A Constitutive Law Modeling the Mixed Hardening Behavior of Particle-Reinforced Composites

Abstract

A homogenized elasto-plastic constitutive law (including both constitutive equations and inversed constitutive equations) is proposed in an incremental form for the particle-reinforced composites based on the flow theory of plasticity and the asymptotic homogenization method. The constitutive law can be used to predict the mixed hardening behavior of particle-reinforced composites under arbitrary loading conditions if the uniaxial tension test curve of matrix materials is known. It is found that the constitutive law of particle-reinforced composites is similar in form to the law of matrix materials. There is a simple proportional relationship between the yield stress, the plastic modulus, and the deviatoric back stress of particle-reinforced composites and the corresponding parameters of matrix materials, which is equal to the ratio of the shear modulus of composites to the shear modulus of matrix materials. The tangent modulus of particle-reinforced composites can be calculated using a simple arithmetic formula according to the tangent modulus of matrix materials. A numerical algorithm is suggested.