Sensitivity analysis for failure and damage in dynamically loaded tensile bars

A computational procedure is presented for evaluating the sensitivity coefficients of porous viscoplastic solids under dynamic loading conditions. The effects of finite strains, material strain and strain-rate hardening, and the thermal softening due to adiabatic heating are incorporated into the formulation. A critical void volume fraction criterion is used to identify the initiation of failure. The equations of motion emanating from a finite element semi-discretization are integrated using an explicit central difference scheme. First- and second-order sensitivity coefficients of the response quantities (derivatives with respect to various material parameters) are evaluated using a direct differentiation approach in conjunction with an automatic differentiation software facility. Numerical results are presented for tensile specimens subjected to impact loading. Both axisymmetric and plane strain states are considered. The first- and second-order sensitivity coefficients are generated by evaluating the derivatives of the response quantities with respect to various macroscopic and microscopic material parameters. Time histories of the response and sensitivity coefficients, and their spatial distributions at selected times are presented.