Elastoplastic implicit integration algorithm applicable to both plane stress and three-dimensional stress states

An elastoplastic implicit integration algorithm applicable to both plane stress and three-dimensional stress states is developed for a general class of combined nonlinear kinematic–isotropic hardening models. The algorithm is first built for three-dimensional stress states in a general manner using the return mapping procedure and the Newton–Raphson method. The plane stress constraint is then incorporated into the Newton–Raphson iteration loop derived for three-dimensional stress states. The resulting algorithm has a mode patch that makes the algorithm applicable to both plane stress and three-dimensional stress states. The algorithm is specified by assuming an advanced evolution model of multiple back stresses, and is verified by performing numerical tests using plane stress, shell, and brick elements. The numerical tests are finite element analyses of homogeneously deformed plates and a cyclically loaded single-hole plate. It is demonstrated that the developed algorithm provides the quadratic convergence of iterations for implicit stress integration in plane stress, shell, and brick elements. It is also demonstrated that the algorithm is stable even in large incremental steps.

► An implicit integration algorithm applicable to both plane stress and three-dimensional stress states is developed.
► The algorithm is effective for a general class of nonlinear kinematic–isotropic hardening models.
► The algorithm has a mode patch that makes the algorithm applicable to both plane stress and three-dimensional stress states.
► The algorithm is specified for an advanced evolution model of back stress, and is verified by performing numerical tests.