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

The chapter delves into the advanced application of the Boundary Element Method (BEM) to three-dimensional exponentially graded viscoelastic solids. It begins by highlighting the significance of functionally graded materials (FGMs) in modern engineering, particularly their ability to tailor mechanical properties. The BEM is introduced as a powerful alternative to the traditional finite element method (FEM) for solving viscoelastic problems in FGMs. The chapter then details the mathematical formulation of BEM for viscoelastic materials, incorporating constitutive equations for Kelvin-Voigt and Boltzmann models. Numerical integration techniques and element subdivision procedures are discussed to handle singularities and improve computational efficiency. Practical examples, including a regular hexahedron under traction, a disc under displacement, a hollow cylinder under pressure, and a thick plate with a center crack, are presented to demonstrate the method's accuracy and versatility. The results are validated through comparisons with analytical solutions and finite element software, showcasing the BEM's potential in predicting material behavior and fracture mechanics parameters. The chapter concludes with insights into future research directions, emphasizing the method's utility in solving complex engineering problems involving FGMs.