Elastic–viscoplastic implicit integration algorithm applicable to both plane stress and three-dimensional stress states

• An implicit algorithm applicable to both plane stress and three-dimensional stress integrations is developed.
• The algorithm is effective for a general class of nonlinear kinematic–isotropic hardening models.
• A mode patch that makes the algorithm applicable to both plane stress and three-dimensional stress states.
• Two trial stresses are examined to be initial values for the Newton-Raphson iteration in the algorithm.
• Elastic–viscoplastic trial stress enables quadratic convergence to occur much earlier than elastic one.

An elastic–viscoplastic 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 based on an elastic–plastic algorithm developed by the authors and accordingly has a simple mode patch that makes the algorithm applicable to both the stress states. The algorithm is verified by performing numerical tests using plane stress, shell, and brick elements. In the numerical tests, an elastic trial stress and an elastic–viscoplastic trial stress based on linear kinematic hardening are examined to provide the initial value to start the Newton-Raphson iteration in the algorithm. It is demonstrated that the developed algorithm gives the quadratic convergence to the iterations for implicit stress integration in plane stress, shell, and brick elements. It is also demonstrated that the elastic–viscoplastic trial stress enables the quadratic convergence to occur much earlier than the elastic trial stress.