The continuum sensitivity method for the computational design of three-dimensional deformation processes

Although simulation of metal forming processes using modern computational tools has reached an advanced stage, there is still a great need to develop computational techniques for process design. In this work, the continuum sensitivity method (CSM) is extended to three-dimensions (3D) to accurately compute sensitivity fields and in particular changes in the design objectives as a result of infinitesimal perturbations to the design parameters. CSM involves differentiation of the governing field equations of the direct problem (constitutive, contact and kinematic problems) with respect to the design variables and development of the weak forms for the corresponding sensitivity equations. The present 3D developments include a novel regularized approach to the contact sensitivity problem that addresses the non-differentiability of the contact constraints. The computed sensitivity fields are used in a gradient-based optimization framework for process design (optimization) in 3D metal forming applications. A typical design problem at each optimization iteration involves simultaneous solution of a direct problem and a number of sensitivity problems corresponding to each of the design variables. Relevant 3D design problems related to preform and die design for desired properties in the final product are considered highlighting the features and potential of the metal forming design simulator developed.