ABSTRACT
Today, there is increasing emphasis on the analysis of crack initiation and propagation in materials for effective design of high-performance and reliable structural components. The difficulty in obtaining analytical solutions for many of these problems, especially those associated with crack propagation, has prompted the use of numerical methods like the finite element method for the determination of fracture mechanics parameters such as stress intensity factors, energy release rates, J-integrals, crack tip stresses, and opening displacements. However, numerical simulation and analysis of the growth and interaction of multiple cracks in materials is a challenging enterprise due to various kinematic, morphological, and constitutive complexities that govern this process. Conventional finite element approaches suffer from very slow convergence since the element formulation does not inherently account for high gradients and singularities. Even a very high density mesh cannot overcome pathological mesh dependence near the crack tips and avoid biasing the direction of crack propagation. The difficulties aggravate significantly in the presence of multiple cracks, due to their interaction with each other.
