Cohesive-zone-model formulation and implementation using the symmetric Galerkin boundary element method for homogeneous solids

摘要

A new symmetric boundary integral formulation for cohesive cracks growing in the interior of homogeneous linear elastic isotropic media with a known crack path is developed and implemented in a numerical code. A crack path can be known due to some symmetry implications or the presence of a weak or bonded surface between two solids. The use of a two-dimensional exponential cohesive law and of a special technique for its inclusion in the symmetric Galerkin boundary element method allows us to develop a simple and efficient formulation and implementation of a cohesive zone model. This formulation is dependent on only one variable in the cohesive zone (relative displacement). The corresponding constitutive cohesive equations present a softening branch which induces to the problem a potential instability. The development and implementation of a suitable solution algorithm capable of following the growth of the cohesive zone and subsequent crack growth becomes an important issue. An arc-length control combined with a Newton-Raphson algorithm for iterative solution of nonlinear equations is developed. The boundary element method is very attractive for modeling cohesive crack problems as all nonlinearities are located along the boundaries (including the crack boundaries) of linear elastic domains. A Galerkin approximation scheme, applied to a suitable symmetric integral formulation, ensures an easy treatment of cracks in homogeneous media and excellent convergence behavior of the numerical solution. Numerical results for the wedge split and mixed-mode flexure tests are presented.