tailieunhanh - CAST3M implementation of the extended finite element method for cohesive crack

In this paper, the finite element for cohesive crack for quasi-brittle materials is constructed by XFEM, which allows incorporation of the displacement discontinuities in the element. The algorithm of construction and procedures for involving this finite element into code Cast3M are presented. The numerical calculations in fracture mechanics are presented to demonstrate the benefits of the proposed implementation. | Vietnam Journal of Mechanics, VAST, Vol. 33, No. 1 (2011), pp. 55 – 64 CAST3M IMPLEMENTATION OF THE EXTENDED FINITE ELEMENT METHOD FOR COHESIVE CRACK Nguyen Truong Giang, Ngo Huong Nhu Institute of Mechanics, VAST Abstract. In this paper, the finite element for cohesive crack for quasi-brittle materials is constructed by XFEM, which allows incorporation of the displacement discontinuities in the element. The algorithm of construction and procedures for involving this finite element into code Cast3M are presented. The numerical calculations in fracture mechanics are presented to demonstrate the benefits of the proposed implementation. Key words: Fracture, cohesive crack, quasi-brittle material, XFEM, Cast3M. 1. INTRODUCTION The extended finite element method (XFEM ) was first developed for two-dimensional linear elastic fracture mechanics [1, 2, 3], then it was used for crack growth, intersecting cracks and fluid mechanics. In the recent years, XFEM has been also applied to the cohesive crack model [4], [6]-[9]. The model which Hillerborg introduced in [5] has been used extensively in non-linear fracture mechanics of quasi-brittle materials and is applied in this paper. There are other developments of XFEM to existing codes. An implementation of the extended finite element method for linear elastic fracture mechanics problem within the finite element software Abaqus is introduced in [11]. In the same interest, an object enriched finite element library, named OpenXFEM++ which has been built and used to solve various 2D linear elastic fracture problems with great success, is presented in [12]. The finite element for the brittle crack by XFEM is constructed and involved into code Cast3M [3]. In order to produce extendable code, the objective of this paper is to present the algorithm of construction of new extended cohesive crack element 4 nodes and the way to add it into an existing finite element code Cast3M. 2. COHESIVE CRACK FOR QUASI-BRITTLE MATERIALS The .