Shear, compressive and dilatational response of rubberlike solids subject to cavitation damage

Dorfmann, Luis; Fuller, K. N. G.; Ogden, Ray W.

doi:10.1016/s0020-7683(02)00008-2

Cited by 54 publications

(43 citation statements)

References 25 publications

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“…This change in stiffness is associated with a reduction in the bulk modulus of the material. The same conclusion was found in a recent publication [3], where it was shown that dilatational softening does not effect the shear and compression response of the material. Fig.…”

Section: Resultssupporting

confidence: 89%

The pseudo‐elastic response of rubberlike solids

Dorfmann¹

2004

Proc Appl Math and Mech

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In this paper we focus on the mechanical behaviour of filled natural rubber. Filled elastomers under cyclic loading show noticeable differences between the mechanical response under loading and unloading during the first cycles in oscillation tests. We examine the change in material response associated with the Mullins effect and with cavitation, the latter arising from hydrostatic tensile stresses of sufficient magnitude. Then, we focus on constitutive equations using the theory of pseudoelasticity. Specifically, the strain-energy function depends on a scalar parameter, which provides a means for modifying the form, thereby reflecting stress softening observed during unloading. The dissipation of energy is also accounted for by the use of a dissipation function, which evolves with the deformation history.

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Section: Resultssupporting

confidence: 89%

The pseudo‐elastic response of rubberlike solids

Dorfmann¹

2004

Proc Appl Math and Mech

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“…These isotropic properties can be predicted in a similar fashion to that of bulk compression discussed in Section 6.1. Since cavitation damage is isotropic, the use of Dorfmann et al [5] isotropic model to predict the stress-softening behaviour due to cavitation seems appropriate and their results compare well with their hydrostatic tension experimental data. However, their experiment consists of a sequence of shear, bulk-compression and hydrostatic-tension deformations.…”

Section: Shear Bulk Compression and Hydrostatic Tension: Comparison mentioning

confidence: 81%

“…In this section we demonstrate an application of our theory to stress softening due to hydrostatic cavitation damage. An experiment by Dorfmann et al [5] suggests that the tensile bulk modulus is affected by cavitation damage due to hydrostatic tension and the hydrostatic stress is softened significantly during unloading. However, their experiment also suggests that bulk compression and shear moduli are not significantly affected by cavitation damage.…”

Section: Shear Bulk Compression and Hydrostatic Tension: Comparison mentioning

confidence: 99%

Anisotropic stress-softening model for compressible solids

Shariff

2009

Z. Angew. Math. Phys.

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A general constitutive theory for anisotropic stress softening in compressible solids is presented. The constitutive equation describes anisotropic strain induced behaviour of an initially "isotropic" virgin material. Parameters which characterise damage are proposed together with a concept of damage function. In order to develop an anisotropic stress-softening theory for compressible materials in close parallel to a recent incompressible anisotropic theory, the right stretch tensor is decomposed into its isochoric and dilatational parts. The 'free' energy is expressed as a function of the dilatation, modified principal stretches, a volume change parameter and invariants of the dyadic products of the principal directions of the right stretch tensor and two structural tensors. A class of free energy functions is discussed and a special form of this class which satisfies the Clausius-Duhem inequality is proposed. Results of the theory applied to uniaxial tension, bulk compression and simple shear deformations are given. A sequence of deformations involving shear, hydrostatic-compression and hydrostatic-tension deformations is also investigated. In the case of hydrostatic-tension deformation, the stress softening is due to cavitation damage. The theoretical results obtained are consistent with expected behaviour and compare well with experimental data. (2000). 74R20, 74D10, 74E10, 74L99. Mathematics Subject Classification

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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%

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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Shear, compressive and dilatational response of rubberlike solids subject to cavitation damage

Cited by 54 publications

References 25 publications

The pseudo‐elastic response of rubberlike solids

The pseudo‐elastic response of rubberlike solids

Anisotropic stress-softening model for compressible solids

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

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