Homogenization of elastoplastic composites with generalized periodicity in the microstructure

In this paper, a consistent theory of homogenization for complex heterogeneous elastoplastic structures with generalized periodicity is proposed. The structures under consideration are not necessarily periodic, but their properties (geometry and material) exhibit periodicity with respect to non-linear periodicity functions. The proposed theory is based on an adequate definition of the admissible deformation fields and the corresponding functional setting, and results from the generalization of the two-scale convergence theory. Moreover, the discrete variational formulation is presented, for both the global and local problems. Additionally, the implicit formulation of the homogenization problem is proposed for elastic-image-plastic constituents with linear hardening in the context of infinitesimal elastoplasticity, including the numerical scheme for homogenization and the derivation of the consistent elastoplastic tangent modulus. Finally, the computational algorithm for the proposed theory is deployed, consisting of four interacting problems, the macroscale, the microscale, the iterative plastic scheme and the effective tangent modulus problem. The theory and the numerical and computational scheme are supplemented by two examples, one of a wavy multilayered structure and one of a multilayered tube.