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 nite 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 de ned in a rigorous sense and the sensitivity analysis is performed in an in nite-dimensional continuum framework. The e ects 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 elds. The direct deformation and sensitivity deformation problems are solved using the nite element method. The results of the continuum sensitivity analysis are validated extensively by a comparison with those obtained by nite di erence approximations (i.e. using the solution of a deformation problem with perturbed design variables). The e ectiveness of the method is demonstrated with a number of applications in the design optimization of metal forming processes