A new dual boundary element formulation for cohesive crack propagation

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.