期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 393, 期 -, 页码 -出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2022.114790
关键词
Physics informed neural networks; Micromechanics; Adaptivity; Domain decomposition; mu CT -scans; Heterogeneous materials
资金
- German Ministerium fur Kultur und Wissenschaft des Landes NRW
Physics informed neural networks are a method used in applied mathematics and engineering to solve partial differential equations. However, due to their global approximation approach, they face challenges in displaying localized effects and strong nonlinear solution fields. To overcome these issues, researchers have studied adaptive training strategies and domain decomposition.
Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is the usage of a neural network as a global ansatz function for partial differential equations. Due to the global approximation, physics informed neural networks have difficulties in displaying localized effects and strong nonlinear solution fields by optimization. In this work we consider nonlinear stress and displacement fields invoked by material inhomogeneities with sharp phase interfaces. This constitutes a challenging problem for a method relying on a global ansatz. To overcome convergence issues, adaptive training strategies and domain decomposition are studied. It is shown, that the domain decomposition approach is capable to accurately resolve nonlinear stress, displacement and energy fields in heterogeneous microstructures obtained from real-world mu CT-scans. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
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