Sur les solides hyperélastiques à compressibilité induite par l'endommagement

Andrieux, Florence; Saanouni, Khémaïs; Sidoroff, F.

doi:10.1016/s1251-8069(99)80035-9

Cited by 6 publications

(7 citation statements)

References 5 publications

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“…It introduces fairly complex large strain constitutive equations coupled with damage able to model Mullins effect. Most recent models for rubber depend on the maximum stretch history (Ogden and roxburgh, 1999;Miehe, 1995;Andrieux et al, 1997). Simo's model was improved by use of microscopic considerations (Godvindjee and Simo, 1991).…”

Section: Introductionmentioning

confidence: 99%

Mullins effect and cyclic stress softening of filled elastomers by internal sliding and friction thermodynamics model

Cantournet

Desmorat

Besson

2009

International Journal of Solids and Structures

213

126

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International audienceElastomers are characterized by their ability to undergo large elastic deformation. Nevertheless, their behavior exhibits stress softening, hysteresis and cyclic softening. The first phenomenon, known as Mullins effect, is commonly assumed to be either the result of an evolution in the hard and soft domain microstructure whereby the effective volume fraction of the soft domain increases with stretch or the result of irreversible damage in the material or combination of both. Hysteresis and cyclic stress softening are often considered as the result of the effect of stress relaxation. Based on the physical structure of filled elastomers, the present study shows that the Mullins effect, hysteresis and cyclic softening can be modeled by dissipative friction phenomena due to internal sliding of the macromolecular chains and to sliding of the connecting chains on the reinforcing filler particles. This implies that the three effects are in fact related to one single deformation process. The proposed analysis allows to identify the state variables and to build a thermodynamic potential which accounts for the nonlinearity of the material behavior and for a time independent hysteresis. The constitutive model is 3D. Written in a rate form it applies to complex loadings: monotonic, cyclic, random fatigue, etc. Filled elastomers hysteresis loops and cyclic softening are represented with no need to introduce neither damage nor viscosity. The model was implemented in a Finite Element software to simulate a metal/elastomer lap joint. Good agreement with experiment was achieved

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Section: Introductionmentioning

confidence: 99%

Mullins effect and cyclic stress softening of filled elastomers by internal sliding and friction thermodynamics model

Cantournet

Desmorat

Besson

2009

International Journal of Solids and Structures

213

126

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“…However, for large deformations the predictions diverge. [82][83][84][85][86] These models can also be extended to cavitation by adapting the rate equation for the damage variable. Finally, note that for large deformations in crystallizable rubbers, the approaches of Ogden 72 75 Gent and Wang, 76 and Legorju-Jago and Bathias, 77 were carried out to highlight the sudden initiation and growth of cavities in bulk material.…”

Section: B Modeling the Reversible Change In Volume Under Multiaxialmentioning

confidence: 99%

A Review of Volume Changes in Rubbers: The Effect of Stretching

Cam

2010

Rubber Chemistry and Technology

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“…For modelling, on the one hand the cavitation phenomenon under hydrostatic loading conditions is studied considering the stability conditions for the sudden growth of microscopic cavities in the incompressible bulk (see Ball (1982), Horgan and Abeyaratne (1986) for example). On the other hand, several phenomenological approaches have been proposed to predict the growth of pre-existing cavities; the corresponding models incorporate damage variables into compressible hyperelastic approaches (see Boyce and Arruda (2000) for a short review) to quantify the irreversible change of porosity (Andrieux et al 1997;Dorfmann et al 2002;Layouni et al 2003;Li et al 2007). These models can also be extended to cavitation by adapting the rate equation of the damage variable (Dorfmann 2003).…”

Section: Introductionmentioning

confidence: 99%

“…In the present paper, similarly to Andrieux et al (1997), we propose a simple theoretical framework to model the compressibility induced by damage in hyperelastic materials. Our approach is phenomenological and is restricted to small values of porosity, such that the growing cavities do not interfere.…”

Section: Introductionmentioning

confidence: 99%

“…These models can also be extended to cavitation by adapting the rate equation of the damage variable (Dorfmann 2003). Nevertheless, they are limited to small values of the porosity.In the present paper, similarly to Andrieux et al (1997), we propose a simple theoretical framework to model the compressibility induced by damage in hyperelastic materials. Our approach is phenomenological and is restricted to small values of porosity, such that the growing cavities do not interfere.…”

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confidence: 99%

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The effect of pre-stressing on the equi-biaxial fatigue life of EPDM

2009

Constitutive Models for Rubber VI

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The present paper presents a simple framework to model continuous volumetric damage in elastomers. The formulation predicts phenomenologically the growth of microscopic cavities, and can be applied to both static and fatigue loading conditions. This first version of the approach cannot handle cavitation and is limited to small values of porosities. The derivation is based on the use of a simple scalar damage parameter, the irreversible volume change, and takes naturally into account the change in stiffness through the explicit dependence of the material parameters on the damage variable. The thermodynamic force which drives the volume change contains the hydrostatic stress and also a contribution due to stiffness evolution. As a first application, a damage compressible neo-Hookean constitutive equation is derived and a simple example is studied. INTRODUCTIONRubber-like materials are usually considered as incompressible. However, under multiaxial or fatigue loading conditions, cavitation and cavities growth take place, and lead to damage and finally to fracture (Farris 1968;Le Cam et al. 2004;Le Gorju 2007). Special experiments can be carried out to exhibit this behaviour as proposed by Thomas (1958), Gent andWang (1991) or Legorju-Jago and Bathias (2002). For modelling, on the one hand the cavitation phenomenon under hydrostatic loading conditions is studied considering the stability conditions for the sudden growth of microscopic cavities in the incompressible bulk (see Ball (1982), Horgan and Abeyaratne (1986) for example). On the other hand, several phenomenological approaches have been proposed to predict the growth of pre-existing cavities; the corresponding models incorporate damage variables into compressible hyperelastic approaches (see Boyce and Arruda (2000) for a short review) to quantify the irreversible change of porosity (Andrieux et al. 1997;Dorfmann et al. 2002;Layouni et al. 2003;Li et al. 2007). These models can also be extended to cavitation by adapting the rate equation of the damage variable (Dorfmann 2003). Nevertheless, they are limited to small values of the porosity.In the present paper, similarly to Andrieux et al. (1997), we propose a simple theoretical framework to model the compressibility induced by damage in hyperelastic materials. Our approach is phenomenological and is restricted to small values of porosity, such that the growing cavities do not interfere. The scalar damage variable is the irreversible volume change and its influence on the stiffness of the material is taken into account through the material parameters. The rate equation chosen here is not adapted to sudden volume change (cavitation) but only to continuous volume change (damage by continuous growth of cavities).The derivation of the model is described in the next section, the emphasize being laid on the determination of the thermodynamic force which drives the volume change. Then, a very simple constitutive equation which generalizes the compressible neo-Hookean model is considered to illustrate the rel...

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Sur les solides hyperélastiques à compressibilité induite par l'endommagement

Cited by 6 publications

References 5 publications

Mullins effect and cyclic stress softening of filled elastomers by internal sliding and friction thermodynamics model

Mullins effect and cyclic stress softening of filled elastomers by internal sliding and friction thermodynamics model

A Review of Volume Changes in Rubbers: The Effect of Stretching

The effect of pre-stressing on the equi-biaxial fatigue life of EPDM

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