Modeling of voids/cracks and their interactions

Numerical modeling of a two-dimensional elastic body containing multiple voids/cracks to study the interaction between these defects can be  significantly simplified by developing special finite elements, each containing an internal circular/elliptic hole or a slit crack. These finite elements are developed using complex potentials and the conformal mapping technique. The elements developed can be divided into two categories, namely, the semi-analytic-type and hybrid-type elements. The latter element type is an improved version of the former due to the implementation of displacement continuity along the inter-element boundary. All the proposed elements can be easily combined with the conventional displacement elements, such as isoparametric elements, to analyze the above-mentioned problems without using complicated finite element meshes. Numerical examples have been employed to illustrate the modeling of voids/cracks and their interactions. The results obtained using the semi-analytic-type elements are in good agreement with the theoretical results, and the corresponding results obtained using the hybrid-type elements show an improvement of the agreement with the theoretical results. However, the former element type is much easier to construct.