Radial Point Interpolation Meshless Methods for applications in Mechan- ics and Biomechanics

Resumo

Computational mechanics emerged alongside the advent of the first computers and has undergone significant development since then. Presently, the literature describes numerous advanced numerical techniques for discretization that are capable of efficiently conducting structural analyses. The finite element method (FEM) was one of the earliest discrete numerical methods to be developed and remains the most popular technique among the computational mechanics research community. FEM is known for its ease of programming, robustness, and ability to provide reasonable approximations. However, despite its efficiency and success, the last decade of the previous century witnessed the emergence of new, mature advanced discretization techniques known as meshless methods. In contrast to FEM, which discretizes the problem domain using a structured element mesh comprising a grid of nodes, meshless methods discretize the domain with an unstructured nodal distribution. Consequently, meshless methods enable the creation of discrete geometric models directly from medical images or CAD geometries. This advantage in meshing is a valuable asset in the fields of computational mechanics and biomechanics. This work presents a brief description of the evolution of advanced discretization meshless techniques in computational mechanics and biomechanics, highlighting the most significant ones and their formulations. Furthermore, it presents several demanding numerical applications in computational mechanics and biomechanics developed by the author and his research team. These applications encompass the analysis of transient behavior in bone tissue, the study of elastoplastic behavior in metallic and biological tissues, examination of blood fluid flow, and investigation of the structural response of implants and bio-structures. The results obtained using meshless methods are compared with FEM solutions to provide insights into the efficiency and accuracy of meshless techniques.