An Analysis of Large Strain Viscoplasticity Problems Including the Effects of Induced Material Anisotropy

This paper examines the modeling of large shearing of solids that exhibit induced anisotropy during inelastic deformation. The “traditional” approach uses integration of material rates of certain tensors which are obtained from Jaumann rates of these tensors delivered by a material constitutive model. This leads to erroneous results (spurious oscillations) in a simple shear example. Several previous authors have suggested resolutions to this dilemma based on modification of the constitutive model — usually based upon changing the interpretation of the tensor rates delivered by a constitutive model. This paper draws attention to another aspect of the modeling process — that of obtaining the components of tensors such as the Cauchy stress in a global, space-fixed basis, from the objective rates of these tensors as delivered by the material constitutive model. In essence, it is suggested here that the elastic rotation rather than the spin should be used to achieve the above objective. The rotation idea is first discussed in the context of a simple shear example. This philosophy is then incorporated in a general purpose two-dimensional boundary element method (BEM) formulation and computer program. Numerical results for the simple shear problem, using the rotation idea, are obtained both by direct integration and from the general BEM computer program.