In this work, we proposed a robust radial point interpolation method empowered with neural network solvers (RPIM-NNS) for solving highly nonlinear solid mechanics problems. It is enabled by neural network solvers via minimizing an energy-based functional loss. The RPIM-NNS has the following key ingredients: (1) It uses radial basis functions (RBFs) for displacement interpolation at arbitrary points in the problem domain, permitting irregular node distributions. (2) Nodes are placed also beyond the domain boundary, allowing the convenient implementation of boundary conditions of both Dirichlet and Neumann types. (3) It uses strain energy in an integral form as a part of the loss function, ensuring solution stability. (4) A well-developed gradient descendant algorithm in machine learning is employed to find the optimal solution, enabling robustness and ease in handling material and geometrical nonlinearities. (5) The proposed RPIM-NNS is compatible with parallel computing schemes. The performance of this method is tested using nonlinear problems including Cook's membrane and 3D twisting rubber problems, demonstrating its remarkable stability and robustness. This work, which seamlessly integrates the neural network solvers with mechanics governing equations and computational mechanics techniques, offers an excellent alternative for nonlinear solid mechanics problems. MATLAB codes are made available at for free downloading.

中文翻译：

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一种采用神经网络求解器 (RPIM-NNS) 的稳健径向点插值方法，适用于非线性固体力学


在这项工作中，我们提出了一种采用神经网络求解器（RPIM-NNS）的鲁棒径向点插值方法，用于解决高度非线性固体力学问题。它是由神经网络求解器通过最小化基于能量的功能损失来实现的。 RPIM-NNS 具有以下关键要素：（1）它使用径向基函数（RBF）在问题域中的任意点进行位移插值，允许不规则的节点分布。 (2) 节点也放置在域边界之外，从而可以方便地实现 Dirichlet 和 Neumann 类型的边界条件。 (3)采用积分形式的应变能作为损失函数的一部分，保证了解的稳定性。 (4) 采用机器学习中成熟的梯度下降算法来寻找最佳解决方案，从而实现鲁棒性并轻松处理材料和几何非线性。 (5)所提出的RPIM-NNS与并行计算方案兼容。该方法的性能通过库克膜和 3D 扭曲橡胶问题等非线性问题进行了测试，证明了其卓越的稳定性和鲁棒性。这项工作将神经网络求解器与力学控制方程和计算力学技术无缝集成，为非线性固体力学问题提供了一个极好的替代方案。 MATLAB 代码可免费下载。