Abstract
The present article presents theoretical basis for modeling large deformations of shells using isoparametric finite element approximations. A physical model of an elastoplastic material is based on multiplicative decomposition of the deformation gradient into elastic and plastic components. The deformation process is described in curvilinear coordinates using Lagrange description. Constitutive equations and the law of plastic flow are obtained from thermodynamic equations for Almansi tensor and Kirchhoff tensor. The tensor equations are reduced to a scalar form which includes free energy gradients, gradients of the equation of ultimate state and a special tensor characterizing the plastic deformation level. An explicit and implicit integration schemes for the equation of plastic flow are discussed. The issues of applying the constructed relations to analyzing shells are tackled. Initially, the use of the stepped loading method (integration in time) is discussed, hence some relations for incrementing the basic vector and tensor values are presented. Key words: shells, large elastoplastic deformations, finite elements, isoparametric approximation, stepped loading method.  
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