A Nonlocal Model of Materials with Periodic Microstructure Based on Asymptotic Homogenization Method

The asymptotic homogenization method within the framework of the updated Lagrangian formulation is employed to derive a nonlocal constitutive equation for finitely deformed rate-independent materials with a periodic microstructure. Higher-order asymptotic terms naturally introduce strain gradient terms into constitutive equations for macroscopically homogeneous materials. Macroscopic properties, which are the ensemble average of their counterparts over a microscopic unit cell, are discussed. The variational principle of macroscopically homogeneous materials is then established and the complete boundary value problem is formulated.