Dual finite element methods in homogenization for elastic–plastic fibrous composite material

The problem of homogenization for a periodic, elastic–perfectly plastic, fiber reinforced, composite material is considered. The overall mechanical behavior of the material is described using the anisotropic model of elastic–plastic body with kinematic hardening. The appropriate initial–boundary value problem, set for one repeatable cell of the composite, is solved in order to find the effective constitutive relations. The cell problem is solved using the finite element method formulated in two dual forms: in displacements and in stresses. Stress functions are used in the latter formulation.