Efficient adjoint sensitivity analysis of isotropic hardening elastoplasticity via load steps reduction approximation

Sensitivity analysis plays a key role in gradient-based shape optimization. In this paper, a highly efficient procedure for design sensitivity analysis of elastoplastic material with isotropic hardening rule is presented. Here, an adjoint variable method is employed, where the adjoint sensitivity formulation is derived from the discrete master equation, yield condition, and consistency condition. Due to history dependence of plasticity, adjoint variables must be solved via a stepwise backward procedure. Therefore, the computational cost increases in proportion to the number of load steps. To address this cost and improve efficiency, condensation rules are proposed to reduce the number of load steps in the sensitivity analysis based on properties of adjoint variables. The properties of adjoint variables and proposed condensation rules are all theoretically proven in this paper. The accuracy and efficiency of the proposed techniques are demonstrated using bar truss structures and solid structures in various complex load cases. The results show that the techniques significantly reduce the number of load steps required in the sensitivity analysis while keeping satisfying accuracy.