New General and Complementary Energy Theorems, Finite Strain, Rate-Sensitive Inelasticity, and Finite Elements: Some Computational Studies

摘要

General variational theorems for the rate problems of rate-dependent finite strain inelasticity, in terms of the appropriate rates of the first and second Piola-Kirchhoff stress tensors, the symmetrized Biot-Lure' stress tensor, and their conjugate measures of strain-rate are discussed. Certain new rate-complementary-energy principles, involving the rate of spin and the rate of the symmetrized Biot-Lure' stress tensor as variables, are stated for finite strain analysis of rate-sensitive materials, such as those exhibiting elasto-visco-plastic and creep behavior. Uniqueness and stability criteria for those inelastic solids, using the finite element counterparts of the new complementary energy rate principles, are discussed. Computational studies, using the complementary energy methods, discussed herein incude: (i) bifurcation necking and post-buckling analyses of initially perfect elasto-plastic bars and (ii) post-buckling and large-deformation analyses of thin elastic plates under inplane compression and transverse bending loads. (Author)