MESHFREE METHOD FOR ANALYSIS OF ELASTODYNAMIC FRACTURE MECHANICS PROBLEMS WITH THE SINGULARITY SUBTRACTION TECHNIQUE

Local Mesh Free Method, Moving Least Squares, Newmark Method, Mechanics of Elastodynamic Fracture, Singularity Subtraction Technique, SST.

Numerical methods are widely used to solve linear elastic fracture mechanics problems, with the Finite Element Method (FEM) as the main highlight. However, the FEM has several limitations that are influenced by singularities, computational cost, and adaptive analysis when modeling the growth of cracks; as a result, the meshes generated by the method have a certain degree of inaccuracy in the results. In order to circumvent those dificulties, other methods have been developed over the years. Among those, there are meshless methods that establish the balance of an algebraic system corresponding to a physical problem without using a specific discretization mesh. This study aims to apply a method without local mesh in the solution of two-dimensional problems in the mechanics of elastodynamic fractures. The Integrated Local Mesh Free Method (ILMF) is based on the weighted residual method, wherein, in a given local region, the work theorem establishes an energy relationship between a statically permissible stress field and a cinematically permissible strain field. ILMF presents a formulation totally free of numerical integration and with only one point per contour segment, with the approximation of the elastic field using the method of Moving Least Squares (MLS) in the formation of shape functions. In local mesh free methods, two parameters are used: the domain of the compact support and the placement domain. In the numerical integration over time, a method of direct integration in discrete time intervals, the Newmark Method, was used to obtain the displacements, velocities, and accelerations of the applied models. Also, parameters that make the method unconditionally stable were assumed.

In the Mechanics of Elastodynamic Fracture, the Singularity Subtraction Technique (SST) was adopted, so that the geometric singularities of structural parts as slits and manufacturing failings are modeled by stress intensity factors as a function of the crack opening mode. Finally, a series of classic examples are presented, whose behaviors are compared with the known analytical expressions or with other numerical methods, validating the accuracy and precision of the method proposed in the dynamic analysis.