# A new dual boundary element formulation for cohesive crack propagation

## Palavras-chave:

dual boundary element method, cohesive model, path-following methods## Resumo

A cohesive dual boundary element formulation is presented for crack propagation analysis and a path-

following method is proposed to solve the nonlinear system of equations by the direct control of one of the known

degrees of freedom. The simple linear cohesive model is introduced into the algebraic boundary element equations

by local stiffness matrices. According to the cohesive law, the stiffness coefficients decays as crack displacement

discontinuities increases. The acting loads are divided into two groups: one in which the load is perfectly known

and another in which only the direction is known. The magnitude (or load factor) of the latter is determined with

respect to the equilibrium of the boundary fields (indirectly controlled) and an additional path-following constraint

equation. The resulting non-linear system is solved using an incremental iterative scheme. For each iteration, the

corrections to the boundary fields are obtained in a partitioned manner, in which the load factor is calculated

independently using the direct control of the degree of freedom as the path-equation. The results show that the

proposed approach can efficiently capture the equilibrium curves.