Existence result of an effective stress for an isotropic visco-plastic composite

We define and present some theoretical characterizations of associated constitutive equations for a visco-plastic deformation of a composite. Introducing of an adequate topological framework for some visco-plastic state parameters, when considered a nonlinear stress–strain relations of Prandtl–Reuss type, we obtain the existence and uniqueness results of a steady state for a composite reinforced with other inclusions. The time-dependent plastic strains of these Al based composites reinforced with SiC inclusions are then calculated as a function of inclusion volume concentration, effective stress and effective visco-plastic strain, following an dynamical yield function of power type. Viewed as a Drucker–Prager material, a selection criterion for visco-plastic strain rate, permit us a formulation as an isotropic hardening problem and their reduction to a sweeping process problem for an elastic component of the strain. In this paper a family of models for the composite deformation, defined by Halphen and Nguyen Quoc Son, enlarges the classical class of generalized standard materials, ant they are characterized by monotone-gradient flow function. These models improve the tensile process of Al based composite, in order to allow new practical solutions in civil engineering.