The theory of elastic-plastic deformation at finite strain with induced anisotropy modeled as combined isotropic-kinematic hardening
A theory of elastic-plastic deformation with strain induced anisotropy based on finite-deformation-valid continuum mechanics is presented. On the foundation of nonlinear kinematics which provides strict uncoupling of elastic and plastic deformation rate terms according to their physical origins, it introduces a basis for the modified plastic rate of deformation \(\hat D^ p\) suggested by \textit{G. J. Creus, A. G. Groehs} and \textit{E. T. Onat} in a Yale Technical Report entitled ''Constitutive equations for finite deformations of elastic-plastic solids'' (1984) in which this variable was suggested in order to give an elegant mathematical structure to the theory. \(\hat D^ p\) is shown to express the resultant rate of deformation in the current configuration of the elastically-plastically deforming material which is envisaged to be generated by the pure plastic flow and the anisotropy-caused spin, both considered to be occurring in the unstressed state. From this basis an elastic-plastic theory is developed in the case where the strain-induced anisotropy takes the form of combined isotropic- kinematic hardening, although the concepts involved also apply to more general anisotropic characteristics. A general evolution equation is adopted for the back stress \(\alpha\), the kinematic-hardening shift of the yield surface, its rate of growth being expressed as a general form- invariant function of \(\alpha\) and \(\hat D^ p\), including a general term expressing the influence of the spin of \(\alpha\) because it is embedded in the deforming material. By providing an expression for the total strain rate as the sum of the strain rate \(\hat D^ p\) and an elastic term, linear in the Jaumann derivative of Kirchhoff stress, it is shown that \((\hat D^ pdt)\) is the residual strain increment following a loading/unloading cycle imposed by a stress increment. By considering materials which obey the normality rule it is also shown that the instantaneous elastic-plastic moduli have the symmetries necessary for generating a rate potential function and hence can be incorporated into Hill's variational principle valid for solving problems involving finite deformation and convenient for finite-element exploitation.
kinematic-hardening shift of the yield surface
scientific article; zbMATH DE number 4001601