Boundary element method applied to three-dimensional crack analysis in exponentially graded viscoelastic materials

In the present work, three-dimensional crack problems in viscoelastic isotropic exponentially graded solids are investigated using the boundary element method (BEM). To reproduce the viscoelastic behaviour of the material, the BEM formulation is incorporated with an approach based on the differential constitutive relations for linear viscoelasticity employing Kelvin- Voigt and Boltzmann models. Moreover, the special case of material exponential gradation which is governed by a fundamental solution available in the literature is included into the boundary integral kernels. Because this methodology allows the material response to vary in time and space, it can be used to obtain the effects on the stress intensity factors, crack opening displacements, and energy release rates in practical fracture problems. Numerical examples are presented to demonstrate the applicability of the used methodology.