A fully equilibrated microsphere model with damage for rubberlike materials

Abstract : A non-affine microsphere model for rubberlike materials is proposed, based on a local minimization of the network free energy under a maximal advance path constraint. It accounts for any chain weight distribution and for damage such as Mullins softening observed in filled rubber materials. The non-affine equal-force model is compared to the common affine model and a hybrid equal-force model from the literature, when considering the isotropic hyperelastic behavior without damage of rubber materials presenting chains of various lengths. The non-affine model shows an improved deformability compared to the affine model limited by the maximal extension of the shorter chains and a significantly softer behavior. Possible damage is introduced by increasing the chain lengths according to the submitted maximal chain traction force. Each chain are impacted independently resulting in a directional softening that introduces the evolution of the stress-free configuration that needs to be assessed over the loadings. The model was successfully tested on the cyclic uniaxial tension stretch-stress responses of carbon-black filled styrene butadiene rubbers that were well fitted with three parameters only.
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J. Diani, Patrick Le Tallec. A fully equilibrated microsphere model with damage for rubberlike materials. Journal of the Mechanics and Physics of Solids, Elsevier, 2019, 124, pp.702-713. ⟨10.1016/j.jmps.2018.11.021⟩. ⟨hal-01986861⟩

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