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Enriched physics-informed neural networks for in-plane crack problems: Theory and MATLAB codes
Computational Engineering, Finance, and Science · Submitted 12 Jun 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Results show that the present method allows the calculation of accurate stress intensity factors (SIFs) with far fewer degrees of freedom.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 0.97 | 0.87 | 0.06 | asserted 0.99 |
| s1 | Instead of forming a mesh, the PINNs is meshless and can be trained on batches of randomly sampled collocation points. | method 0.96 | 0.23 | 0.03 | asserted 1.00 |
| s2 | 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. | method 0.79 | 0.87 | 0.10 | asserted 0.99 |
| s3 | The learnable parameters of the enriched PINNs are trained to satisfy the governing equations of the cracked body and the corresponding boundary conditions. | method 1.00 | 0.79 | 0.05 | asserted 0.99 |
| s4 | 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. | result 0.80 | 0.87 | 0.22 | asserted 1.00 |
| s5 | The present algorithm is tested on a class of representative benchmarks with different modes of loading types. | method 0.91 | 0.90 | 0.04 | asserted 0.95 |
| s6 | Results show that the present method allows the calculation of accurate stress intensity factors (SIFs) with far fewer degrees of freedom. | result 0.99 | 0.94 | 0.55 | asserted 0.99 |
| s7 | A self-contained MATLAB code and data-sets accompanying this manuscript are also provided. | contribution 0.98 | 0.77 | 0.03 | asserted 1.00 |
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Original abstract
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.
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