This paper presents a novel neural network non-ordinary state-based peridynamic (NOSB PD) algorithm for large deformation and fracture analysis of hyperelastic membranes. A non-local membrane theory has been developed by approximating the curved horizon of the membrane as a flat surface and applying the plane stress assumption locally. This allows the simulation of the membrane structure using a single layer of material points, simplifying implementation, improving efficiency, and avoiding volume locking. In the framework of NOSB PD, the deformation gradients are represented by their corresponding bond vectors based on the non-local geometry relationship. Then, the nonlinear bijection between bond vectors and force density is obtained using a developed neural network model. This approach successfully overcomes the zero-energy problem and significantly improves the efficiency. Three representative numerical examples: out of plane deformation, out of plane loading crack propagation and penetrating of a ball are simulated to validate the developed algorithm. The results demonstrate that the developed method can accurately and efficiently achieve the large deformation, out of plane tearing, wrinkle as well as fracture of hyperelastic membranes.

中文翻译：

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一种用于超弹性膜大变形和断裂分析的新型神经网络非普通状态近场动力学方法


本文提出了一种新颖的神经网络非普通状态近场动力学（NOSB PD）算法，用于超弹性膜的大变形和断裂分析。通过将膜的弯曲水平线近似为平坦表面并局部应用平面应力假设，发展了非局部膜理论。这允许使用单层材料点来模拟膜结构，从而简化实施、提高效率并避免体积锁定。在NOSB PD的框架中，变形梯度由基于非局部几何关系的相应键向量表示。然后，使用开发的神经网络模型获得键向量和力密度之间的非线性双射。这种方法成功克服了零能耗问题并显着提高了效率。模拟了三个代表性数值示例：平面外变形、平面外加载裂纹扩展和球的穿透，以验证所开发的算法。结果表明，所开发的方法能够准确、高效地实现超弹性膜的大变形、面外撕裂、起皱以及断裂。