This work extends our research on the strong-form meshless Radial Basis Function - Finite Difference (RBF-FD) method for solving non-linear visco-plastic mechanical problems. The polyharmonic splines with second-order polynomial augmentation are used for the shape functions. Their coefficients are determined by collocation. Three different approaches (, and ) are used for the numerical evaluation of the divergence operator in the equilibrium equation. They are presented and assessed for a visco-plastic material model with continuously differentiable material properties. It is shown that the approach is not suitable in this respect. In comparison to the previously investigated elasto-plasticity, it is shown that the approach can successfully cope with visco-plastic problems and is found to be even more accurate than the approach, which has previously proven to be most stable and effective in solving elasto-plasticity. This work extends the applicability of strong-form RBF-FD methods and opens up new areas of modelling non-linear solid mechanics.

中文翻译：

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粘塑性材料的强形式无网格数值模拟


这项工作扩展了我们对用于解决非线性粘塑性力学问题的强形式无网格径向基函数 - 有限差分 (RBF-FD) 方法的研究。具有二阶多项式增广的多调和样条用于形状函数。它们的系数由搭配决定。使用三种不同的方法 (、 和 ) 对平衡方程中的散度算子进行数值计算。它们针对具有连续可微分材料属性的粘塑性材料模型进行了呈现和评估。事实证明，该方法在这方面并不合适。与之前研究的弹塑性问题相比，该方法可以成功地解决粘塑性问题，并且比之前被证明在解决弹塑性问题方面最稳定、最有效的方法更准确。可塑性。这项工作扩展了强形式 RBF-FD 方法的适用性，并开辟了非线性固体力学建模的新领域。