A continuum sensitivity method for finite thermo-inelastic deformations with applications to the design of hot forming processes

A computational framework is presented to evaluate the shape as well as non-shape (parameter) sensitivity of finite thermo-inelastic deformations using the continuum sensitivity method (CSM). Weak sensitivity equations are developed for the large thermo-mechanical deformation of hyperelastic thermoviscoplastic materials that are consistent with the kinematic, constitutive, contact and thermal analyses used in the solution of the direct deformation problem. The sensitivities are defined in a rigorous sense and the sensitivity analysis is performed in an infinite-dimensional continuum framework. The effects of perturbation in the preform, die surface, or other process parameters are carefully considered in the CSM development for the computation of the die temperature sensitivity fields. The direct deformation and sensitivity deformation problems are solved using the finite element method. The results of the continuum sensitivity analysis are validated extensively by a comparison with those obtained by finite difference approximations (i.e. using the solution of a deformation problem with perturbed design variables). The effectiveness of the method is demonstrated with a number of applications in the design optimization of metal forming processes. Copyright (C) 2002 John Wiley Sons, Ltd.