Finite element response sensitivity analysis of multi-yield-surface J2 plasticity model by direct differentiation method

Finite element (FE) response sensitivity analysis is an essential tool for gradient-based optimization methods used in various sub-fields of civil engineering such as structural optimization, reliability analysis, system identification, and finite element model updating. Furthermore, stand-alone sensitivity analysis is invaluable for gaining insight into the effects and relative importance of various system and loading parameters on system response. The direct differentiation method (DDM) is a general, accurate and efficient method to compute FE response sensitivities to FE model parameters. In this paper, the DDM-based response sensitivity analysis methodology is applied to a pressure independent multi-yield-surface J2 plasticity material model, which has been used extensively to simulate the nonlinear undrained shear behavior of cohesive soils subjected to static and dynamic loading conditions. The complete derivation of the DDM-based response sensitivity algorithm is presented. This algorithm is implemented in a general-purpose nonlinear finite element analysis program. The work presented in this paper extends significantly the framework of DDM-based response sensitivity analysis, since it enables numerous applications involving the use of the multi-yield-surface J2 plasticity material model. The new algorithm and its software implementation are validated through two application examples, in which DDM-based response sensitivities are compared with their counterparts obtained using forward finite difference (FFD) analysis. The normalized response sensitivity analysis results are then used to measure the relative importance of the soil constitutive parameters on the system response.