Microscopic limit analysis of cohesive-frictional composites with non-associated plastic flow

Abstract

Incorporating homogenization theory into the classical kinematic theorem of limit analysis, a nonlinear microstructure approach is developed to directly solve the plastic limit status of a heterogeneous or composite material with cohesive-frictional constituents. The macroscopic strength domain of such heterogeneous or composite materials can be quantitatively calculated at the microscopic scale, which is obtained through a periodic Representative Volume Element (RVE). Pressure-dependence and non-associated plastic flow of cohesive-frictional materials are formulated into limit analysis via a general yield condition with a two-parameter plastic flow rule. Based on the mathematical programming technique and the finite element method, kinematic limit analysis of a cohesive-frictional composite is finally formulated as a nonlinear programming problem subject to only one equality constraint. A generalized direct iterative algorithm is then developed to solve the resulting nonlinear programming problem. The proposed approach is based on a purely kinematical velocity field without calculation of stress fields. And only one equality constraint is introduced into the nonlinear programming problem. So the computational cost is very modest. Both non-associated plastic flow and pressure-dependence are well modeled for cohesive-frictional materials. Meanwhile, their effects on the plastic limit status and the macroscopic strength domain of heterogeneous materials are quantitatively calculated at the microscopic scale. The developed method can serve as a powerful tool for microstructure design of cohesive-frictional heterogeneous or composite materials.