A homogenization result in finite plasticity

Abstract

We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the composite has a periodic microscopic structure, we establish the $\Gamma$-convergence of the energies in the limiting of vanishing periodicity. The constraint that plastic deformations belong to $\mathsf{SL}(3)$ poses the biggest hurdle to the analysis, and we address it by regarding $\mathsf{SL}(3)$ as a Finsler manifold.

22 pages

References in corpus (3)

• Kinematic description of crystal plasticity in the finite kinematic framework: a micromechanical understanding of F=FeFp
• Derivation of $\mathbf{F}={\mathbf{F}}^e{\mathbf{F}}^p$ as the continuum limit of crystalline slip
• Asymptotic rigidity of layered structures and its application in homogenization theory

Cited by in corpus (2)

• Homogenization of high-contrast media in finite-strain elastoplasticity
• On the existence of extensions for manifold-valued Sobolev maps on perforated domains