A two-field modified Lagrangian formulation for robust simulations of extrinsic cohesive zone models

• Published in: Computational mechanics Vol. 51; no. 6; pp. 865 - 884
• Main Authors: Cazes, F., Coret, M., Combescure, A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.06.2013; Springer; Springer Nature B.V; Springer Verlag
• Subjects: Classical and Continuum Physics; Cohesion; Computational Science and Engineering; Computer simulation; Engineering; Engineering Sciences; Equivalence; Formulations; Fracture mechanics; Laws; Mathematical analysis; Mathematical models; Mechanics; Original Paper; Physics; Robustness (mathematics); Solid mechanics; Stiffness; Theoretical and Applied Mechanics; Traction; Lagrangian multiplier; Failure; Finite element
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-012-0763-1

This paper presents the robust implementation of a cohesive zone model based on extrinsic cohesive laws (i.e. laws involving an infinite initial stiffness). To this end, a two-field Lagrangian weak formulation in which cohesive tractions are chosen as the field variables along the crack’s path is presented. Unfortunately, this formulation cannot model the infinite compliance of the broken elements accurately, and no simple criterion can be defined to determine the loading–unloading change of state at the integration points of the cohesive elements. Therefore, a modified Lagrangian formulation using a fictitious cohesive traction instead of the classical cohesive traction as the field variable is proposed. Thanks to this change of variable, the cohesive law becomes an increasing function of the equivalent displacement jump, which eliminates the problems mentioned previously. The ability of the proposed formulations to simulate fracture accurately and without field oscillations is investigated through three numerical test examples.