Abstract
Theoretical issues related to the covariant structure of non-isothermal generalized plasticity in large deformations are studied in depth. For this purpose, the tensor analysis on manifolds is utilized and the manifold structure of both the ambient and the state spaces is postulated. Building on this, a covariant structure of the theory is constructed within a strain–space formulation. Thermomechanical loading criteria in both Lagrangian and Eulerian descriptions are derived in a deformation–temperature space. Based on geometrical concepts, classical non-isothermal plasticity is derived as a special case. The invariance properties of the local form of the balance of energy equation are systematically engaged for the derivation of the thermomechanical state equations. It is specifically shown that the local form of the covariant balance of energy equation does not yield the Doyle–Ericksen formula and the standard entropy–temperature constitutive relation, unless a further assumption is made. A derivation of the spatial form of the Duhamel–Neumann hypothesis on a decomposition of the rate of deformation tensor into its mechanical and thermal parts is performed as well. The covariance concept is specialized further by the construction of a material model within the context of classical metal plasticity. The proposed model is tested numerically for the solution of two problems of non-isothermal large-scale plastic flow.
Published Version
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