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Patrick Le Tallec, "Polymer modelling: From macroscopic hyperelasticity to strain induced crystallisation"
The purpose of the talk is to review the numerical modelling of the large deformation of structures made of soft materials and to outline present directions of research. The original models in isotropic finite elasticity consider the simplest case where stresses derive from an isotropic energy density function of the invariants of Cauchy Green strain tensor or of its eigenvalues. This has been extended to anisotropic hyperelasticity with the help of additional invariants and to more general constitutive behavior such as plasticity, viscoelastic or damage. In most cases, such models are based on a multiplicative split of the deformation gradient, and evolution laws governing the additional internal variables are obtained by postulating a specific form of dissipation within the material [5], [8]. From a numerical perspective, these internal variables can be eliminated from the tangent problem, reducing the general case to a succession of hyperelastic problems. This phenomenological approach is now used in most models, with different levels of complexity to take into account clusterisation, ageing, crystallization and so on.
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