Simulation by periodic homogenization of the behavior of a polycrystalline material in large elastoplastic transformations

We present an approach based on periodic homogenization theory, in order to numerically study the anisotropy due to large elastic-plastic strains. This work presents a two levels finite element method to calculate an elastic-plastic polycristalline structure. The first level, at the scale of the structure, is classical, except that the constitutive material behavior in each integration point is numerically obtained by a second level of finite element calculations on a representative polycristalline basic cell made of several FCC single cristal with different orientations. A parallel numerical approach is also used

On cyclic steady states and elastic shakedown in diffusion-induced plasticity

International audienceThis chapter is devoted to media in which plasticity and diffusion are coupled, such as electrode materials in lithium ion batteries. We present some recent results on the large time behavior of such media when they are submitted to cyclic chemo-mechanical loadings. Under suitable technical assumptions, we notably show that there is convergence towards a cyclic steady state in which the stress, the plastic strain rate, the chemical potential and the concentration of guest atoms are all periodic in time (with the same period as the applied loading). A special case of interest is that of elastic shakedown, which corresponds to the situation where the medium behaves elastically in the large time limit. We present general theorem that allow one to construct both lower and upper bounds of the set of loadings for which elastic shakedown occurs, in the spirit of Melan and Koiter theorems in classical plasticity. An illustrative example-for which all the relevant calculations can be done in closed-form-is presented