In this paper, a method based on the physics-informed neural networks (PINNs) is presented to model in-plane crack problems in the linear elastic fracture mechanics. Instead of forming a mesh, the PINNs is meshless and can be trained on batches of randomly sampled collocation points. In order to capture the theoretical singular behavior of the near-tip stress and strain fields, the standard PINNs formulation is enriched here by including the crack-tip asymptotic functions such that the singular solutions at the crack-tip region can be modeled accurately without a high degree of nodal refinement. The learnable parameters of the enriched PINNs are trained to satisfy the governing equations of the cracked body and the corresponding boundary conditions. It was found that the incorporation of the crack-tip enrichment functions in PINNs is substantially simpler and more trouble-free than in the finite element (FEM) or boundary element (BEM) methods. The present algorithm is tested on a class of representative benchmarks with different modes of loading types. Results show that the present method allows the calculation of accurate stress intensity factors (SIFs) with far fewer degrees of freedom. A self-contained MATLAB code and data-sets accompanying this manuscript are also provided.
翻译:本文介绍了一种基于物理知情神经网络(PINNs)的方法,用于模拟线状弹性骨折力力学中的机内裂缝问题。PINNs不是形成网状,而是无网状的,可以随机抽样的合用点进行分批培训。为了捕捉近潮压力和紧张场的理论独有行为,标准PINNs配制在此添加了裂缝消瘦功能,使裂缝区域的单项解决办法可以精确地模型化,而没有高度的节点改进。浓缩的PINNs的可学习参数经过培训,以满足断裂体的方程式和相应的边界条件。发现,将裂缝浓缩功能纳入PINNs与有限元素(FEM)或边界元素(BEM)方法相比,容易发生问题。目前的算法是按不同装货方式的代表性基准进行测试的。结果显示,目前采用的方法可以计算出精确的A-A-A型自由度指数。