On the determination of specific elastic energy flow to the vertex of a physical cut via a finite element solution

The finite element approximation of a double cantilever beam (DCB) specimen with a physical cut in a linear elastic medium is considered. The thickness of the physical cut specifies a linear parameter of the problem. The $J$-integral is determined as the product of the linear parameter and the average value of the specific elastic energy on the dead-end edge of the finite element. For the considered loading schemes of the DCB specimen in modes I and II with zero linear parameter set in ANSYS, the stress intensity factors are obtained and used to determine the $J$-integrals. The convergence of the product of the linear parameter and the average value of the specific elastic energy on the dead-end edge of the finite element to the reference values of the $J$-integrals is shown for equivalent loading of the specimen with a physical cut and with a linear parameter tending to zero. The specific work of nodal forces is studied during the dead-end finite element removing. The convergence of the specific work of nodal forces when removing the dead-end element by simple unloading of adjacent edges to the value of the reference $J$-integral is observed.