论文标题
小型晶体可塑性问题的无网溶液
A Meshless Solution of a Small-Strain Plasticity Problem
论文作者
论文摘要
当固体的变形足够大时，体的一部分会经历永久性变形，通常会反应为塑性变形。已经提出了一些描述这种现象的可塑性模型，例如冯·米塞斯（Von Mises），特雷斯卡（Tresca）等。传统上，有限元方法（fem）是解决此类问题的工程师的选择工具。但是，在这项工作中，我们利用一种无网状方法的变体，在我们内部开发的Medusa库中介绍了具有非线性各向同性硬化的von Mises可塑性模型 - 即径向基函数生成的有限差异（RBF-FD）。我们定义了一个简单的平面应力案例，其中2D块固定在一个边缘，而导致块变形的拉伸力则在相反的边缘施加。我们表明，结果与商业FEM求解器Abaqus FEA获得的数值解决方案非常吻合。
When the deformations of a solid body are sufficiently large, parts of the body undergo a permanent deformation commonly refereed to as plastic deformation. Several plasticity models describing such phenomenon have been proposed, e.g. von Mises, Tresca, etc. 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 a variant of meshless methods -- namely the radial basis function-generated finite differences (RBF-FD). 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. We show that results are in good agreement with the numerical solution obtained by Abaqus FEA, a commercial FEM solver.
