The Natural Neighbour Radial Point Interpolation Method to Predict the Compression and Traction Behavior of Thermoplastics

Abstract

Nowadays, the Finite Element Method is the most used discretization technique in structural computational mechanics. However, recently, new discretization techniques—such as meshless methods (Belinha in methods in biomechanics: bone tissue remodelling analysis. Springer International Publishing, Porto, Portugal, 2014 [1])—have been proposed. These numerical techniques are able to efficiently handle some of the FEM’s drawbacks, such as the re-meshing requirement in crack propagation or large deformations problems. Meshless methods only require an unstructured nodal mesh to discretize the problem domain, and the numerical integration of the discrete system of equations obtained from the Galerkin weak form is performed using a background integration mesh. Additionally, the nodal connectivity is imposed using the influence-domain concept, which allows to construct the interpolation functions. The Natural Neighbor Radial Point Interpolation Method (NNRPIM) is a recently developed truly meshless method, which in this work is used to analyze a thermoplastic assuming an elasto-plastic behavior. Benchmark numerical examples are solved in both traction and compression, and in the end, the NNRPIM results obtained are compared with FEM solutions.