Large viscoplastic deformations of shells. Theory and finite element formulation

Abstract

The paper is concerned with large viscoplastic deformations of shells when the constitutive model is based on the concept of uni®ed evolution equations. Speci®cally the model due to Bodner and Partom is modi®ed so as to ®t in the frame of multiplicative viscoplasticity. Although the decomposition of the deformation gradient in elastic and inelastic parts is employed, no use is made of the concept of the intermediate con®guration. A logarithmic elastic strain measure is used. An algorithm for the evaluation of the exponential map for nonsymmetric arguments as well as a closed form of the tangent operator are given. On the side of the shell theory itself, the shell model is chosen so as to allow for the application of a three-dimensional constitutive law. The shell theory, accordingly, allows for thickness change and is characterized by seven parameters. The constitutive law is evaluated pointwise over the shell thickness to allow for general cyclic loading. An enhanced strain ®nite element method is given and various examples of large shell deformations including loading-unloading cycles are presented.

An anisotropic fibre-matrix material model at finite elastic-plastic strains

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