Tangent operators and design sensitivity formulations for transient nonlinear coupled problems with applications to elasto-plasticity

Tangent operators and design sensitivities are derived for transient nonlinear coupled problems. The solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response function are formulated via both the direct differentiation and adjoint methods. The derived formulations are suitable for finite element implementations. Analyses of systems with materials that exhibit history dependent response, may be obtained directly by applying the analyses of transient nonlinear coupled systems. Rate-independent elasto-plasticity is investigated as a case study and a problem with an analytical solution is analyzed for demonstration purposes