Abstract
Computationally oriented formulation of the isothermal, rate-independent theory of non-associative elasto-plasticity is extended in this paper to describe coupled thermo-elastic-plastic and thermo-elastic-visco-plastic behaviour of materials. This is done by additionally considering thermal strains, assumming all material properties to be temperature dependent and accounting for the mechanical coupling terms in the non-stationary heat conduction equation. The finite deformation effects are included in the analysis. The theory is employed for the analysis of thermo-mechanical response of ductile metals with damage effects modelled by a generalization of the so-called Gurson approach. This constitutive model is known to generate equations typical of non-associative plasticity and hence it can be consistently incorporated into the present more general considerations. The finite element assessment of combined thermal and damage effects on the axisymmetric necking process illustrates the paper. Numerical aspects such as a ‘tangent’ stiffness for rate-dependent thermo-plasticity and the algorithmic (or consistent) tangent stiffness matrix for non-associative plasticity are discussed as well.
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