ON THEORY AND NUMERICS OF LARGE VISCOPLASTIC DEFORMATION

A multiplicative theory and corresponding computations of finite elast ic-viscoplastic deformations based on unified constitutive equations a re presented. Basic features of theory are: (I) The inelastic part of the deformation gradient is understood as a material stretch-type tens or, no need arises for the notion of the intermediate configuration. ( 2) In the isotropic case, the use of an elastic logarithmic strain ten sor is shown to lead to the identification that the elastic strains ar e given by the quantity Cp-1C with C-p being an inelastic Cauchy-Green type tenser. (3) In spite of the fact that the logarithmic strain mea sure is used, closed forms of the tangent operator within an implicit time integration scheme are given circumventing very involved elaborat ions when the spectral decomposition is used. (4) Evolution equations of the Bodner and Partom type are employed. A general formalism is dev eloped for the application of the evolution laws of the unified type w ithin the theoretical framework. The formalism can be used to generali ze any unified evolution equations formulated for infinetismal strains to the range of finite strains. (5) For the axisymmetric case, in add ition to the displacement-based 4-node and 9-node finite elements, an enhanced strain 4-node element is presented. It is shown, anyhow, that in the highly nonlinear regime the enhanced strain formulation may ex hibit numerical instabilities. Different numerical examples of finite strain deformations are presented.