Design sensitivity analysis in large deformation elasto-plastic and elasto-viscoplastic problems

Implicit time integration algorithm derived by Simo for his large-deformation elasto-plastic constitutive model is generalized, for the case of isotropy and associative flow rule, towards viscoplastic material behaviour and consistently differentiated with respect to its input parameters. Combining it with the general formulation of design sensitivity analysis (DSA) for non-linear finite element transient equilibrium problem, we come at a numerically efficient, closed-form finite element formulation of DSA for large deformation elasto-plastic and elasto-viscoplastic problems, with various types of design variables (material constants, shape parameters). The paper handles several specific issues, like the use of a non-algorithmic coefficient matrix or sensitivity discontinuities at points of instantaneous structural stiffness change. Computational examples demonstrate abilities of the formulation and quality of results