Volume averaging based integration method in the context of XFEM-cohesive zone model coupling

Konstantinos Nikolakopoulos (1) , Jean-Philippe Crété (2, 3) , Patrice Longère (1)

1 ICA - Institut Clément Ader
2 QUARTZ - Laboratoire QUARTZ
3 SUPMECA - SUPMECA - Institut supérieur de mécanique de Paris

The main issue of the extended finite element method (XFEM) is the numerical integration of the system of equilibrium equations. Indeed, in order to have a correct displacement jump vector, the integration needs to be achieved on both sides of the discontinuity and thus requires the existence of integration points on both sides of the discontinuity. A volume averaging based integration method is developed in the present work alleviating this constraint and applied to XFEM coupled with cohesive zone model in a three-dimensional formulation. Moreover, unlike other widely used integration methods, the proposed method does not require the a priori knowledge of the position of the discontinuity inside the finite element nor the projection of the state variables.

Mots clés: X-FEM; Cohesive zone model; Numerical integration; Volume averaging scheme; Incompressibility

Domaines: Mécanique des matériaux [physics.class-ph]

Konstantinos Nikolakopoulos, Jean-Philippe Crété, Patrice Longère. Volume averaging based integration method in the context of XFEM-cohesive zone model coupling. Mechanics Research Communications, 2020, 104, pp.103485. ⟨10.1016/j.mechrescom.2020.103485⟩. ⟨hal-02485656⟩