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Thermo-plastic constitutive relations and a variational solution technique using finite elements Charlwood, Robin Gurney

Abstract

This study is concerned with a thermo-elasto-plastic continuum in which the thermodynamic coupling between material deformations, heat generation and flow are included. The elasto-plastic behavior is represented by a linear "rate-type" theory and restricted to infinitesimal deformations. The heat flow equations are posed in incremental form for the linear theory of heat conduction. The theory is such that the conservation laws of thermodynamics are satisfied. A displacement formulation is used and the field equations are shown to be linear operator equations. The operators are tested for symmetry and positive-definiteness in order to test their suitability for solution by a variational method. It is shown that the special case of thermo-elasticity may be solved by minimisation of a functional and that convergence of approximate solutions may be predicted. In the general case of thermo-elasto-plasticity, the operator is shown to be unsymmetric. Therefore an iterative functional is introduced in order to obtain a solution by a variational method. Approximate solutions to some illustrative problems are found using a finite-element-formulation, and it is shown that the results are consistent with expected physical behavior.

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