# Constitutive Models for Rubber X

DOI link for Constitutive Models for Rubber X

Constitutive Models for Rubber X book

# Constitutive Models for Rubber X

DOI link for Constitutive Models for Rubber X

Constitutive Models for Rubber X book

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In order to develop innovative products, to reduce development costs and the number of prototypes and to accelerate development processes, numerical simulations become more and more attractive. As such, numerical simulations are instrumental in understanding complicated material properties like chemical ageing, crack propagation or the strain- and temperature-induced crystallisation of rubber. Therefore, experimentally validated and physically meaningful constitutive models are indispensable. Elastomers are used for products like tyres, engine and suspension mounts or seals, to name a few. The interest in modelling the quasi-static stress-strain behaviour was dominant in the past decades, but nowadays the interests also include influences of environmental conditions. The latest developments on the material behaviour of elastomers are collected in the present volume.

**Constitutive Models for Rubber X** is a comprehensive compilation of nearly all oral and poster contributions to the European Conference on Constitutive Models for Rubber (Munich, 28-31 August 2017). The 95 highly topical contributions reflect the state of-the-art in material modelling and testing of elastomers. They cover the fields of material testing and processing, filler reinforcement, electromagnetic sensitive elastomers, dynamic properties, constitutive modelling, micromechanics, finite element implementation, stress softening, chemical ageing, fatigue and durability. In the area of rubbery materials and structures, applied research will play an important role also in the coming decades.

**Constitutive Models for Rubber X** is of interest to developers and researchers involved in the rubber processing and CAE software industries, as well as for academics in nearly all disciplines of engineering and material sciences.

## TABLE OF CONTENTS

part 1|29 pages

Keynote lectures

chapter 1|8 pages

#### Effect of filler content and crosslink density on the mechanical properties of carbon-black filled SBRs

chapter 2|8 pages

#### Experimental research and numerical simulation of the damping properties of Magnetorheological Elastomers

chapter 3|11 pages

#### Efficiency of rubber material modelling and characterisation

part 2|64 pages

Ageing

chapter 4|6 pages

#### Modelling of reaction-diffusion induced oxidation of elastomers in two spatial dimensions by means of ADI method

chapter 5|5 pages

#### A study on characterising ageing phenomena via the dynamic flocculation model

chapter 6|7 pages

#### Comparison between thermo-oxidative aging and pure thermal aging of an industrial elastomer for anti-vibration automotive applications

chapter 7|5 pages

#### Influence of antioxidant type on the thermo-oxidative aging of rubber vulcanizates

chapter 8|6 pages

#### On the thermal aging of a filled butadiene rubber

chapter 9|5 pages

#### Role of strain-induced crystallization on fatigue properties of natural rubber after realistic aerobic ageing

chapter 10|6 pages

#### Service life determination of rubber fuel hose used in aircraft applications

chapter 11|6 pages

#### Simulation of oxidative aging processes in elastomer components using a dynamic network model

chapter 12|8 pages

#### Modeling and simulation of couplings between chemical aging and dissipative heating in dynamic processes on the example of an NBR elastomer

chapter 13|4 pages

#### Nitrile rubber—the influence of acrylonitrile content on the thermo-oxidative aging

part 3|70 pages

Constitutive models and their implementation in FEM

chapter 14|6 pages

#### A time-dependent hyperelastic approach for evaluation on rubber creep and stress relaxation

chapter 15|6 pages

#### Modeling the Payne effect with Marc in the frequency response of rubber

chapter 16|5 pages

#### Eversion of tubes: Comparison of material models

chapter 17|4 pages

#### A new constitutive model for carbon-black reinforced rubber in medium dynamic strains and medium strain rates

chapter 18|7 pages

#### An affine full network model for strain-induced crystallization in rubbers

chapter 19|7 pages

#### Constitutive modelling of the amplitude and rate dependency of carbon black-filled SBR vulcanizate and its implementation into Abaqus

chapter 20|7 pages

#### Application and extension of the MORPH model to represent curing phenomena in a PU based adhesive

chapter 21|7 pages

#### A RVE procedure to estimate the J-Integral for rubber like materials

chapter 23|6 pages

#### Finite element implementation of a constitutive model of rubber ageing

part 4|118 pages

Experimental characterisation

chapter 24|5 pages

#### Internal failure behavior of rubber vulcanizates under constraint conditions

chapter 25|5 pages

#### Investigation of time dependence of dissipation and strain induced crystallization in natural rubber under cyclic and impact loading

chapter 26|3 pages

#### The study of local deformations of stretched filled rubber surface

chapter 27|6 pages

#### Experimental characterisation and modelling of the thermomechanical behaviour of foamed rubber

chapter 28|6 pages

#### Some cautions when applying nanoindentation tests on a fluoroelastomer: Experimental researches and application

chapter 29|7 pages

#### New ideas to represent strain induced crystallisation in elastomers

chapter 30|6 pages

#### Experimental investigation of the compression modulus at a technical EPDM, exposed to cyclic compressive hydrostatic loadings

chapter 31|5 pages

#### A novel algorithm

chapter 32|6 pages

#### Influence of dissipative specimen heating on the tearing energy of elastomers estimated by global and local characterization methods

chapter 33|5 pages

#### Crack growth under long-term static loads

chapter 34|6 pages

#### Mechanical characterization under CO2 of HNBR and FKM grade elastomers for oilfield applications—effects of 10GE reinforcements

chapter 35|6 pages

#### Sequential automated time-temperature algorithm for dynamic mechanical analysis

chapter 36|4 pages

#### New biaxial test method for the characterization of hyperelastic rubber-like materials

chapter 37|5 pages

#### Thermomechanical analysis of energy dissipation in natural rubber

chapter 38|5 pages

#### Investigation of crosslinking kinetics of silicone rubber/POSS nanocomposites

chapter 39|4 pages

#### Diffusion of oils in elastomers—determination of concentration profiles

chapter 40|4 pages

#### Mechanical characterization of highly aligned polyurethane microfibers

chapter 41|5 pages

#### Sorption experiments on elastomers assisted by Gas Chromatography/Mass Spectrometry (GC/MS)

chapter 42|6 pages

#### Multi-objective optimization of hyperelastic material constants

chapter 43|4 pages

#### Strain-induced crystallization ability of hydrogenated nitrile butadiene rubber

part 5|92 pages

Fracture, fatigue and lifetime prediction of rubber

chapter 44|6 pages

#### Rubber reinforcing carbon fibre cord under tension and bending Part 1

chapter 45|4 pages

#### Fatigue behaviour of unidirectional carbon-cord reinforced composites and parametric models for life prediction

chapter 46|6 pages

#### Service life prediction under combined cyclic and steady state tearing

chapter 47|5 pages

#### Impact of stress softening on tearing energy of filled rubbers as evaluated by the J-Integral

chapter 48|6 pages

#### Influence of discontinuous thermo-oxidative ageing on the fatigue life of a NR-compound used for engine-mount application

chapter 49|5 pages

#### Effect of filler-polymer interfacial phenomena on fracture of SSBR-silica composites

chapter 50|6 pages

#### True stress control for fatigue life experiments of inelastic elastomers

chapter 51|6 pages

#### Experimental study of dynamic crack growth in elastomers

chapter 52|4 pages

#### Characterising the cyclic fatigue performance of HNBR after aging in high temperatures and organic solvents for dynamic rubber seals

chapter 53|6 pages

#### Gradient damage models in large deformation

chapter 54|6 pages

#### Thermomechanical characterization of the dissipation fields around microscale inclusions in elastomers

chapter 55|4 pages

#### Influence of test specimen thickness on the fatigue crack growth of rubber

chapter 56|6 pages

#### Fracture analysis of a rolling tire at steady state by the phase-field method

chapter 57|7 pages

#### Modelling and finite element analysis of cavitation and isochoric failure of hyperelastic adhesives

chapter 58|6 pages

#### The study of fatigue behavior of thermally aged rubber based on natural rubber and butadiene rubber

chapter 59|4 pages

#### Characterization of ageing effect on the intrinsic strength of NR, BR and NR/BR blends

part 6|18 pages

Filler reinforcement

chapter 60|7 pages

#### Non-entropic contribution to reinforcement in filled elastomers

chapter 61|8 pages

#### A novel reinforcement structure in tire tread compounds

part 7|9 pages

Stress softening

chapter 62|7 pages

#### A physical interpretation for network alterations of filled elastomers under deformation

part 8|8 pages

Rheology and processing

chapter 63|6 pages

#### The evolution of viscoelastic properties of silicone rubber during cross-linking investigated by thickness-shear mode quartz resonator

part 9|18 pages

Special elastomers

chapter 64|4 pages

#### Modeling and simulation of magnetic-sensitive elastomer immersed in surrounding medium

chapter 65|6 pages

#### A simple Mullins model applied to a constitutive model for foamed rubber

chapter 66|4 pages

#### Torsional wave propagation in tough, rubber like, doubly crosslinked hydrogel

chapter 67|2 pages

#### Preparation of electroactive elastomers: Stress relaxation and crosslinking aspects

part 10|36 pages

Industrial applications

chapter 68|6 pages

#### Modelling of the mechanical behaviour of elastomer seal at low temperature

chapter 70|7 pages

#### Nanoparticles effects on the thermomechanical properties of a fluoroelastomer

chapter 71|6 pages

#### Improvement of leak tightness for swellable elastomeric seals through the shape optimization

chapter 72|6 pages

#### Comparison of experimental and numerical fatigue lives of rolling lobe air-springs for different diameters, inner pressures and temperatures

part 11|9 pages

Design issues

chapter 73|7 pages

#### Computational material design of filled rubbers using multi-objective design exploration

part 12|68 pages

Modelling of viscoelastic and hyperelastic behaviour

chapter 75|6 pages

#### Constitutive modelling of nonlinear viscoelastic behaviour for Poly (L-Lactic Acid) above glass transition

chapter 76|6 pages

#### Thermo-mechanical properties of strain-crystallizing elastomer nanocomposites

chapter 77|7 pages

#### Vibration isolators with stiffness nonlinearity using Maxwell-Voigt models

chapter 78|6 pages

#### Calibration of advanced material models for elastomers

chapter 79|7 pages

#### Influence of nonlinear viscoelasticity for steady state rolling

chapter 80|6 pages

#### Comparison of the implicit and explicit finite element methods in quasi-static analyses of rubber-like materials

chapter 81|6 pages

#### Micro-mechanical modeling of visco-elastic behavior of elastomers with respect to time-dependent response of single polymer chains

chapter 82|7 pages

#### A framework for analyzing hyper-viscoelastic polymers

chapter 83|6 pages

#### On the influence of swelling on the viscoelastic material behaviour of natural rubber

part 13|65 pages

Micro-structural theories of rubber

chapter 84|6 pages

#### Electroelasticity of dielectric elastomers based on molecular chain statistics

chapter 85|7 pages

#### Analytical network averaging: A general concept for material modeling of elastomers

chapter 86|7 pages

#### A hyperelastic physically based model for filled elastomers including continuous damage effects and viscoelasticity

chapter 87|7 pages

#### A micro-mechanical model based on the hydrodynamic strain amplification in filled elastomers

chapter 88|5 pages

#### Effect of microscopic structure on mechanical characteristics of foam rubber

chapter 89|6 pages

#### Three-dimensional homogenization finite element analysis of open cell polyurethane foam

chapter 90|6 pages

#### Derivation of full-network models with chain length distribution

chapter 92|3 pages

#### Evaluation of rheological parameters for injection molding simulations

chapter 93|7 pages

#### Statistical investigation of self-organization processes in filled rubber

part 14|15 pages

Tyres and friction