Tangent operators and design sensitivity formulations for transient non‐linear coupled problems with applications to elastoplasticity

TLDR

Tangent operators and design sensitivities for transient nonlinear coupled problems are derived and shown to be suitable for finite element implementation. The study investigates rate‑independent elastoplasticity as a case study and analyzes an analytical problem to demonstrate the approach. The authors present a systematic solution process that constructs tangent operators and formulates sensitivities for a generalized response functional using both direct differentiation and adjoint methods, enabling analyses of history‑dependent materials within transient nonlinear coupled systems.

Abstract

Abstract Tangent operators and design sensitivities are derived for transient non‐linear coupled problems. The solution process and the formation of tangent operators are presented in a systematic manner and sensitivities for a generalized response functional 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 non‐linear coupled systems. Rate‐independent elastoplasticity is investigated as a case study and a problem with an analytical solution is analysed for demonstration purposes.