A Meshless Solution of a Small-Strain Plasticity Problem
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Plasticity is a branch of solid mechanics, which deals with materials that upon sufficient deformation do not return to their original shape once the deforming force is released.Several plasticity models describing the yield condition exist, e.g. von Mises, Tresca, etc. Plasticity problems are usually solved by assuming an elastic deformation under the applied load, and correcting the stress-strain field iteratively, should the local yield criterion be violated. Traditionally the finite element method (FEM) is the numerical tool of choice for engineers who are solving such problems. In this work, however, we present the implementation of the von Mises plasticity model with non-linear isotropic hardening in our in-house developed MEDUSA library, utilizing radial basis function-generated finite differences (RBF-FD), which is beneficial compared to FEM, as it does not require a meshing step to discretize the domain. We define a simple plane stress case, where a 2D block is fixed at one edge, and a tensile force, which causes the block to deform, is applied to it at the opposite edge. Results are in good agreement with solutions obtained by Abaqus FEA, a commercial FEM solver.
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