Integral-equation representations of flow elastoplasticity derived from rate-equation models

Abstract

Two integral-equation representations are presented in this paper, based on the exact integrations of the conventional rate-equation model of associative J2 flow elastoplasticity with combined-isotropic-kinematic hardening-softening. Among them the strain-controlled integral-equation representation has two new naturally defined material functions Y(Z) and U(Z) of the normalized active work Z, which plays the role of intrinsic time. One of the immediate benefits derivable from the new representations is, owing to the explicit unfolding of the highly nonlinear path-dependence between stress and strain without a detour to the evolutions of internal state variables, their adaptability for direct calculations without any iteration. Indeed, it is itself a constructive algorithm. It is shown that at a realistic level of precision, the strain-controlled integral-equation representation saves 99% or more of the CPU time compared with the widely used elastic predictor-radial return algorithm of the rate-equation representation.

Lorentz group on Minkowski spacetime for construction of the two basic principles of plasticity

“…As indicated within the square brackets [2] in Fig. 1, among the sixteen systems, there are four, four, sixteen, two, one system(s) violating the restrictions (a) , (b) , (b) , (ab) , (ab) , respectively.…”

“…"exp , has been de"ned with its evolution explored seriously (see, e.g., [1,2]). Fifth, X has been recognized as a new dimension in the augmented stress space of (X, X, 2 , XL, X) de"ned as…”

Internal symmetry in the constitutive model of perfect elastoplasticity

“…However, a numerical scheme based on the representation (28) in the Q-space su!ers from non-linearity. A numerical scheme based on the representation in the (Q, X)-space, being non-linear but essentially `lineara in the above sense, has been shown to be much more e$cient [8].…”

A coupled FE–EFG approach for modelling crack growth in ductile materials

“…An analytical solution for the von‐Mises model with linear kinematic hardening was obtained by Yoder and Whirley . The von‐Mises criterion in conjunction with mixed hardening was extended by Dodds, Hong and Liou and Chan to develop an integral form of constitutive equations.…”