Elastoplastic damage analysis with algebraic derivation of consistent tangent by block Newton method

Abstract

The simultaneously iterative procedure proposed by the authors is applied to elastoplastic problems with damage. From the definition of a coupled problem of the weak form of the equilibrium equation and the constraint conditions for plastic yielding and damage evolution at every material point, the authors develop a numerical procedure based on the block Newton method to solve them with simultaneous linearization. In the proposed block Newton method, the consistent tangent can be derived algebraically, and the internal variables, which consist of the plastic parameter and the damage parameter, can also be updated algebraically without any local iterative calculations. Furthermore, the pseudo-stress for the residuals of both the yield condition and the damage evolution law is incorporated into the linearized weak form of the equilibrium equation. Thus, the proposed approach allows us to simultaneously reduce the residuals in the coupled boundary value problems. Some numerical examples illustrate the validity and effectiveness of the presented procedure for elastoplastic problems with Lemaitre damage model.

Keywords

• block newton method
• elastoplasticity
• lemaitre damage model
• finite element analysis
• small strains