Arbitrary multiphase hybrid stress finite element method for composite materials

In this paper, A new Arbitrary Multiphase Hybrid Stress Finite Element (AMHSFE) and its element formulation are established, for which the number of material phases (ph >= 2) and the number of element sides are arbitrary. A new modified complementary energy functional considering plasticity is proposed, into which the continuity of displacements and the continuity of tractions on the phase interface of the multiphase material are introduced by Lagrange multiplier method, based on the newly established AMHSFE model and the theory of hybrid stress element method. A new stress function that fully accounts for the reciprocal stress functions at multiple interfaces is constructed. By comparing the results with Finite Element Method (FEM) models, the accuracy and validity of the new AMHSFE considering plasticity is verified. The effect of different terms of the three types of stress functions and the number of integration points on the accuracy of the calculations is discussed. At the end of the article, the accuracy of AMHSFE is further demonstrated by a high volume fraction Particulate Reinforced Composites (PRCs) example, from which it is possible to foresee the possibilities and advantages of AMHSFE for the numerical simulation of tremendous amounts of particle phases of real multiphase materials.