Volume averaging based integration method in the context of XFEM-cohesive zone model coupling. (March 2020)

• Record Type: Journal Article
• Authors: Nikolakopoulos, Konstantinos; Crete, Jean-Philippe; Longere, Patrice
• Is Part Of: Mechanics research communications. Volume 104(2020)
• Publication Date: 2020-03
• Subjects: X-FEM -- Cohesive zone model -- Numerical integration -- Volume averaging scheme -- Incompressibility; Mechanics, Applied -- Periodicals; Mécanique appliquée -- Périodiques; Mechanics, Applied; Periodicals; 530
• DOI: 10.1016/j.mechrescom.2020.103485
• Languages: English
• ISSNs: 0093-6413

Abstract

Highlights: A volume averaging scheme (VAI) is proposed for the integration of equilibrium equations in the framework of cohesive XFEM. VAI uses a modified quadrature rule that performs the integration as an averaging of the contributions of two sub-volumes. The proposed scheme is compared with element sub-division, the standard 8-GP quadrature and Abaqus cohesive elements. VAI eliminates state variables projection and is performant even when one of the sub-volumes created is infinitely small. Abstract: 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.