ViVaCE „Virtual Materials and their

Validation: German-French School of

Computational Engineering” – IRTG 1627

Results

Multiscale FEM for Rubber Friction on Rough Surfaces

Motivation

Prof. Dr.-Ing. habil. Dr. h.c. mult. P. Wriggers

Goals

Methods

• Hysteresis: Internal energy dissipation due to

cyclic loading and unloading, induced by the

asperities of the rough surface

• High contribution of small road track length

scales (λ < 0.1 mm), see Persson.2010

Dipl.-Ing. P. Wagner

0%

20%

40%

60%

80%

100%

Dry Wet

Per

centa

ge

µ(t

)

t ε

σ

Homogenization

µ(p, v)

p v

Some aspects available in

Wriggers/Reinelt.2009

µ(t

)

t [s]

Finite Linear Viscoelastic Model A power spectrum of a

surface is calculated

Real surface approximated with a

sum of sinusoidal waves

Decomposition of reconstructed

surface

Real surf.

Surface fit

Macro

Micro

Simulation µ(v) vs. experiment, Grosch.1953

Finer and rougher models increase µ

2

1

0

µ

log v

Multiscale calc.

Comparison

Full calc.

Coefficient of friction

0% 20% 40% 60% 80% 100% 120%

tcalc.

µ

Model represents qualitative behavior

Prediction of frictional response Frictional response: Sum of physical influences

Rough surface decomposition The Multiscale FEM concept

Microscale results Numerical validation of the method

Macr

osc

ale

Hysteresis Adhesion Lubrication, Cohesion

(not considered)

Mic

rosc

ale

Experimental Setup Coefficient of friction Frictional Force,

guess

Hysteresis friction is modeled → Significant influence of small length scales → Therefore Multiscale FEM

Split in macro- and micro-part → Micro friction law → Include friction law in macro calculation

Macr

osc

ale

M

icro

scale

Reasonable results on microscale – Good agreement of multiscale and full simulation – 90% less calculation time

• Multiphysics Homogenization Schemes for

Microstructured Interfaces (N. Noii)

• Development of Non-Convex Shaped Particles for

the Discrete Element Method (DEM) (M. Hothan)

• Application of Plasticity Models at the Contact Layer

(C. Weißenfels)

• Multi-Scale Constitutive Modeling of Carbon Black

Reinforced Rubber in a Finite Strain Framework for

FE Analysis (O. Stegen)

• Development of a Friction Approach for the FE

Method of Sheet Metal Forming Based on Multi-

Scale Modeling (B. Homann)

• hp-BEM for Contact Problems and Extended Ms-

FEM in Linear Elasticity (A. Issaoui)

ViVaCE-Projects with strong

Interaction