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.

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The accuracy of a new integration algorithm is examined for a von Mises-type model of thermal-elastic-plasticity with nonlinear, mixed isotropic-kinematic hardening. The algorithm is founded on the frame of an integral representation of the conventional rate constitutive equations in contrast to the conventional rate equations themselves. The thermal effect on the yield surface is built in this approach without any difficulty. Under a generalized assumption of a constant strain rate, the model can be reduced to two scalar first-order ordinary differential equations which make an error-controllable integration method possible. Furthermore, for a nonconstant strain rate, e.g., a linear strain rate, the same idea of derivation achieves a similar conclusion. Errors of single-step stress predictions for given total strain increments are discussed.