Finite Strain Viscoplasticity Based on Unified Constitutive Equations and Decomposition of Logarithmic Strain: Applications to Shells

The paper is concerned with a formulation of large strain viscoplasticity based on the concept of unified constitutive models as well as on an additive decomposition of a logarithmic strain tensor. The constitutive model due to Bodner and Partom is modified as to fit within the theoretical framework presented. A basic feature of the formulation is the fact that the additive structure of the infinitesimal theory is preserved in the finite strain range. Based on an essential result, a closed form of the tangent operator is derived which is very efficient from the numerical point of view. As an application, finite shell deformations are considered. The shell theory used allows for the application of three-dimensional constitutive laws and is geometrically exact. The computations are based on an enhanced strain functional where the right Cauchy-Green tensor is enhanced. Two examples of large shell deformations including loading-unloading cycles are presented.