Two simple numerical implementation methods for damage coupled viscoplastic constitutive model

This paper is concerned with the two simple numerical implementation methods for a damage-coupled Chaboche-type viscoplastic constitutive model. By considering the damage variable as a constant in each incremental step, the return-mapping procedure is reduced to the solution of only one nonlinear scalar equation. Depending on the use of damage value in the current or prior incremental state, the two methods are named the backward difference implicit integration scheme and the two-step explicit integration scheme respectively. These two numerical algorithms are implemented into the ANSYS software by developing the USERMAT subroutine and verified by comparing them with available experimental data. Several numerical examples on the Gauss point level are studied in terms of stability, accuracy, computational efficiency, and applicability for further numerical observation. In addition to higher computational efficiency and lower memory requirements, the two methods can be easily extended to other damage models due to their simplicity.