A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber

Dorfmann, Luis; Ogden, Ray W.

doi:10.1016/j.ijsolstr.2003.11.014

Cited by 387 publications

(316 citation statements)

References 53 publications

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“…Most theories, however, are based on phenomenological continuum models of various features of the constitutive response of filled elastomers. Examples include Dorfmann and Ogden's analysis of the Mullins effect [26], Kaliske and Rothert's work on the internal friction [27] and Miehe and Keck's stress decomposition model of damage evolution [28].…”

Section: Introductionmentioning

confidence: 99%

Multiscale modelling of particle debonding in reinforced elastomers subjected to finite deformations

Matouš

Geubelle

2005

Numerical Meth Engineering

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SUMMARYInterfacial damage nucleation and evolution in reinforced elastomers subjected to finite strains is modelled using the mathematical theory of homogenization based on the asymptotic expansion of unknown variables. The microscale is characterized by a periodic unit cell, which contains particles dispersed in a blend and the particle matrix interface is characterized by a cohesive law. A novel numerical framework based on the perturbed Petrov-Galerkin method for the treatment of nearly incompressible behaviour is employed to solve the resulting boundary value problem on the microscale and the deformation path of a macroscale particle is predefined as in the micro-history recovery procedure. A fully implicit and efficient finite element formulation, including consistent linearization, is presented. The proposed multiscale framework is capable of predicting the non-homogeneous microfields and damage nucleation and propagation along the particle matrix interface, as well as the macroscopic response and mechanical properties of the damaged continuum. Examples are considered involving simple unit cells in order to illustrate the multiscale algorithm and demonstrate the complexity of the underlying physical processes.

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Section: Introductionmentioning

confidence: 99%

Multiscale modelling of particle debonding in reinforced elastomers subjected to finite deformations

Matouš

Geubelle

2005

Numerical Meth Engineering

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“…Filled rubbers are of course renowned for their inelastic behaviour (e.g. the Mullins effect [8], [35]) due to microstructural effects. Such inelastic behaviour has thus far been incorporated via pseudo-elastic strain energy functions using damage parameters for example.…”

Section: Discussionmentioning

confidence: 99%

“…Layered media have been considered recently by deBotton [4]. Important contributions regarding the constitutive behaviour of filled rubbers, modelled via pseudo-elastic strain energy functions has been carried out by Ogden and Roxburgh [35] and Dorfmann and Ogden [7], [8] for example, without relation to the microstructure of the material.…”

Section: Introductionmentioning

confidence: 99%

Effective wave propagation in a prestressed nonlinear elastic composite bar

Parnell

2007

IMA Journal of Applied Mathematics

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The problem of determining the effective incremental response of nonlinearly elastic composite materials given some initial pre-stress, is of interest in numerous application areas. In particular the case when small amplitude elastic waves pass through a pre-stressed inhomogeneous structure is of great importance. Of specific interest is how the initial finite deformation affects the microstructure and thus the subsequent response of the structure. Modelling this effect is in general extremely difficult.In this article we consider the simplest problem of this type where the material is a one dimensional composite bar consisting of two distinct phases, periodically distributed. Neglecting lateral contractions, the initial deformation is thus piecewise homogeneous and we can therefore determine the incremental behaviour semi-analytically, given the constitutive behaviour (strain energy function) of the phases in question. We apply asymptotic homogenization theory in the deformed configuration in order to find the effective response of the deformed material in the low frequency limit where the wavelength of the propagating waves is much longer than the characteristic lengthscale of the microstructure. We close by considering the arbitrary frequency case and illustrate how the initial deformation affects the location of stop and pass bands of the material. Work is underway to confirm these results experimentally.

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“…6). This incremental procedure was adopted to investigate the presence of the Mullins effect in the material following previous guidelines and usage by Dorfmann & Ogden (2004) and Diani et al (2009). The Poisson's ratio was an important parameter to measure as only compressive loading tests were conducted; this ratio is the sole determinant of volumetric change in the material and therefore the behaviour in other mechanical loading directions.…”

Section: Low Strain Rate Testsmentioning

confidence: 99%

Development of novel synthetic muscle tissues for sports impact surrogates

Payne

Mitchell

Bibb

et al. 2015

Journal of the Mechanical Behavior of Biomedical Materials

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Impact injuries are commonplace in sport and often lead to performance detriment and debilitation. Personal Protective Equipment (PPE) is prescribed as a mandatory requirement in most sports where these impacts are likely to occur, though the methods of governance and evaluation criteria often do not accurately represent sports specific injury scenarios. One of the key shortcomings of such safety test standards is the human surrogate to which the PPE is affixed; this typically embodies unrepresentative geometries, masses, stiffness and levels of constraint when compared to humans.A key aspect of any human surrogate element is the simulant material used. Most previous sports specific surrogates tend to use off-the-shelf silicone blends to represent all the soft tissue structures within the human limb segment or organ; this approach potentially neglects important human response phenomena caused by the different tissue structures.This study presents an investigation into the use of bespoke additive cure Polydimethysiloxane (PDMS) silicone blends to match the reported mechanical properties of human relaxed and contracted skeletal muscle tissues. The silicone simulants have been tested in uniaxial compression through a range of strain rates and fit with a range of constitutive hyperelastic models (Mooney Rivlin, Ogden and Neo Hookean) and a viscoelastic Prony series.

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A constitutive model for the Mullins effect with permanent set in particle-reinforced rubber

Cited by 387 publications

References 53 publications

Multiscale modelling of particle debonding in reinforced elastomers subjected to finite deformations

Multiscale modelling of particle debonding in reinforced elastomers subjected to finite deformations

Effective wave propagation in a prestressed nonlinear elastic composite bar

Development of novel synthetic muscle tissues for sports impact surrogates

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