The Boundary Element Method Applied to Three-Dimensional Exponentially Graded Viscoelastic Solids

Exponentially graded viscoelastic solids constitute an important class of advanced composite materials. Such materials exhibit physical, chemical or both properties enriched in order to satisfy specifics applications. This work presents an investigation of the linear elastic and viscoelastic behaviour of three-dimensional isotropic Functionally Graded Materials (FGMs) using the Boundary Element Method (BEM). The present work considers here a special FGM which presents an exponential gradient of the elastic modulus along one, two, or three directions. The material gradation is modelled using a fundamental solution available in the literature which is readily incorporated into the traditional boundary integral kernels. To include the viscoelastic behaviour of the material into the BEM formulation an approach based on the differential constitutive relations for linear viscoelasticity employing rheological solids models has been used. Practical problems involving displacement and fracture mechanics parameters have been presented herein assuming creep behaviour of the Kelvin-Voigt and Boltzmann materials. Useful informations regarding displacement, traction and stress intensity factors are discussed.