Influence of geometry and design parameters on flexural behaviour of dynamic compression plates (dcp) - experiment and finite element analysis.pdf

INFLUENCE OF GEOMETRY AND DESIGN

PARAMETERS ON FLEXURAL BEHAVIOR

OF DYNAMIC COMPRESSION PLATES

(DCP): EXPERIMENT AND FINITE

ELEMENT ANALYSIS

SADREDDIN BAHARNEZHAD*

Department of Materials Engineering

Islamic Azad University South Tehran

Tehran 11369, Iran

[email protected]

HASSAN FARHANGI

School of Materials and Metallurgical Engineering

University of Tehran

Tehran 11369, Iran

ALI AMMARI ALLAHYARI

School of Materials and Metallurgical Engineering

University of Tehran, Tehran 11369, Iran

Received 18 August 2012

Revised 7 November 2012

Accepted 11 November 2012

Published 24 December 2012

This work aimed to study the effect of various geometric parameters on bending behavior in

orthopedic dynamic compression plates (DCPs) in order to achieve suitable criteria in an

optimum design of these plates. Modeling, simulation, and analysis were performed through

the finite element software of ABAQUS. In order to verify the model, four-point bending tests

on several actual plates were conducted. In addition, the classical beam theory was applied for

the theoretical estimation of the maximum tensile stress in the outer fiber and the longitudinal

stresses of plates. Finite element analysis (FEA) results indicated relatively good conformity

with the empirical results and those of beam theory. Based on the results, the distance of the

holes from the plate edge was observed to be the most effective parameters on flexural beha-

vior. It was also found that the flexural properties are maximized at a unique distance between

the outside edge of the hole and the edge of the plate.

Keywords: Dynamic compression plate (DCP); finite element analysis (FEA); stress; flexural

behavior; beam theory.

*Corresponding author.

Journal of Mechanics in Medicine and Biology

Vol. 13, No. 3 (2013) 1350032 (20 pages)

°c World Scientific Publishing Company

DOI: 10.1142/S0219519413500322

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http://dx.doi.org/10.1142/S0219519413500322

1. Introduction

Recently, bone fracture fixations have been widely used to stabilize and treat the

fractured bone. One of the more common devices is the dynamic compression plate

(DCP) which is used for the treatment of simple bone fractures. These plates are

attached to the bone using a series of screws. The interaction between the plate and

screws introduces a critical compressive force which accelerates healing. Generally,

the approval and verification of the plates to be implanted in the body should be based

on the provision of adequate strength and stiffness.1 One of the pioneers who per-

formed extensive tests on the stiffness and strength of bone fracture fixations was

Lindahl.2�4 Laurence et al.,5 also studied extensively several fracture plates and

examined the effects of flexural and torsion loads on them. Since the existence of the

inherent flexural loads on the body structure can severely affect the plate’s function,

and because surgeons usually bend and deform the plates before implanting them in

the desired location to achieve a good connection between the plate and bone, this

type of loading gains more importance. In fact, determining the strength and stiffness

of the plates as well as the factors affecting them, helps engineers designmore efficient

plates. Recent researches on different designs of orthopedic plates have been mainly

followed by two approaches including first, the production of new materials and

second, the application of new analyticalmethods for an optimal design. For instance,

Koo et al.,6 designed a finite element model to simulate the stiffness of fixation in case

of aDynafix plate in arbitrary configurations and under pressure with twisting three-

and four-point bending, and concluded that a proper modeling of finite element

analysis (FEA) will provide useful information about the strength of some of the

configurations to stabilize the position of broken bone sand treat the fracture. Said-

pour also used FEA to investigate and compare the mechanical performances of

various six-hole composites and steel plates under bending and torsion loading con-

ditions. He also determined the regions with the greatest stress concentrations and

optimized the design of the plate by reducing the width around the two central holes.7

In the present study, the performance of the DCPs in four-point bending test

conditions were investigated by using FEA, beam theory, and experimental

methods in order to determine the effective geometry and design parameters on

their flexural behavior.

2. Simulating the Four-Point Bending Test in ABAQUS Software

Analytical methods used in describing the details of the precise shaping of metals,

their behavior, and the applied boundary conditions are imperfect and their

relative data are unrepeatable. In other words, presenting an accurate solution for

the problem of shaping metals is very difficult and sometimes impossible since a

precise solution must satisfy all the equations of both equilibrium and compatibility.

Although the theory of plasticity, the slip line field theory, the upper bound

method, the slab method, and other similar methods to review the processes for

S. Baharnezhad et al.

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shaping metals yield good results, their disadvantages include the limited use in the

case of specific forms in addition to the fact that the particular equivalents must be

written for each model and the results of the same specific form should be obtained.

Numerical methods are used for the analysis of complex processes of shaping

metals. Hence, the finite element method is one of the most widely used numerical

methods. Currently, FEA as an invaluable implant designing tool allows researchers

to study the quality and parameters of many complex mechanical phenomena as

well as the effects of various design factors such as size, shape, position, elastic

modulus, implanting conditions by surveying the plots of internal stress�strain,

and other parameters such as the main stresses and von Misses and Tresca yield

criteria. A good estimate of the applied loads is another important factor in

designing an implant.7,8 Various software packages are presented in the field of the

finite element method and the ABAQUS software was applied in this paper due to

its high capability and accuracy in either plastic and nonlinear analyses in order to

model and simulate the three-dimensional four-point bending process. Because the

four-point bending process can be considered as a static process, the standard

method is used for simulation analysis.

2.1. Modeling

To draw the geometric model of the plates and holes, the ABAQUS/CAE software,

which is a subset of the ABAQUS software, was applied. Samples were modeled in

both actual conventional dimensions and other hypothetical dimensions in order to

make comparisons.

The applied finite element models were the three-dimensional models of the

plates with eight holes and the four-point bending tests were simulated under the

ISO 9585 standard procedure by applying the appropriate boundary conditions and

external load. The dimensional details of the basic broad and narrow eight-hole

plates used in the simulation are presented in Table 1. As mentioned, these details

have been considered in accordance with the actual conventional plates. The elastic

and plastic properties of plates were taken to be equal to the 316-L stainless steel

medical grade (Tables 2(a) and 2(b)). These plates were assumed to have isotropic

properties. Considering these criteria, the model was created following an iterative

process of mesh generation and mesh refinement (Fig. 1).

The ABAQUS/STANDARD was used for three-dimensional analysis. The bulk

of the models were meshed by using the solid 20-noded hexahedral elements

(C3D20R) for the broad and narrow models with standard dimensions,and the

10-noded tetrahedral elements (C3D10M) for the broad models with the symmetric

hole arrangement. The locations of loading were meshed by using the 15-noded

quadratic triangular prism elements (C3D15) and the 10-noded tetrahedral elements

(3D10M). All elements were used by quadratic shape functions and a reduced

(2� 2� 3) integration scheme. In actual fact, these elements were opted to avert the

Influence of Geometry and Design Parameters on Flexural Behavior of DCP

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shear locking in bending, which is common in first order.10 Table 3 shows the type

and number of elements used in the simulation of the three types of eight-hole plates.

The input comprised the discretized mesh with elemental properties determining

the boundary conditions and loading history. The output of this program in addition

Table 1. The dimensional details of the simulated standard broad and narrow basic eight-hole models,

all numbers are in mm.

Type of plate Thickness Width Length Width of hole Length of hole

Distance between

two central holes

Broad 4.5 16 135 5.8 8.5 17

Narrow 3.5 12 135 5.8 8.5 17

Table 2. Properties applied in finite

element analysis with respect to the 316-L

medical grade. (a) General and elastic

properties and (b) plastic properties.9

(a)

Young’s Modulus (GPa) 200

Poisson’s ratio 0.28

(b)

Plastic stress (MPa) Plastic strain

800 0

850 0.125

960 0.250

(a) (b)

Fig. 1. The part of partitioned and meshed models with two hole arrangement. (a) Asymmetric and

(b) symmetric.


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to nodal displacements presented the state of stress at any location of the model. In

the regions with high stress gradients and in the locations of applied loads, finer

meshes and suitable partitions were required to achieve the accurate solutions. Mesh

refinement is the process of systematically increasing the mesh density in these

regions to produce a more accurate stress contour plot where the greatest stress

gradient takes place in the models. Preliminary model solutions were used to

identify regions with high discretization error. From these initial results, it was

apparent that the most important regions for mesh refinement were in the regions

adjacent to the screw holes and the locations of applied loads, thus a fine second

mesh was generated to achieve an acceptable level of numerical accuracy.

2.2. Loading

The models were loaded with two strips of uniform pressure and applying of

appropriate constraints. Also, the locations of these loads and constraints were

defined according to the ISO 9585 standard procedure.11 The ABAQUS/standard

automatically increases the load applied to each increment. Thus, the solution of

nonlinear problems (like in this study) is not so complicated and only the first

increment size must be correctly defined at each step. To achieve convergence at

every increment, the software performs iterations are highly dependent on the

degree of nonlinearity of a system. As the default, if convergence is not achieved

subsequent to sixteen iterations at each step, the operation is stopped and a new

step size that is 25% higher than the previous one will be solved again. Figure 2(a)

shows the loading and the corresponding constraints.

2.3. Validation of the model

2.3.1. Final deformation in four-point bending

Based on empirical experiments, it was noticed that when a plate is placed under

four-point bending test (according to ISO 9585), it bends in the middle exactly along

the distance between two central holes. Figure 2(b) shows a schematic configuration

of this flexure. The bent form can be divided into three segments of 1, 2 and 3,

among which the middle segment (segment 2) is flat as shown in Fig. 3. In

Table 3. Type and number of elements applied in the simulation of plates.

Type of eight-hole model Bulk elements

Load positions

elements

Total number

of elements

Total number

of nodes

Standard broada C3D20R C3D15 8,288 42,515

Symmetric broadb C3D10M 3D10M 11,636 19,462

Standard narrowc C3D20R C3D15 6,128 29,552

aDimensions in accordance with Table 1, a broad plate with the asymmetric hole arrangement.bDimensions in accordance with Table 1, a broad plate but with the symmetric hole arrangement.cDimensions in accordance with Table 1, a narrow plate with the symmetric hole arrangement.


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simulation, if the strain hardening properties are considered, the middle segment of

the model will completely flatten (not arc-shaped) and the final deformed shape

(Fig. 4(a)) will look similar to the actual pattern as shown in Fig. 3, while if only the

linear properties are defined, the middle segment will be arc-shaped and differ from

the real pattern (Fig. 4(b)).

2.3.2. Yield criteria

The equivalent plastic strain (PEEQ) was used to evaluate the yield condition of the

plates. In the case of most materials in an isotropic hardening plasticity theory, the

PEEQ is defined as Eq. (1): ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2

3d"pl : d"pl

rð1Þ

and is the total accumulation of plastic strain to define the size of yield surface,

where d"pl is the plastic strain rate. If the PEEQ, which is a scalar variable, is

(a)

(b)

Fig. 2. Typical set-up of a four-point bending test according to the ISO 9585 standard. (a) Typical

simulated eight-hole broad model with its corresponding constraints and two bar loading bars and

(b) schematic configuration for the flexure test of actual plates.


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positive, it means that the material has yielded. In fact, even if the final form of the

model output file is similar to the one expected, simulation should be such that the

output file of maximum equivalent plastic strain must not become zero.10 Figure 5

shows the similar PEEQ developed in a broad eight-hole plate. The regions sur-

rounding two middle holes have been identified as critical due to their relatively

large plastic deformation. It should be considered that there is no plastic defor-

mation in the other regions during bending.

Fig. 3. Actual deformation of a typical broad eight-hole plate after a four-point bending test with three

marked segments (1, 2 and 3).

(a)

(b)

Fig. 4. Final bent model in four-point bending test under the ISO 9585 procedure by considering

(a) strain hardening properties and (b) only linear properties.


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2.3.3. Load�deflection curve

Empirically speaking and according to the ISO 9585 standard procedure, some

conventional standard eight-hole plates were tested under the four-point bending

test under ISO 9585 conditions, and their respective load�deflection curves were

compared with a curve obtained from a simulated model of similar geometry and

properties (with regards to Tables 1 and 2). As a sample that is shown in Fig. 6, the

empirical test and FEA have excellent conformity with each other.

Fig. 5. Typical PEEQ contour for an eight-hole broad plate.

0

1

2

3

4

5

6

7

8

0 1 2 3 4 5 6

Lo

ad(K

N)

Defllection(mm)

4-point bending testFEAoffset line (ISO 9585)

Fig. 6. Comparison of load�deflection curves of a typical eight-hole plate obtained from the FEA and

four-point bending test in accordance to ISO 9585.


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3. Results and Discussion

3.1. Study of the regions with stress concentration and comparsion

between the beam theory and FEA

Generally, there are two ways that beam bending problems are typically solved:

analytically using statics (e.g., beam theory), and computationally using the finite

element method. Regarding simplifying the assumptions of the classical beam the-

ory such as homogenous and isotropic material and the actual plates geometry that

are three-dimensional, the beam theory cannot predict the flexural phenomenon

with high accuracy, therefore, the beam theory and the simulation results were

compared to determine deviations from each other. On the other hand, although the

results of simulation can have more accuracy than the classical beam theory, it

should follow a general pattern similar to those of the beam theory. Considering

Figs. 7(a)�7(c), it was found that the adjacent regions of the two central holes in

these plates are the regions with the highest stress concentration during bending

loading. Using the classical beam theory, the maximum tensile stress in the outer

surface of a four-point bending model was obtained from Eq. (2),12

� ¼ 3pa

bt2; ð2Þ

where p is the maximum load, b is the width of the plate, t is plate thickness, and a is

the distance between the inner and outer rollers in the four-point bending set. As

(a)

Fig. 7. Three-dimensional deformed eight-hole models with different hole arrangement and Mises stress

distribution with regards to Tables 1 and 3. (a) An actual standard broad plate, (b) a symmetric broad

plate and (c) an actual standard narrow plate.


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shown in Fig. 8, the maximum tensile stress obtained from simulation is relatively

consistent with beam theory results. Therefore, if the graph of tensile stresses

(longitudinal stress of plate or �3) versus the outer span length is plotted using

both the beam theory and FEA as shown in Fig. 9, it can be seen that there are two

peaks (A and B) in the graph obtained from FEA that are located in the adjacent

regions to the two central holes, indicating two regions with the greatest stress

(b)

(c)

Fig. 7. (Continued )


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concentrations. This graph also exhibited a relatively good conformity with the

beam theory pattern.

3.2. Effect of different geometrical parameters on the flexural

behavior of the models

Since studying of the effects of geometry and design parameters on the bending

performance of the plates was not empirically possible, these plates were modeled

and simulated under the terms of a four-point bending load where by its effects were

investigated. The parameters studied and the range of their changes have been

selected by deriving inspiration from the actual plates (more than 20 plates from

various prominent manufacturers). The basic model is equivalent to a broad plate

938.5

1115

0

200

400

600

800

1000

1200

Max

imu

m o

ute

r fi

ber

str

ess(

Mp

a)

Beam theory

FEA

Fig. 8. Comparison between the maximum tensile stresses on the outer surface of plate derived from

FEA and beam theory.

0

200

400

600

800

1000

1200

1400

0 20 40 60 80

L (mm)

FEA

Beam Theory

A B

Beam Theory

FEA

Ten

sile

str

ess

(MP

a)

Fig. 9. Graph of tensile stresses �3 versus the longitudinal distance of the plate.


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with a thickness of 4mm, a width of 16mm, the distance between two central holes

of 17mm, and the distance between holes and edge of 3mm.

3.2.1. Effect of thickness

To examine the effect of this parameter, two similar models of only different

thicknesses were simulated (4 and 4.5mm). The obtained load�deflection curves

(Fig. 10(a)) and the maximumMises stresses (Fig. 10(b)) showed that as the thickness

increases, this curve undergoes an upward shift and there would be a subsequent

increase in bending strength and stiffness. Naturally, the increase in the thickness of

the plates should be avoided during both phases of design and manufacturing as

much as possible due to the problems arising from stress shielding,which is one of

the most common problems encountered in the treatment of fractured bones.13�15

Considering Fig. 11, it was found that all components of shear stresses of the thicker

model are greater than the thinner one, and typically in these plates, the component

of shear stress S13 is larger than the two other components.

3.2.2. Effect of the distance between two central holes

To examine the effect of this parameter, two similar models of only different dis-

tances between the two middle holes were simulated (15 and 17mm). The obtained

load�deflection curves (Fig. 12(a)) and the maximum Mises stresses (Fig. 12(b))

showed that a variation of up to 2mm in this parameter would lead to no significant

difference in bending strength and stiffness of the two models. As Fig. 13 shows, it is

obvious that the principal stresses in the transverse component of plates (S11) are

several times larger than the other two components (S22 and S33), although these

values did not show much difference between these two models.

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 0.001 0.002 0.003 0.004

Lo

ad(N

)

Deflection(m)

t=4.5mmt=4mm

(a)

1041

1291

0

200

400

600

800

1000

1200

1400

Max

imu

m m

ises

str

ess(

Mp

a)

t=4.5 mm t=4 mm

(b)

Fig. 10. Comparison of two models with different thicknes. (a) Load�deflection curves. (b) Maximum

Mises stresses.


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3.2.3. Effect of hole size

To examine the effect of this parameter, two similar models of only different hole

sizes were simulated. In the two-dimensional mode, the geometry of the hole does

not look like an ellipse, but in the meantime, it consists of two elliptical halves

placed on the two ends of a rectangle (Fig. 1). The width of the holes in the first

model is 5.8mm (exactly similar to that of the common original eight-hole plates)

and it is 4.8mm in the case of the second model. Figure 14(a) shows that if the hole

S12

25%

18%

S13 S23

37%

0

100

200

300

400

500

600

Sh

ear

stre

ss(M

pa)

t=4.5mm

t=4mm

Fig. 11. Comparison of the typical shear stresses in two models with two different thicknesses.

Lo

ad(N

)

Deflection(m)

0

1000

2000

3000

4000

5000

6000

7000

8000

0 0.002 0.004 0.006 0.008 0.01

mid-dist=17mm

mid-dist=15mm

(a)

1290 1290

0

200

400

600

800

1000

1200

1400

Max

imu

m M

ises

str

ess(

Mp

a)

Mid-dist=17 mm Mid-dist=15 mm

(b)

Fig. 12. Comparison of two models with different distances of the two central holes. (a) Load�deflection

curves. (b) Maximum Mises stresses.


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size is reduced, the load�deflection curve shifts higher and the flexural strength and

stiffness would increase due to its larger cross-section in bending. The maximum

Mises stresses are also reduced (Fig. 14(b)).

3.2.4. Effect of the arrangement of holes

In this section, two similar models, where only symmetric and asymmetric hole

arrangement differ, the shapes of conventional narrow and broad plates were

simulated, respectively. Figure 15(a) shows that the sample with a symmetric hole

0

1000

2000Original holes

Smaller holes

3000

4000

5000

6000

7000

8000

9000

0 0.002 0.004 0.006

Lo

ad(N

)

Deflection(m)

(a)

1290

1152

0

200

400

600

800

1000

1200

1400

Max

imu

m M

ises

str

ess(

Mp

a)

Original holes Smaller holes

(b)

Fig. 14. Comparison of two models with different hole sizes. (a) Load�deflection curves. (b) Maximum

Mises stresses.

3%

5%0.7%

s11 s330

100

200

300

400

500

600

700

800

900

Str

ess(

Mp

a)

s22

mid-dist=17mmmid-dist=15mm

Fig. 13. Typical principal Mises stresses for two models with different distances of the two central holes.

S11 is the component of principal stress through the plate width.


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arrangement (narrow plate) has a higher curve than an asymmetric sample (broad

plate); in other words, narrow samples present higher bending strength and stiffness

than the broad ones. Considering Fig. 15(b), it is clear that the sample with an

asymmetric hole arrangement has a larger maximum Mises stress than a symmetric

one. Generally, in the asymmetric samples, only the lowest distance from the middle

holes to the edge of plate endure the highest stress concentrations, while for the

symmetric samples, the stress concentrations in these two sides are also the same

since both of the distances between the edges of the plate and middle holes are equal

to each other.

3.2.5. Effect of width

Here, two similar models of only different widths (15 and 16mm) were simulated.

The obtained result indicated that the greater the width is, the higher the

bending strength and stiffness (Fig. 16(a)) and the lower the maximum Mises stress

(Fig. 16(b)).

3.2.6. Effect of the distance between holes and edge of plate

In this section, four similar models with only difference in the distance between the

holes and the edge of the plate were simulated. Practically, because these distances,

similar to those in the real plates, are small, there was no need to study more

models. For the first model, the distance between the outside edge of the hole to the

edge of the plate was 3mm (the holes were far from the central axis of the model),

while it was 4mm for the second (the holes were closer to the central axis of the

model), 4.5mm for the third, and 5.1mm in the case of the last (the centers of holes

placed on the central axis of the model). Comparing the load�deflection curves of

Lo

ad(N

)

Deflection(m)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 0.002 0.004 0.006 0.008 0.01

Broad

Narrow

(a)

12901172

0

200

400

600

800

1000

1200

1400

Max

imu

m M

ises

str

ess(

Mp

a)

Broad Narrow

(b)

Fig. 15. Comparison of two models with symmetric (narrow) and asymmetric (broad) hole arrangement.

(a) Load�deflection curves. (b) Maximum Mises stresses.


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both the initial and ultimate models presented in Fig. 17(a), it is found that if the

holes in the model are initially more distant from the edges of plates, the load will be

greater and the model would have better bending properties. However, on the other

hand, considering Fig. 17(b) and curves A�D, especially curve B, it is important to

note that the curve of load�deflection would not always ascend due to the

approximation of the holes toward the central axis of the model and a symmetrical

hole arrangement since this curve and consequently the flexural properties will

be maximized at a point along this distance (3 to 5.1mm). Thus, in identical

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 0.0005 0.001 0.0015 0.002 0.0025

w=15mm

w=16mm

Lo

ad(N

)

Deflection(m)

(a)

1058 1041

0

200

400

600

800

1000

1200

Max

imu

m M

ises

str

ess(

Mp

a)

W=15 mm W=16 mm

(b)

Fig. 16. Comparison of two models with different widths. (a) Load�deflection curves. (b) Maximum

Mises stresses.

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

400.0200.00

Lo

ad(N

)

Deflection(m)

edge=3mm

edge=4mm

(a)

edge=3 mm

edge=5.1 mm(symm)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 0.002 0.004 0.006 0.008 0.01

Lo

ad(N

)

Deflection(m)

edge= 4 mm

edge=4.5 mm

C DB A

(b)

Fig. 17. Comparison of load�deflection curves and maximum Mises stresses for several similar models

with only a difference in the distance between the holes and plate edge. (a) Two models, (b) four models

and (c) maximum Mises stresses.


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conditions, if this optimal point is precisely defined and implemented in design, a

plate with the asymmetric hole arrangement can ultimately provide the maximum

flexural strength even greater than a plate with asymmetric hole arrangement. This

optimized distance between the outside edge of the hole and the edge of the plate

was concluded to be 4mm in the case of these models. In fact, it seems that among

all geometry and design factors considered, this factor has the most important

influence on the bending behavior of plates. Also, according to Fig. 17(c), it is clear

that on a model with a lower load�deflection curve, the maximum Mises stress is

greater than the model with an higher curve.

3.2.7. The effect of changing more than one parameter and an all-inclusive

comparison of geometry and design elements

Thus far, the effects of individual parameters on load�deflection were studied

separately. As will be explained in the next section, the simultaneous changing

effects of more than one parameter plays an important role. Here, the range of

variables selected were also the same previous quantities and they were in such way

that can be practically duplicated and implemented in the manufacture of the actual

plates.

As can be seen in Fig. 18, by increasing the thickness and decreasing the distance

between two central holes simultaneously, the flexural properties slightly are

increased. Also, by increasing the thickness and decreasing the width of the model

concurrently, a slight decrease in flexural properties can be seen. In the designing

process of orthopedic plates by increasing the thickness, the effects of stress

shielding should always be considered as a crucial limitation. Eventually, if the

distance between two central holes also decreases while the distance between holes

and the edge of the plate is considered optimal (i.e., 4mm), the flexural properties

will be slightly higher than when the optimized edge distance only is applied.

1290

1040

1220 1195

0

200

400

600

800

1000

1200

1400

Max

imu

m M

ises

str

ess(

Mp

a)Edge=3 mm

Edge=4 mm

Edge=5.1 mmEdge=4.5 mm

3 4 5.1 4.5

(c)

Fig. 17. (Continued )


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According to all obtained results, it can be generally said that among all the

geometrical factors discussed, the distance between the outside edge of the holes and

the edge of the plate, thickness, hole size, and width of the plates have the greatest

impact on bending behavior of plates, respectively.

4. Conclusions

Although as the thickness and width of the plates increase, the flexural properties

also increase, the effect of thickness is much greater than that of the width. Of

course, the design limitations arising from stress shielding and the relevant bone size

should also be accounted for, and increasing the thickness is not necessarily a safe

way to increase the flexural strength. The smaller the hole size, the higher the

bending strength and stiffness will be; however, it should also be noted that a hole

could be designed so small to the extent that there is no limitation on the manu-

facturing of a thinner plate screw with weaker mechanical properties.

As the simulation results showed, the highest concentration of stress in the four-

point bending test is accumulated in the distances between the two central holes and

the edge of the plate, hence the hole drilling technique by CNC machine is of

particular importance.

FEA results had excellent conformity with those of the empirical flexure, and

also had the relative conformity with the classical beam theory in predicting both

the maximum tensile stresses in the outer fiber and longitudinal stresses of plates.

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 0.002 0.004 0.006 0.008 0.01

Lo

ad(N

)

Deflection(m)

shorter mid-dist

edge dist= 4.5 mm symm holegreater thk basic model-broad

(asymm)

symm hole & greater thkgreater thk &

smaller width

optimizededge dist&

shorter mid-dist

optimizededge

dist=4mm

smaller hole

Fig. 18. Comparison of changing the geometry and design parameters, both one and more than one

parameter all together.


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Among all geometric parameters considered, the distance between the hole edge

to the edge of the plate and the degree of symmetry or asymmetry of the hole

arrangement were found to be the most important factors in determining the flexural

behavior of plates. The significant point is that by shifting the location of holes

toward the central axis of the plate and approaching a more symmetric hole

arrangement, but even though the flexural strength would increase in the first place

so that it becomes maximum at a special point along this distance, after that point,

the flexure strength would decrease. This optimized point was found to be 4mm for a

broad eight-hole plate. The results also demonstrated that the impact of applying

this optimal distance on flexural properties is approximately equal to the impact of

increasing the thickness size to 0.5mm. It was also observed that next to this par-

ameter, the thickness, hole size, and width of the plates have the greatest impact on

the flexural behavior of plates. While a single variation of up to 2mm in the distance

between the two central holes would have no significant effect, by decreasing this

parameter in conjunction with considering the optimum distance between the hole

edge to the edge of the plate, a slight increase in mechanical properties was seen.

Even though a slight impact in changing more than one parameter on the curves

of load�deflection rather than changing only one parameter was observed, results

showed that by concurrently applying the optimum distance between the hole edge

to the edge of the plate and reducing the distance between two central holes, sized

2mm, the maximum flexural properties can be obtained.

Acknowledgments

The authors would like to thank the Pooyandegan Pezeshki Pardis Company for

their financial support and cooperation.

References

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4. Lindahl O, The rigidity of fracture immobilization with plates, Acta Orthop Scand38:101�114, 1967.

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Strength Tests, ASM International, Vol. 8, 10th ed., Ohio, pp. 132�136, 1990.13. Terjesen T, Apalset K, The influence of different degrees of stiffness of fixation plates on

experimental bone healing, J Orthop Res 6:293�299, 1988.14. Hente R, Cordey J, Perren SM, In vivo measurement of bending stiffness in fracture

healing, Biomed Eng Online 2:8, 2003.15. Au AG, Raso V, Liggins A, Amirfazli A, Contribution of loading conditions and material

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Documents

Influence of geometry and design parameters on flexural behaviour of dynamic compression plates (dcp) - experiment and finite element analysis.pdf