... 84

Concluding Remarks .............................................................................. 84

Future Work ........................................................................................... 85

REFERENCES .............................................................................................................. 86

vi

LIST OF TABLES

Table Page

3.1 Material properties of aluminum alloy .......................................................... 8

3.2 Geometric parameters of regular and auxetic honeycomb cell ...................... 9

3.3 Mass configurations of in-plane model........................................................ 13

3.4 Mass configurations of out-of-plane model ................................................. 15

5.1 The velocity effect of the rigid ball of the impact to

X1-direction in-plane impact to regular model ..................................... 24

5.2 The initial and returning kinetic energies of the impacting

ball during X1-direction in-plane impact to regular model .................. 25


X1-direction in-plane impact to auxetic model .................................... 32

5.4 The initial and returning kinetic energies of the impacting

ball during X1-direction in-plane impact to auxetic model .................. 33

5.5 COR of the X1 in-plane impact at different velocities ................................ 42


X2 direction in-plane impact to the regular model ............................... 43

5.7 The initial and returning kinetic energy of the impacting ball

during X1 in-plane impact to regular model ......................................... 44


X2-direction in-plane impact to auxetic model .................................... 50

5.9 The initial and returning kinetic energy of the impacting

ball during X1-direction in-plane impact to regular model .................. 51

5.10 COR of the X2 in-plane impact at different velocities ................................ 60

5.11 The velocity effect of the rigid ball after the impact of an

out-of-plane impact to regular model ................................................... 61

vii

List of Tables (Continued)

Table Page


during out-of-plane impact to regular model ....................................... 63

5.13 The velocity effect of the rigid ball of the impact to out-of-plane

impact to auxetic model ........................................................................ 69


during out-of-plane impact to the auxetic model .................................. 70

5.15 COR of the out-of-plane impact at different velocities ............................... 79

viii

LIST OF FIGURES

Figure Page

1.1 Fatigue failure envelopes for sound level vs. time of

sandwich structure and skin-stiffened structure 2

1.2 Unit cell geometry of regular and auxetic honeycombs 3

3.1 Dimensions of regular and auxetic unit cell 10

3.2 Overall dimension of regular and auxetic cores with

in-plane model 11

3.3 The complete assembled composite sandwich plate of

in-plane model (impact from X1 direction) 12


in-plane model (impact from X2 direction) 13

3.5 The honeycomb core of out-of-plane model 14


out-of-plane model 15

4.1 Meshed face sheet and cores for in-plane model 17

4.2 Meshed face sheet and cores for out-of-plane model 18

4.3 Meshed rigid ball 19

4.4 Tie constraint of out-of-plane impact model 20

4.5 Boundary Condition imposed on in-plane model 21

4.6 Boundary condition imposed on out-of-plane model 22

5.1 Velocity-time history of the impacting ball for X1-direction

in-plane impact to regular honeycomb model 24

ix

List of Figures (Continued)

Figure Page

5.2 Time histories of the kinetic energy of rigid ball for

X1-direction in-plane impact to regular model 25

5.3 The reaction force history of X1-direction in-plane impact

to regular model 26

5.4 Velocity history of the point on the spot of the X1-direction

in-plane impact to regular model 27

5.5 Kinetic energy-time history of the whole regular structure for

X1-direction in-plane impact 28

5.6 Displacement history of the point on the spot of the


5.7 Strain energy-time history of the whole regular structure for


5.8 Energy-time history of the whole regular structure for

X1-direction in-plane impact at 400 m/s 31


in-plane impact to auxetic model 32

5.10 Time histories of the kinetic energy for X1-direction in-plane

impact to auxetic model 33

5.11 The reaction force history of the auxetic model to




5.13 Kinetic energy-time history of the whole auxetic structure for



X1-direction in-plane impact to auxetic model 37

x


Figure Page

5.15 Strain energy-time history of the whole auxetic structure for


5.16 Energy-time history of the whole auxetic structure for

X1-direction in-plane impact at 400 m/sec 39

5.17 Strain energy-time history of both whole for X1-direction

in-plane impact at 400 m/s 40

5.18 Kinetic energy-time history of both whole for X1-direction


5.19 Total energy-time history of both model for X1-direction



in-plane impact to regular honeycomb model 43



5.22 The reaction force history of X2-direction in-plane impact

to regular model 45


in-plane impact to regular model 46







5.27 Total energy-time history of the whole regular structure for


xi


Figure Page



5.29 Time histories of the kinetic energy for X2-direction in-plane









X2-direction in-plane impact to auxetic model 55




X2-direction in-plane impact at 400 m/sec 57

5.36 Strain energy-time history of both whole for X2-direction


5.37 Kinetic energy-time history of both whole for X2-direction


5.38 Total energy-time history of both model for X1-direction


5.39 Velocity-time history of the impacting ball for out-of-plane

impact to regular honeycomb model 61


out-of-plane impact to regular model 62

xii


Figure Page

5.41 The reaction force history of out-of-plane impact

to regular model 63

5.42 Velocity history of the point on the spot of the out-of-plane

impact to regular model 64


out-of-plane impact 65


out-of-plane impact to regular model 66



5.46 Total energy-time history of the whole regular structure for


5.47 Velocity-time history of the impacting ball for out-of-plane


5.48 Time histories of the kinetic energy for out-of-plane




5.50 Velocity history of the point on the spot of the out-of-plane





out-of-plane impact to auxetic model 74



xiii


Figure Page


out-of-plane impact at 400 m/s 76

5.55 Strain energy-time history of both whole for out-of-plane

impact at 400 m/s 77

5.56 Kinetic energy-time history of both whole for out-of-plane


5.57 Total energy-time history of both model for out-of-plane


1

CHAPTER ONE

INTRODUCTION

The use of sandwich construction is prevalent in many structures due to the

various advantages it offers in terms of weight-savings and high stiffness [1]. Generally

consisting of two laminated face sheets on both sides and a core in the middle, sandwich

panels are able to offer numerous applications in aerospace and automotive industries.

Commonly cores are made of cellular foams, trusses and honeycombs. Many studies

have attempted to model the mechanical properties of the sandwich structure, both using

mathematical modeling and finite element analyses (FEA). Masashi Hayase and Richard

Eckfund [2] published a patent in 1981 on making a metallic sandwich structure in which

metal sheets preferably by intermittent or discontinuous weld. Sun and Zhang [3] in

1995, published an extensive research on the use of thickness-shear mode in adaptive

sandwich structure with piezoelectric materials. In 2001, V. Dattoma and R.Marcuccio

[4] detected some typical defects existing in composite material sandwich structures by

using thermographic technique.

Conventional hexagonal honeycombs are typically employed for the cores of the

sandwich construction. An advantage for the honeycomb structure is its fatigue

resistance. Figure.1 shows the result of sonic fatigue tests between honeycomb panel and

skin-stiffened structure [5]. Notice that the sandwich structure lasts 460 hours at 167 dB

while skin-stiffened structure last only 3 minutes at 167 dB. The reason for the greater

fatigue resistance of the honeycomb is that its panels are continuously bonded to the core

and therefore it does not have stress concentrations.

2

Another main reason for using honeycomb core sandwich structure is to provide

high stiffness with weight savings and therefore is one of the structures available as a

state-of-art choice for weight sensitive applications such as aircraft and satellites [6]. The

base concept of sandwich construction is to use thick and light core bonded with thin,

dense strong sheet materials. Each component is relatively weak and flexible but provides

a stiff, strong and lightweight structure when working together as a composite structure.

Figure 1.1 Fatigue failure envelopes for sound level vs. time of sandwich structure and

skin-stiffened structure

Auxetic honeycombs are cellular structures that invert the angle of a unit cell to

negative. This auxetic structure with the change of angle is reported to have negative

Poisson's ratio in the cell plain [7]. Figure 2 shows the difference between regular and

3

auxetic honeycombs in unit cells.

Figure 1.2 Unit cell geometry of regular and auxetic honeycombs

Scarp [8, 9], analyzed the dynamic properties of auxetic honeycomb through

simulation methods. Found [10] applied a modal analysis in auxetic structure. Ruzzene

[11] has studied the wave propagation in sandwich beams with auxetic honeycomb core.

Abrate [12] presented an overview of mathematical models for the impact analysis

between a foreign object and a composite structure. Sourish and Atul have explored the

behavior of the auxetic honeycomb by applying a resonance to the model and found out

the predominant mode of cell wall deformation is always flexural [13]. Zou and .Reid

have simulated the in-plane dynamic crushing of hexagonal-cell honeycomb and explored

the dynamic response in 2009 [14]. Chi and Langdon published a paper to report the

behaviour of circular sandwich panels with honeycomb cores subjected to air blast

loading [15]. Recently, Crupi and Epasto have performed low-velocity impact test to

investigate the failure mode and damage of the honeycomb panels [16]. Also, Tan and

4

Akil conducted a series of low-velocity impact test to study the sandwich structure with

honeycomb core made of fiber metal laminates [17].

While there have been several studies on impact and blast loading of composite

plates with regular honeycomb core, there are few studies of impact with auxetic

honeycomb core. In this work, the main question, which is investigated, is whether

auxetic honeycombs in comparison to the regular structure, can absorb more or less

energy of the impact and offer more or less elastic rebound as measured by an effective

coefficient of restitution (COR) for the honeycomb structure. In this work, the effect of

different impacting velocities of a rigid ball impacting a composite sandwich panel

comparing regular and auxetic honeycomb is investigated using the commercial finite

element software ABAQUS. Both in-plane loading in two different perpendicular

directions, and out-of-plane impact are studied.

Chapter 2 overviews the concepts of the momentum and impulse which play an

important role in understanding the behavior of impacting mass bodies.

Chapter 3 gives details to the material and geometry properties of the

honeycomb core, face sheets, and impactor used in this study. The design of in-plane and

out-of-plane impact configurations is also discussed.

Chapter 4 discusses the specific steps to develop the finite element models of the

impactor-plate model in ABAQUS. Meshing, constraint, boundary condition and

predefined field are included.

Chapter 5 presents and discusses the result of the impact performance of

different impacting directions. Composite panels with regular and auxetic cores are

5

compared with results of velocity and energy time histories during the simulation for both

the impactor and composite plate.

Chapter 6 summarizes the results of the study and provides suggestions for

future work.

6

CHAPTER TWO

MOMENTUM AND IMPULSE THEORY FOR IMPACT

Linear momentum P mv of a mass m at an instant of time has both magnitude

and direction and is defined by the mass of the body multiplied by the velocity of the

body [18]. The principle of impulse-momentum can be used to predict the resulting

direction and speed of objects after they collide into each other.

An impact is a force or shock over a relatively short period during the time that

two or more moving bodies collide. In general, the basic equation of motion for the

object may be written as [19]:

( )d

F mv mvdt

(2.2)

or F P (2.3)

The effect of the resultant force on the linear momentum of the body over a

finite period of time may be obtained by integrating Equation 2.3 from the period time t1

to time t2 , resulting in the impulse of the force [20]:

2 2

1 1

t t

x

t t

F dt dP (2.4)

Using this result, integrating Equation 2.2 over a time interval gives the impulse-

momentum equation [21]:

2

1

2 1

t

t

Fdt mv mv (2.5)

7

By measuring the velocity at time 1, and velocity at time 2, and the time interval, the

impacting force resultant can calculated using this equation during the integrating time

[22].

The coefficient of restitution (COR) gives the ratio of the relative speed at the

contact point between two colliding objects after and before an impact in the line of

impact. The coefficient of restitution is given by [23]:

2 2

1 1

( ) ( )

( ) ( )

b a

a b

v vCOR

v v

(2.6)

where av is the velocity of the point on the impacting spot on the surface of the structure,

and bv is the velocity of the impactor ball. In the above, the 1 means velocity just prior to

impact, while ther 2 means just after the impact at the instance when the ball separates.

Each of the velocities in this equation are speeds at the contact point in the direction of

the line of impact defined by the normal coordinate perpendicular to the tangent plane

defined at the contact point between the colliding bodies. In the studies in this work, a

spherical ball is used as the impactor with direct impact velocity along the normal line of

impact passing through the mass center. As a result, the ball impactor rebounds without

rotation after separating after collision with the honeycomb composite structures

investigated.

The value of the COR depends on the material and construction of the impacting

bodies. Collisions characterized by COR=1 are defined as perfectly elastic. In the other

extreme limit COR = 0, defines two bodies which stick together after collision. In

general, a larger COR indicates more relative rebound speed and less energy absorption.

8

A goal of this work is the estimate the effective COR for composite sandwich structures

comparing regular and auxetic honeycomb cores.

9

CHAPTER THREE

MATERIAL AND GEOMETRIC PROPERTIES OF HONEYCOMB SANDWICH

STRUCTURES

3.1 Material Properties

Aluminum alloy (A5052-H34) is chosen to be the base material of the

honeycomb sandwich panel since it is stiff and has a negligible viscoelastic material

damping effect. Table 3.1 defines the material properties of A5052-H34.

Material Young's Modulus,

E ( GPa )

Poisson's Ratio, v Density,

ρ (kg/m3)

A5052-H34 68.97 0.34 2700

Table 3.1 Material properties of aluminum alloy used for the composite

sandwich panel

The impactor is modeled as a rigid ball with a mass density of 1000

kg/m3corresponding to a rubber material. A rigid ball is used so that the coefficient of

restitution calculated is due to the material and geometric stiffness properties of the

impacting honeycomb structure only.

10

Impact crush performance is determined largely by the honeycomb panel

density, the panel configuration subjected to impact velocity, material properties of the

core, and cell size of the core.

Ashby and Gibson are the first to give the effective properties of honeycomb

based on beam theory. According to Ashby and Gibson, a unit cell of honeycomb

structure is used to predict the behavior of the sandwich panel. The unit cell of the regular

and auxetic honeycombs are as shown in Figure 3.1, with the parameters that define the

honeycomb cell geometry. The parameters are h (height of cell), l (length of cell wall), d

(depth of cell wall) and θ (angle between the horizontal and the inclined cell wall). In

addition,α stands for the cell aspect ratio that equals to be h/l, while β stands for the

thickness to length ratio, t/l. For regular honeycomb, θ=30, α = 1. For the comparison

study, an auxetic cell is defined as θ = -30 and α = 2. With this choice of auxetic unit cell

parameters, the effective in-plane modulus is the same in the two perpendicular

directions, similar to the behavior of regular honeycomb. The parameters of the regular

and auxetic honeycomb core unit cell are listed in Table 3.2.

Geometric parameters Regular honeycomb Auxetic honeycomb

Height of the cell wall (mm) 4.23 8.46

Inclined length of the cell wall (mm) 4.23 4.23

Thickness of the cell wall (mm) 0.423 0.423

Cell angel (θ) 30 30

Cell aspect ratio (α) 1 0.5

11

Thickness to length ratio (β) 0.1 0.05

Table 3.2 Geometric parameters of regular and auxetic honeycomb cell

The overall dimensions of unit regular honeycomb cell are given by:

The overall width of the unit cell: L = 2 l cosθ (3.3)

The overall height of the unit cell: H = 2 (h + l sinθ) (3.4)

While the overall dimensions of unit auxetic honeycomb cell are given by :

The overall width of the unit cell: L = 2 l cosθ (3.5)

The overall height of the unit cell: H = 2(h – l sinθ) (3.6)

Figure 3.3 Dimensions of regular and auxetic unit cell

12

3.2 Model of Sandwich Panel and Rigid Ball

Abaqus 6.10 is used to model the composite aluminum sandwich panel and the

projectile rigid ball. Two different composite sandwich models are created for the two

configurations of cores .Those models consist of in-plane model and out-of plane model.

The in-plane model corresponds to a model which is impacted by the projectile moving

along either X1 or X2 directions. The out-of-plane model corresponds to a model which

is impact by the projectile moving along the X3 direction. In addition, for the honeycomb

core the elastic moduli is higher in the out-of-plane direction compared to in-plane

direction.

3.2.1 In-Plane Model

In this case the rigid ball will hit the panel only along the X1 and X2 directions.

Therefore the number of the unit cells along the X1 direction are chosen to be 10 and

along X2 direction to be 3. According to the dimensions of the unit cell and the equations

3.5 and 3.6, the overall dimensions of the honeycomb core are 80.59 in X1 direction and

25.38 in X2 direction. The base feature is chosen to be a deformable shell in order to

reduce computational time. The critical configuration of the honeycomb such as material

and thickness are set up in the section assignment. Figure 3.2 shows the regular and

auxetic honeycomb cores. Table 3.3 shows the mass property of the sandwich panel.

13

Figure 3.4 Overall dimension of regular and auxetic cores with in-plane model

For the impact from X1 direction, a face sheet of 80 mm in length and 25.38 mm

in width is created. For the in-plane impact from X2 direction, the dimension of the face

sheet is 80 mm in length and 73.27 mm in width. The type of shell is picked up for the

face sheet and the material of aluminum is assigned. The honeycomb core is sandwiched

by double face sheets on the top and bottom. Figure 3.3 and Figure 3.4 show the

complete assembled composite sandwich plate.

14

Figure 3.5 The complete assembled composite sandwich plate of in-plane model

(impact from X1 direction)

Figure 3.6 The complete assembled composite sandwich plate of in-plane model

(impact from X2 direction)

15

Table 3.3 Mass configurations of in-plane model

3.2.2 Out-of-Plane Model

In the other case the sandwich panel is impacted by the ball from out-of-plane

direction. In the Abaqus model, the number of the unit cells is 12 in X1 direction and 11

in X2 direction. So Table 3 and the equations 3.5 and 3.6 are used to calculate the overall

dimension of the honeycomb core to be 87.92 mm along the X1 direction and 76.14 mm

along the X2 direction. And the depth of the core extruded along the X3 direction is

4.23mm. Figure 3.5 shows the regular and auxetic honeycomb core in out-of-plane.

Honeycomb

geometry

Mass of

sandwich

core (kg)

Mass of top

face sheet

(kg)

Total mass

of sandwich

panel (kg)

Mass of the

face sheet

(kg)

Total mass

of sandwich

panel (kg)

Regular 0.04723 0.00232 0.05187 0.00696 0.06115

Auxetic 0.08459 0.00232 0.08923 0.00696 0.09851

16

Figure 3.7 The complete assembled composite sandwich plate of out-of-plane

model

Next, a face sheet of 87.92 mm in length and 76.14 mm in width is created. The

type of shell is picked up for the face sheet and the material of aluminum is assigned. The

honeycomb core is sandwiched by double face sheets on the top and bottom. Figure 3.6

shows the complete assembled composite sandwich plate. Mass properties of the

sandwich plates are shown in Table 3.4.

Figure 3.8 The complete assembled composite sandwich plate of out-of-plane

model

17

Table 3.4 Mass configurations of out-of-plane model

3.2.3 The Model of Rigid Ball

The radius of the ball is 8 mm and its mass is 0.00214 kg.

Honeycomb

geometry

Mass of

sandwich core

(kg)

Mass of face

sheet (kg)

Total mass of

sandwich panel

(kg)

Regular 0.00895 0.00764 0.02423

Auxetic 0.01201 0.00764 0.02729

18

CHAPTER FOUR

FINITE ELEMENT MODELS

4.1 Finite element models for in-plane and out-of-plane impact

After the geometry of the in-plane impacting and out-of-plane impacting models

were generated, the parts were meshed and set up for impact analysis in Abaqus. This

Chapter discusses the details of the steps used to develop the models for the dynamic,

nonlinear finite element analysis. In related work, Besant and Davies [24] outlined the

finite element procedure for predicting the behavior under low velocity impact of

composite sandwich panels. Yang [25] found that the Poisson's ratio values varied by

changing the configuration of the honeycomb cell length and width. Foo [26] discussed

the failure response of aluminum sandwich panels subjected to low-velocity impact with

the finite element model developed using the commercial software, ABAQUS. Chen and

Ozaki discussed the stress concentration generated in a honeycomb core under a heavy

loading which is analyzed with finite element method [27].

4.2 Mesh

S4R corresponding to 4-node shell elements with reduced integration, hourglass

control and finite membrane strains [28], is assigned to the honeycomb cores and face

sheets for both the in-plane and out-of-plane impact models. Each node of the element

has 3 translational and 3 rotational degrees-of-freedom. The approximate global seed

size for generating the mesh is 3 mm for the honeycomb cores and 1.5 mm for the face

sheets. There are 9840 linear quadrilateral elements for the honeycomb cores and 1040

19

for each face sheet in the in-plane model. For the out-of-plane model, the approximate

global size of 0.84 mm was used for the honeycomb cores and 2.2 mm for the face

sheets. There are 8125 linear quadrilateral elements for honeycomb cores and 1400 for

face sheets. Figure 4.1 and Figure 4.2 illustrate the meshed honeycomb cores and face

sheets for both models.

Figure 4.9(a) Meshed face sheet for in-plane model

Figure 4.1 (b) Meshed regular and auxetic cores for in-plane model

20

Figure 4.10 (a) Meshed face sheet for out-of-plane model

Figure 4.2 (b) Meshed regular and auxetic cores for out-of-plane model

21

The ball is meshed with C3D4, 4-node linear tetrahedron elements[28]. The

approximate global size is 3 mm. Figure 4.3 shows the meshed ball with C3D4 solid

elements. As discussed earlier, the projectile ball is constrained to be a rigid body.

Figure 4.11 Meshed rigid ball

4.2 Constraints

After assembly, the instances are constrained together to form as a single part.

Surface-based tie constrains are used for the two face sheets and a core in each model. In

general, the surface with a larger stiffness is considered to be the master surface. The

constraint ties the core as a slave surface and the face sheet as a master surface. The

master surface has the same motion by constraining each node on the slave surface.

Figure 4.4 shows the master face sheet surfaces are tied to the slave nodes of the core on

both top and bottom.

22

Figure 4.12 Tie constraint of out-of-plane impact model

4.3 Boundary Conditions

For the in-plane models, the edges of the back sheet of the composite structure

are constrained in all 6 degrees of freedom (U1, U2, U3,UR1,UR2 and UR3) as shown in

Figure 4.5. For the out-of-plane models, the edges of the sides are constrained as shown

in Figure 4.6.

23

Figure 4.13 (a) Boundary condition imposed on in-plane model (impact from X1

direction)

Figure 4.5 (b) Boundary condition imposed on in-plane model (impact from X2

direction)

24

Figure 4.14 Boundary condition imposed on out-of-plane model

4.4 Predefined Fields:

The distance between the center of the ball and the front face sheet is 10 mm. Three cases

are considered where the velocities of the projecting ball are changed from 100 m/s, 200

m/s and 400 m/s.

25

CHAPTER FIVE

RESULTS AND DISCUSSION

5.1 Impact Behavior of Honeycomb Sandwich Panels

Dynamic/Explicit analysis is conducted in ABAQUS to compare the result of

different types of the sandwich panels. The steps are set in ABAQUS as follows:

Step 0- Initial: The boundary conditions are specified.

Step 1- Dynamic, Explicit, history output of translational velocities of the

projectile, displacement and velocity of the node point on the structure closest to the

impacting spot, kinetic energy and strain energy of the structure are requested.

5.2 Results of In-Plane Impact Model

5.2.1 Results of in-plane impact from X1 direction

5.2.1.1 Results of in-plane impact to honeycomb model with regular cells

For the honeycomb model with regular cells, crushing occurs during the impact

with each unit cell deforming from compression by the impactor. Figure 5.1 shows the

absolute amplitude of velocity history plot of the rigid ball. For the case of 400 m/s,

around the time of 0.0003 sec where the velocity equals 0, and the ball velocity changes

direction, the deformation of the honeycomb model implies to be the maximum, and the

ball starts to rebound. The results indicate that the returning velocity turns greater with

the increase of impacting velocity. The returning velocities and coefficient of restitution

(COR) defined in Chapter 2, are listed in Table 5.1. The COR is calculated using the

26

impacting and returning velocity of the ball, and the velocity at the impacting point on the

structure surface at the instant the ball velocity reaches a constant return velocity. In

addition, the ROV defined as the ratio (v2/v1) of the impacting velocity and returning

velocity of the ball is also computed. This ratio can also be interpreted as an idealized

COR where the velocity of the structure is assumed to be zero at the time of separation.

The value of COR for 200 m/s is observed to be the largest among the different

velocities, which indicates that the impact with the honeycomb panel at the initial

velocity of 200 m/s is more elastic than the other two velocities.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

50

100

150

200

250

300

350

400

Time (s)

Velo

city (

m/s

)

100m/s

200m/s

400m/s

Figure 5.1 Velocity-time history of the impacting ball for X1-direction in-plane impact to

regular honeycomb model

Impacting

velocity(m/s)

Returning

velocity(m/s)

Velocity of the

impacting point

(m/s)

ROV COR

100 -30.79 -18.38 0.31 0.12

200 -75.12 -3.51 0.37 0.35

400 -113.16 -81.02 0.28 0.08

27

Table 5.2 The velocity effect of the rigid ball of the impact to X1-direction in-plane

impact to regular model

The variation of the kinetic energy of the rigid ball during the impact is shown in

Figure 5.2. Table 5.2 lists the kinetic energy both at the beginning and end of impact. At

the impact velocity of 100 m/s, the returning kinetic energy is 91.6% lower than the

initial kinetic energy. The returning kinetic energies for 200 m/s and 400 m/s are 85.7%

and 92% lower than the initial one. These values are determined from the formula:

2

2

2

1

1( )211

( )2

mv

mv

which can be simplified to:

2

2

2

1

1v

v

,

defining the inverse ratio of the square of velocity. The simplified formula is consistent

with the result of ROV.

28

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

140

160

180

Time (s)

Kin

etic E

nerg

y (

J)

100m/s

200m/s

400m/s

Figure 5.2 Time histories of the kinetic energy of rigid ball for X1-direction in-plane


Impacting velocity (m/s) Initial kinetic energy (J) Returning kinetic energy (J)

100 10.7 1.01

200 42.8 6.13

400 171.2 13.70

Table 5.3 The initial and returning kinetic energies of the impacting ball during X1-

direction in-plane impact to honeycomb model with regular cells

The reaction impacting force to the rigid ball is calculated according to Equation

2.2. For every time-increment, the force is computed from:

1[ ( ) ( )]( )

( )

i ii

i

m v t v tF t

t

where F, v are functions of time, and i indicates the step of time.

29

Figure 5.3 illustrates the variation of reaction impact force to the rigid ball

during the impact event. The force-time curves shows that higher forces occurred as the

velocity increased. For the case of 400 m/s, the force is increasing before 0.00003 s

where the corresponding curve in Figure 5.1 has a sharper decreasing gradient. Around

0.0001 s the velocity starts to keep constant as the force reaches zero. Around 0.0005 s,

the rigid ball and the model start to separate while the force reaches zero again.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10

4

time (s)

Forc

e (

N)

100m/s

200m/s

400m/s

Figure 5.3 The reaction force history of X1-direction in-plane impact to regular model

Figure 5.4 shows the velocity of the point in the impacting area on to face of the

structure. Since compression dominates the crushing process, less oscillation is obtained

in the data. The maximum velocities are 330 m/s, 172 m/s and 94 m/s for 400 m/s, 200

m/s and 100 m/s respectively. For the case of 400 m/s, the velocity of the rigid ball

reaches zero around 0.0003 s, at the same moment a zero value is also observed from the

curve in Figure 5.5. The correlation indicates the deformation is a maximum when both

rigid ball and the impacting point stop moving.

30

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

50

100

150

200

250

300

350

Time (s)

Velo

city (

m/s

)

100m/s

200m/s

400m/s

Figure 5.4 Velocity history of the point on the spot of the X1-direction in-plane impact to

regular model

Figure 5.5 shows the kinetic energy of the sandwich structure. The curve for

100 m/s exhibits a plateau during the crushing process. The curve for 400 m/s reaches its

max value of 89 J around 0.0001 s while the curve for 100 m/s have a relatively minimal

variation. The general trend shows that the kinetic energy of the structure is higher for a

faster impacting speed.

31

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

10

20

30

40

50

60

70

80

90

Time (s)

Kin

etic E

nerg

y (

J)

100m/s

200m/s

400m/s

Figure 5.5 Kinetic energy-time history of the whole regular structure for X1-direction in-

plane impact

Figure 5.6 illustrates the displacement history of the spot in the impacting area.

The maximum value approaches 25 mm for 400 m/s and 10 m/s for 200 m/s, 5 m/s for

100 m/s.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

5

10

15

20

25

30

Time (s)

Dis

pla

cem

ent

(mm

)

100m/s

200m/s

400m/s

Figure 5.6 Displacement history of the point on the spot of the X1-direction in-plane


32

Figure 5.7 illustrates the strain energy of the panel for different velocities. It is

indicated that the honeycomb core absorbed more strain energy from rigid ball with

higher velocity. The strain energy of the structure begins decreasing after reaching 86 J at

0.00016s while strain energy has less variation as the velocity decreases.

The general trend shows that both the kinetic and strain energy of the structure is

higher for a faster impacting speed. This is consistent with the effective COR for the two

limiting ball speeds of 400 m/s and 100 m/s, where the COR decreases, with increase in

energy of the structure. The exception was for the case of 200 m/s where the energy for

the structure increased compared with 100 m/s, while the COR also increased.

Figure 5.8 shows the comparison of the strain and kinetic energy over time for

the ball speed of 400 m/s. Initially the kinetic energy reaches its peak and then decreases.

The decrease is slow for the strain energy until the honeycomb core begins densification.

33

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

10

20

30

40

50

60

70

80

90

Time (s)

Str

ain

Energ

y (

J)

100m/s

200m/s

400m/s

Figure 5.7 Strain energy-time history of the whole regular structure for X1-direction in-

plane impact

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

10

20

30

40

50

60

70

80

90

Time (s)

Energ

y (

J)

Kinetic energy

Strain energy

Figure 5.8 Energy-time history of the whole regular structure for X1-direction in-plane

impact at 400 m/s

34

5.2.1.1 Result of in-plane impact to auxetic model

For the auxetic model, each unit cell undergoes compression and tension from

crushing. Figure 5.9 shows the plot of the velocity history, the returning velocities and

ROV and COR are listed in Table 2. In the figure, the time of impact to auxetic model is

observed to be quicker than the regular one. In addition, the increasing and decreasing

slopes are close to each other. Similarly as the result of regular model, the impact with

the initial velocity of 200 m/s is more elastic than the other twos.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

50

100

150

200

250

300

350

400

Time (s)

Velo

city (

m/s

)

100m/s

200m/s

400m/s

Figure 5.9 Velocity-time history of the impacting ball for X1-direction in-plane impact to

auxetic model

35

Impacting

velocity(m/s)

Returning

velocity(m/s)

Velocity of the

impacting point (m/s)

ROV COV

100 -28.80 -8.27 0.29 0.21

200 -57.51 -28.76 0.29 0.14

400 -115.78 -78.95 0.29 0.09


impact to auxetic model

The kinetic energy of different impacting velocities is shown in Figure 5.10.

Similar to the result of regular model, more kinetic energy is absorbed during the impact

with higher velocity. The kinetic energy of the ball after the impact is shown in table 5.3.

During impact, the kinetic energy decreases by 91.8% for 400 m/s and 91.7% for 200 m/s

and 91.7% for 100 m/s.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

140

160

180

Time (s)

Kin

etic E

nerg

y (

J)

100m/s

200m/s

400m/s

Figure 5.10 Time histories of the kinetic energy for X1-direction in-plane impact to

auxetic model

36


100 10.7 0.88

200 42.8 3.54

400 171.2 14.34

Table 5.5 The initial and returning kinetic energy of the impacting ball during X1-

direction impact

5.2.1.2 In-plane impact to auxetic model

Figure 5.11 illustrates the reaction-force-time curve of auxetic model. The

auxetic structure makes it faster for the compression to propagate. The maximum force

for 400 m/s is over 40000 N while it reaches about 18000 N for 200 m/s and 7500 N for

100 m/s respectively. Since the impact procedure is quick, the force is zero when close to

0.0001 s as the rigid ball is separate from the sandwich structure.

37

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10

4

time (s)

Forc

e (

N)

100m/s

200m/s

400m/s

Figure 5.11 The reaction force history of the auxetic model to X1-direction in-plane

impact

The velocity over the time of the spot on the panel is shown in Figure 5.12.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

50

100

150

200

250

300

350

Time (s)

Velo

city (

m/s

)

100m/s

200m/s

400m/s

Figure 5.12 Velocity history of the point on the spot of the X1-direction in-plane impact

to auxetic model

38

The kinetic energy history is shown in Figure 5.13. The curve with lower

velocity shows a long plateau with oscillations during the crushing process.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

5

10

15

20

25

30

Time (s)

Kenetic E

nerg

y (

J)

100m/s

200m/s

400m/s

Figure 5.13 Kinetic energy-time history of the whole auxetic structure for X1-direction

in-plane impact

Figure 5.14 illustrates the displacement of the impacting spot. It can be observed

that the spot exhibits a clearly predicting behavior. This is believed to be due to the strain

wave travelling in structure.

39

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

1

2

3

4

5

6

Time (s)

Dis

pla

cem

ent

(mm

)

100m/s

200m/s

400m/s



Figure 5.15 presents the strain energy of the whole honeycomb structure. For

400 m/s, the strain energy decreases rapidly while the strain energy for 200 m/s and 100

m/s stay at a relative more stable level of variation. Lower initial velocity results in lower

strain energy and produces long plateaus.

40

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

Time (s)

Str

ain

Energ

y (

J)

100m/s

200m/s

400m/s

Figure 5.15 Strain energy-time history of the whole auxetic structure for X1-direction in-

plane impact

The comparison of the energies between the strain energy and kinetic energy of

400 m/s are shown in Figure 5.16. It is obvious that the strain energy is much higher than

the kinetic energy.

41

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

Time (s)

Energ

y (

J)

Kinetic energy

Strain energy

Figure 5.16 Energy-time history of the whole auxetic structure for X1-direction in-plane

impact at 400 m/sec.

5.2.1.3 Comparison of Regular and Auxetic honeycomb core for in-plane impact from

X1 direction

The strain energy of initial velocity of 400 m/s are compared as shown in Figure

5.17. The curve of auxetic shows a predicting oscillation behavior. For regular structure,

the peak of strain energy reaches 84 J at 0.00012 s while it reaches around 118 J around

0.00007 s for auxetic model.

42

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

Time (s)

Str

ain

Energ

y (

J)

Regular

Auxetic

Figure 5.17 Strain energy-time history of both model for X1-direction in-plane impact at

400 m/s

In Figure 5.18, the kinetic energy of the regular is compared with the auxetic

model. The regular model has more kinetic energy than the auxetic model and more

oscillation behavior is observed from the auxetic curves.

43

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

10

20

30

40

50

60

70

80

90

Time (s)

Kin

etic E

nerg

y (

J)

Regular

Auxetic

Figure 5.18 Kinetic energy-time history of both model for X1-direction in-plane impact

at 400 m/s

The total energy that absorbed from the rigid ball with velocity of 400 m/s

between the two models is compared as shown in Figure 5.19. The performance of

oscillation is observed on the auxetic curve. In addition, the structure with regular core

has absorbed more energy from the impact.

44

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

50

100

150

Time (s)

Tota

l energ

y (

J)

regular

auxetic

Figure 5.19 Total energy-time history of both model for X1-direction in-plane impact at

400 m/s

The coefficients of restitution are compared in Table 5.5. The COR for auxetic is

larger than for the regular honeycomb core. This result shows that the impact to the

auxetic model is more elastic than the impact to the regular model except the case of 200

m/s.

Impacting

velocity

regular auxetic

100m/s 0.12 0.21

200m/s 0.35 0.14

400m/s 0.08 0.09

Table 5.6 COR of the X1 in-plane impact at different velocities

45

5.3 Results of in-plane from X2 direction model:

5.3.1 Results of in-plane impact to regular model from X2 direction

For the regular model, similar as the in-plane impact from X1 direction, only

compression happens in the unit cell of the honeycomb core. Figure 5.20 shows the

velocity of the rigid ball via time. For the case of 400 m/s, when the velocity reaches

zero, the deformation of the structure gets access to the maximum.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

50

100

150

200

250

300

350

400

Time (s)

Velo

city (

m/s

)

100m/s

200m/s

400m/s

Figure 5.20 Velocity-time history of the impacting ball for X2-direction in-plane impact

to regular model

The initial and returning velocities of the impacting ball and COR are listed in

Table 5.6.

46

Impacting

velocity (m/s)

Returning

velocity(m/s)

Velocity of the point on the

impacting spot (m/s)

ROV COR

100 -40.97 -19.26 0.41 0.21

200 -75.53 -20.69 0.38 0.27

400 -98.86 -31.68 0.25 0.17

Table 5.7 The velocities effect of the rigid ball of the impact to X2-direction in-plane

impact to the regular model

The kinetic energy of the rigid ball is plotted in Figure 5.21. From the curves it is

observed that the composite sandwich structure absorbs more kinetic energy from the

rigid ball with higher initial velocity.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

140

160

180

Time (s)

Kin

etic E

nerg

y (

J)

100m/s

200m/s

400m/s


regular model

47

The kinetic energy is listed in Table 5.7:


100 10.7 0.12

200 42.8 1.96

400 171.2 31.36


direction in-plane impact to regular model

The returning kinetic energy for impact velocity of 100 m/s is 98.9% lower than

the initial kinetic energy, and 96.4% for 200 m/s and 81.7% for 400 m/s. The regular

honeycomb core is more effective with absorbing kinetic energy from the impacting ball

with higher initial velocities.

As illustrated in Figure 5.22, the max reaction force for 400 m/s reaches 16300N

compared with 6800 N for 200 m/s and 3500 N for 100 m/s. For the case of 400 m/s, the

secondary peak indicates the variation of the acceleration gradient of 400 m/s shown in

Figure 5.20.

48

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

time (s)

Forc

e (

N)

100m/s

200m/s

400m/s

Figure 5.22 The reaction force history of the regular model to in-plane from X2-direction

impact

The velocity of the point on the spot is shown in Figure 5.23. The amplitude of

the velocity becomes larger with the increase of the initial velocity of the rigid ball. In

addition, the peak is gradually diminishing due to the decrease of the kinetic energy with

the time of the point on the impacting spot.

49

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

50

100

150

Time (s)

Velo

city (

m/s

)

100m/s

200m/s

400m/s


to regular model

The kinetic energy of the whole structure is shown in Figure 5.24.

50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

10

20

30

40

50

60

70

80

Time (s)

Kin

etic E

nerg

y (

J)

100m/s

200m/s

400m/s

Figure 5.24 Kinetic energy-time history of the whole regular structure for X2-direction

in-plane impact

Figure 5.25 shows the displacement of the point on the impacting spot. No

regular oscillation is observed in this figure.

The strain energy of the whole structure is shown in Figure 5.26.

51

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (s)

Dis

pla

cem

ent

(mm

)

100m/s

200m/s

400m/s



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

Time (s)

Str

ain

Energ

y (

J)

100m/s

200m/s

400m/s

Figure 5.26 Strain energy-time history of the whole regular structure for X2-direction in-

plane impact

52

The kinetic energy and strain energy are compared in Figure 5.27. The peak of

strain energy is larger than the peak of kinetic energy. In addition, the strain energy

reaches its maximum in the first step and the kinetic energy has the max value later than

the strain energy.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

Time (s)

Energ

y (

J)

Kinetic energy

Strain energy

Figure 5.27 Total energy-time history of the whole regular structure for X2-direction in-

plane impact

5.3.2.2 Result of in-plane impact to auxetic model from X2 direction

For auxetic model, the impact of the structure produces compression and tension

on the unit cell of the honeycomb core. These two kinds of physical stresses make the

process more complicated. The velocity of the rigid ball is shown in Figure 5.28.

53

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

50

100

150

200

250

300

350

400

Time (s)

Velo

city (

m/s

)

100m/s

200m/s

400m/s

Figure 5.28 Velocity-time history of the impacting ball for X2-direction in-plane impact

to auxetic model

The velocity effects are listed in Table 5.8 :

Impacting velocity Returning

velocity(m/s)

Velocity of the point on

the impacting spot (m/s)

ROV COR

100 -45.43 -5.21 0.45 0.40

200 -93.17 -27.13 0.46 0.33

400 -166.10 65.36 0.29 0.45



54

The kinetic energy of the rigid ball is shown in Figure 5.29.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

140

160

180

Time (s)

Kin

etic E

nerg

y (

J)

100m/s

200m/s

400m/s


auxetic model

And initial kinetic energy and returning kinetic energy are listed in Table 5.9.


100 10.7 2.21

200 42.8 9.29

400 171.2 29.52


direction in-plane impact to auxetic model

The returning kinetic energy for 100 m/s is 79.3% lower than the initial kinetic

energy, while it is 78.3% for 200 m/s and 82.7% for 400 m/s.

55

The reaction force to the rigid ball is shown in Figure 5.30.

Figure 5.30 The reaction force history of the auxetic model to X2-direction in-plane

impact

The velocity of the point on the impacting spot is illustrated in Figure 5.31. The

velocity reaches its maximum in the first step and then a sharp decrease happens in the

following steps.

56

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

50

100

150

200

250

300

350

400

Time (s)

Velo

city (

m/s

)

100m/s

200m/s

400m/s


to auxetic model

In Figure 5.32, the kinetic energy history of the whole structure is illustrated.

The initial velocity of the rigid ball has a major effect on the kinetic energy of the

structure.

57

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

5

10

15

20

25

Time (s)

Kin

etic E

nerg

y (

J)

100m/s

200m/s

400m/s

Figure 5.32 Kinetic energy-time history of the whole auxetic structure for X2-direction

in-plane impact

As shown in Figure 5.33, the displacement of the point on the impacting spot has

intensive oscillation as the velocity of the rigid ball increases. The graph shows a trend

where the first peak has the highest amplitude for different impact velocities.

58

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

1

2

3

4

5

6

Time (s)

Dis

pla

cem

ent

(mm

)

100m/s

200m/s

400m/s



The strain energy of the in-plane bending model is illustrated in Figure 5.34.

Similar observation are observed in the kinetic energy curves.

59

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

Time (s)

Str

ain

Energ

y (

J)

100m/s

200m/s

400m/s

Figure 5.34 Strain energy-time history of the whole auxetic structure for X2-direction in-

plane impact

The kinetic energy and strain energy are compared in Figure 5.35. The figure

shows that the peak of strain energy is larger than the peak of kinetic energy. In addition,

the strain energy reaches its maximum in the first step and the kinetic energy keeps the

relative stable variation.

60

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

Time (s)

Energ

y (

J)

Kinetic energy

Strain energy

Figure 5.35 Energy-time history of the whole auxetic structure for X2-direction in-plane

impact

5.3.2.3 The comparison of the geometries of honeycomb core of in-plane impact from X2

direction

The strain energy of two structures is compared in Figure 5.36. A more apparent

oscillation behavior is observed in auxetic model.

61

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

Time (s)

Str

ain

Energ

y (

J)

Regular

Auxetic

Figure 5.36 Strain energy-time history of both model for X2-direction in-plane impact

As shown in Figure 5.37, the kinetic energy is compared between the two

models. From the figure, it is observed that the regular structure has absorbed more

energy of the rigid ball and transforms into its own kinetic energy.

62

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

10

20

30

40

50

60

70

80

Time (s)

Kin

etic E

nerg

y (

J)

Regular

Auxetic

Figure 5.37 Kinetic energy-time history of both model for X2-direction in-plane impact

The total energy that the composite sandwich panels have absorbed from the

impact at an initial velocity of 400m/s is shown in figure 5.38. Similarly to the in-plane

impact from X1 direction, the regular curve has greater decreasing gradient while the

auxetic curve shows an obvious oscillation during the process.

63

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

140

160

Time (s)

Tota

l energ

y (

J)

regular

auxetic

Figure 5.38 Total energy-time history of both model for X2-direction in-plane impact

The coefficients of restitution are compared in the table below. The “e” in the

right column is larger than the one in the left column. So the impact to the auxetic model

is more elastic than the impact to the regular model.

velocity regular auxetic

100 m/s 0.21 0.40

200 m/s 0.27 0.33

400 m/s 0.17 0.45

Table 5.11 COR of the X2 in-plane impact at different velocities

64

5.4 Result of out-of-plane impact model

5.4.1 Result of out-of-plane impact to regular model

For the regular model, the impact from the X3 direction results in bending that

occurs to the front plate. Each unit cell suffers vertical compression from the influence of

bending. The velocity-time curves from different initial velocities are shown in Figure

5.39. The impacting time is very quick from the figure, this is due to the small thickness

of the honeycomb. The returning velocities ,ROV and COR are listed in the following

table. The COR indicates a predicting trend that the coefficient of restitution becomes

larger with the increase of the impacting velocity.

0 1 2

x 10-4

0

50

100

150

200

250

300

350

400

Time (s)

Velo

city (

m/s

)

100m/s

200m/s

400m/s

Figure 5.39 Velocity-time history of the impacting ball for out-of-plane impact to the

regular model

65

Impacting velocity(m/s) Returning velocity(m/s) Velocity of the point on


ROV COR

100 -11.90 2.21 0.12 0.14

200 -18.71 12.52 0.09 0.15

400 -24.87 48.98 0.06 0.18

Table 5.12 The velocity effects of the rigid ball after the impact of an out-of-plane impact

to regular model

Figure 5.40 shows the kinetic energy-time curves of the rigid ball. The result has

an agreement with the velocity history in Figure 5.39. The rigid ball with higher initial

velocity loses more kinetic energy after impact, and the energy transfer into the

honeycomb as the compression continues.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

140

160

180

Time (s)

Kin

etic E

nerg

y (

J)

100m/s

200m/s

400m/s

Figure 5.40 Time histories of the kinetic energy for out-of-plane impact to regular model

66

From the table it can be inferred that the returning kinetic energy for impact

velocity of 100 m/s is 98.6% lower than the initial kinetic energy. For impact velocities

of 200 m/s and 400 m/s, a 99.14% and 99.6% decrease is observed.


100 10.7 0.15

200 42.8 0.37

400 171.2 0.66

Table 5.13 The initial and returning kinetic energy of the impacting ball during out-of-

plane impact to regular model

The reaction force-time curve is plotted in Figure 5.41. The reaction force

mainly comes from compression due to bending of the front plate. For 400m/s, the max

force reaches 78000N in sharper step while it reaches 39000N for 200m/s and 10000N

for 100m/s respectively.

67

0 1 2 3

x 10-4

0

1

2

3

4

5

6

7

8x 10

4

time (s)

Forc

e (

N)

100m/s

200m/s

400m/s

Figure 5.41 The reaction force history of the regular model with out-of-plane impact

The velocity of the point on the impacting spot over the time is shown in Figure

5.42. A sharp increase that occurred in the first gradient is observed in the curve of 400

m/s. The following peak value are close for the curves of different velocities.

68

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

50

100

150

200

250

300

350

400

Time (s)

Velo

city (

m/s

)

100m/s

200m/s

400m/s

Figure 5.42 Velocity history of the point on the spot of the out-of-plane impact to regular

model

Figure 5.43 shows the kinetic energy of the structure over a period of time. A

decreasing gradient from the oscillation of 400 m/s is observed as the energy travels into

the honeycomb core. Kinetic energy of lower velocity keeps a long plateau with less

variation.

69

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

1

2

3

4

5

6

Time (s)

Kin

etic E

nerg

y (

J)

100m/s

200m/s

400m/s

Figure 5.43 Kinetic energy-time history of the whole regular structure for out-of-plane

impact

The comparison of displacement of regular model at different velocities is

shown in Figure 5.44. The maximum is 2.9 mm for 400 m/s while the peak reaches 1.8

mm for 200 m/s and 1.1 mm for 100 m/s.

70

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

0.5

1

1.5

2

2.5

3

Time (s)

Dis

pla

cem

ent

(mm

)

100m/s

200m/s

400m/s

Figure 5.44 Displacement history of the point on the spot of the out-of-plane impact to

regular model

Figure 5.45 illustrates the strain energy history plot. With the increase of

velocity, the strain energy decreases faster over the time.

71

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

1

2

3

4

5

6

Time (s)

Str

ain

Energ

y (

J)

100m/s

200m/s

400m/s

Figure 5.45 Strain energy-time history of the whole regular structure for out-of-plane

impact

The comparison between the strain energy and kinetic energy of the whole

honeycomb structure is shown in Figure 5.46. The close decreasing slopes of oscillations

are observed between the two kinds of energy.

72

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

1

2

3

4

5

6

Time (s)

Energ

y (

J)

Kinetic energy

Strain energy

Figure 5.46 Energy-time history of the whole regular structure for out-of-plane impact

5.4.2 Result of out-of-plane impact to auxetic model

For auxetic model, the unit cells located in the impacting area suffer from the

vertical compression. The velocities history curves of the rigid ball are illustrated in

Figure 5.47.

73

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

50

100

150

200

250

300

350

400

Time (s)

Velo

city (

m/s

)

100m/s

200m/s

400m/s

Figure 5.47 Velocity-time history of the impacting ball for out-of-plane impact to auxetic

model

The returning velocities, ROV and COR at different initial velocities are listed

below in Table 5.13. The result of COR show the same trend as the regular model.

Impacting velocity(m/s) Returning velocity(m/s) Velocity of the point on


ROV COR

100 -35.00 -15.26 0.35 0.19

200 -93.19 -44.59 0.46 0.24

400 -154.14 22.79 0.39 0.44

Table 5.14 The velocity effect of the rigid ball of the impact to out-of-plane impact to

auxetic model

Figure 5.48 illustrates the kinetic energy history of the rigid ball to the auxetic

model during the impact.

74

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

20

40

60

80

100

120

140

160

180

Time (s)

Kin

etic E

nerg

y (

J)

100m/s

200m/s

400m/s

Figure 5.48 Time histories of the kinetic energy for out-of-plane impact to auxetic model

And both of the initial kinetic energy and final kinetic energy are listed in Table

5.14:


100 10.7 1.31

200 42.8 9.29

400 171.2 25.42

Table 5.15 The initial and returning kinetic energy of the impacting ball during out-of-

plane impact to the auxetic model

For 100 m/s, the returning kinetic energy is 85.2% lower than initial kinetic

energy. And for 200 m/s, it is 78.3% and 87.7% for 400 m/s. The honeycomb structure is

more efficient at absorbing the kinetic energy at velocity of 200 m/s.

75

The reaction force-time curves are shown in Figure 5.49. The max value is

approximately 49000 N in the first peak for velocity of 400 m/s. For velocity of 200 m/s,

the maximum is approximately 20000N, and the maximum occurs at second peak.

0 1 2 3

x 10-4

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

4

time (s)

Forc

e (

N)

100m/s

200m/s

400m/s

Figure 5.49 The reaction force history of the auxetic model to out-of-plane impact

The velocity histories of the point on impacting spot are shown in Figure 5.50.

76

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

50

100

150

200

250

300

350

Time (s)

Velo

city (

m/s

)

100m/s

200m/s

400m/s

Figure 5.50 Velocity history of the point on the spot of the out-of-plane impact to auxetic

model

Figure 5.51 shows the kinetic energy of the whole structure. The oscillation of

energy shows an obvious tendency of decreasing gradient for 400 m/s.

77

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

1

2

3

4

5

6

7

Time (s)

Kin

etic E

nerg

y (

J)

100m/s

200m/s

400m/s

Figure 5.51 Kinetic energy-time history of the whole auxetic structure for out-of-plane

impact

The displacement of the point on the impacting spot is shown in Figure 5.52. It

is obvious that the point on the front plate is vibrating during the impact and losing

energy over time.

78

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Time (s)

Dis

pla

cem

ent

(mm

)

100m/s

200m/s

400m/s

Figure 5.52 Displacement history of the point on the spot of the out-of-plane impact to

auxetic model

The strain energy for the whole structure is shown in Figure 5.53. The

honeycomb core and the back plate support the whole structure and absorb the kinetic

energy of the rigid ball, and the shape of the honeycomb core recovers after the impact.

79

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

1

2

3

4

5

6

7

8

Time (s)

Str

ain

Energ

y (

J)

100m/s

200m/s

400m/s

Figure 5.53 Strain energy-time history of the whole auxetic structure for out-of-plane

impact

Figure 5.54 show a comparison of strain energy and kinetic energy at 400 m/s.

Both curves arrive at the greatest amplitude at the beginning of the oscillation and then

fade to a plateau. The strain energy reaches a higher peak compared to the kinetic energy.

80

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

1

2

3

4

5

6

7

8

Time (s)

Energ

y (

J)

Kinetic energy

Strain energy

Figure 5.54 Energy-time history of the whole auxetic structure for out-of-plane impact

5.4.3 Comparison of the geometries of the honeycomb cores of out-of-plane impact

The comparison of strain energy between the two kind of models at 400 m/s is

shown in Figure 5.55. It takes approximately 0.00002 s for the regular model to reach a

maximum strain value of 5.6 J, while in the auxetic model the strain value reaches 7.3 J

around 0.00025 s. The curves indicate that the auxetic model absorbs more kinetic energy

and transfers it to strain energy at the first step and then the oscillation decays afterwards.

The curve of the auxetic model is below the regular’s in the midway where the strain

energy diminishes after the first peak.

81

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

1

2

3

4

5

6

7

8

Time (s)

Str

ain

Energ

y (

J)

Regular

Auxetic

Figure 5.55 Strain energy-time history of both model for out-of-plane impact

Figure 5.56 shows the comparison of the kinetic energy of the two models. It is

observed that the result is identical to the strain energy plot.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

1

2

3

4

5

6

7

Time (s)

Kin

etic E

nerg

y (

J)

Regular

Auxetic

Figure 5.56 Kinetic energy-time history of both model for out-of-plane impact

82

The total energy history of both models during the impact by the rigid ball with

the initial velocity of 400 m/s is shown in Figure 5.57. The auxetic curve reaches a

higher peak and releases the energy more rapidly than the regular model. Besides there is

no oscillation observed from these two curves.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x 10-3

0

2

4

6

8

10

12

14

Time (s)

Tota

l energ

y (

J)

regular

auxetic

Figure 5.57 Total energy-time history of both model for out-of-plane impact

The coefficients of restitution are compared in the table below. The COR for

regular model is larger than the one for auxetic model. Therefore, the impact of the rigid

ball to auxetic model is more elastic than the regular model.

83

Velocity Regular Auxetic

100 m/s 0.14 0.19

200 m/s 0.16 0.24

400 m/s 0.18 0.44

Table 5.16 COR of the out-of-plane impact at different velocities

84

CHAPTER SIX

CONCLUSIONS AND FUTURE WORK

6.1 Concluding Remarks

In this study, a nonlinear finite element method is used to simulate the impact of

a rigid ball colliding with composite sandwich panels comparing regular hexagonal and

auxetic cores. The dynamic response of different impact velocities and effect of cellular

geometry of honeycomb unit cell with regular and auxetic geometries were investigated.

Additionally, a study is conducted to determine the effect of in-plane and out-of-plane

impact directions relative to the honeycombs.

The dynamic results such as returning velocity, reaction force and displacement

showed increased amplitudes with an increase of velocity of the impactor. For the in-

plane loading model, the dynamic response shows that the honeycomb structure with

regular core has absorbed more energy compared with the impact of the composite

structure with auxetic honeycomb core. For the out-of-plane loading model, the

maximum energy that the regular structure absorbed is larger and the total energy stayed

at a higher level compared to the auxetic structure. Results showed that the COR value

for the structure depends on both the unit cell geometry, and also the velocity of impact.

The effective coefficient of restitution (COR) of the structure with auxetic core is larger

compared to the regular core, which implies that the impact to the auxetic core produces

more rebound for the impactor.

85

6.2 Future Work

1. In this work, only one configuration of auxetic honeycomb core was studied.

The research could be extended by modifying the dimension parameters of the unit cell

and ball size incrementally, and through sensitivity and optimization for maximum

energy absorption and/or limit of coefficient of restitution.

2. Develop experimental models and perform physical tests to validate the

behavior of impact conducted by finite element analysis.

3. The aluminum material of composite sandwich panel could be replaced with

more flexible materials and with viscous damping in order to determine if they could

offer different capability in absorbing energy from impact.

86

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Composite Sandwich Structures with Honeycomb Core