An iterative residual-based procedure for solving coupled elastoplastic damage problems

Abstract

In the computational damage mechanics, the coupled elastoplastic damage model involves a nonsymmetric tangent operator. This implies that a sparse matrix solver is needed, which means more computational cost to solve the problem. In the context of Lemaitre’s coupled damage model, a new iterative residual-based procedure is proposed to solve the Lemaitre’s coupled elastoplastic damage problems. The elastoplastic damaged tangent operator is decomposed into symmetric and nonsymmetric parts. The symmetric part of the tangent operator is contributed to the overall stiffness matrix, while the nonsymmetric part is considered as an additional residual force contributed to the overall force vector. The symmetry and banded format of the stiffness matrix is maintained, consequently the computational costs are largely reduced. The Lemaitre coupled damage model is implemented in ABAQUS commercial Software using a developed user material user subroutine, while the proposed procedure is implemented into a nonlinear 2 D FE model. Two different problems are analyzed to illustrate the applicability and effectiveness of the proposed iterative residual-based procedure. The analysis show that results of the Lemaitre’s coupled damage model and the proposed procedure are very close.

Keywords:

• Continuum damage mechanics (CDM)
• Lemaitre’s damage model
• plasticity
• finite element method (FEM)
• iterative residual-based procedure