A Homogenization Theory and Its Finite Element Discretization for Nonlocal Crystal Plasticity
Dai OKUMURA, Youichi HIGASHI and Nobutada OHNO
Abstract:In this study, we develop a homogenization theory and its finite element discretization based on the nonlocal crystal plasticity theory of Gurtin (J. Mech. Phys. Solids 48 (2000); J. Mech. Phys. Solids 50 (2002)), which includes slip gradients and additional slip boundary conditions with respect to microforce balances for each slip system. Although it is difficult to determine slip boundary conditions, the development of the homogenization theory for the nonlocal crystal plasticity makes it possible to obtain the unified treatment of slip boundary conditions on the periodic boundary in periodic materials. Furthermore, by applying a tangent modulus method to the finite element discretization of rate-dependent small deformation, a strong coupling boundary value problem is derived from homogenization equations which consist of the stress balance, the microforce balances and the macroscopic relation. Finally, the effectiveness of the proposed theory and method is confirmed through finite element analyses of a double slip single crystal model with periodic obstacles. Key Words:Homogenization theory, Nonlocal crystal plasticity, Finite element discretization, Strain gradient, Size effect