A new symmetric boundary integral formulation for embedded cohesive cracks growing in the interior of homogeneous linear elastic isotropic media is developed and implemented in a numerical code. The use of an exponential cohesive law for 2D and the special treatment about the way in which the law is included in the Symmetric Galerkin Boundary Element Method (SGBEM) allow us to develop a simple and efficient formulation that includes a Cohesive Zone Model (CZM). This formulation is only dependent on one variable in the cohesive zone (relative displacement). The corresponding constitutive cohesive equations present a softening branch which induce 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 test are presented and compared with experimental results available in the literature.
Single-Domain Cohesive-Zone-Model Formulation and Implementation using the Symmetric Galerkin Boundary Element Method
SALVADORI, Alberto;
2013-01-01
Abstract
A new symmetric boundary integral formulation for embedded cohesive cracks growing in the interior of homogeneous linear elastic isotropic media is developed and implemented in a numerical code. The use of an exponential cohesive law for 2D and the special treatment about the way in which the law is included in the Symmetric Galerkin Boundary Element Method (SGBEM) allow us to develop a simple and efficient formulation that includes a Cohesive Zone Model (CZM). This formulation is only dependent on one variable in the cohesive zone (relative displacement). The corresponding constitutive cohesive equations present a softening branch which induce 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 test are presented and compared with experimental results available in the literature.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
