A BEM formulation with Tangent Operator for cohesive crack propagation modeling

Resumo

This work presents a Boundary Element Method (BEM) formulation for cohesive crack propagation
analysis, in a 2D approach. The fracture effects are captured by using dipoles of stresses, with the introduction of
an initial stress field to represent the cohesive zone. This formulation represents the presence of the Fracture
Process Zone (FPZ) with only three algebraic equations (equations related to stress correction) per source point
located in the crack line. For comparison, dual formulation requires four algebraic equations (displacements and
forces) per source point, and the multi-domain technique requires eight algebraic equations. The consistent
Tangent Operator (TO) is derived for the linear, bilinear and exponential cohesive laws, in order to speed up the
nonlinear solution. Some examples are presented to illustrate the robustness of the Dipole BEM/TO formulation,
including multiple crack analysis in mixed fracture mode. The responses obtained using this new formulation are
compared with experimental and numerical data available in the literature, and in all applications, the numerical
efficiency of the TO operator is presented.