Physics informed neural networks for continuum micromechanics

被引：131

作者：

Henkes, Alexander ^{[1
]}

Wessels, Henning ^{[1
]}

Mahnken, Rolf ^{[2
]}

机构：

[1] Tech Univ Carolo Wilhelmina Braunschweig, Inst Computat Modeling Civil Engn, Pockelsstr 3, D-38106 Braunschweig, Germany

[2] Univ Paderborn, Chair Engn Mech, Warburger Str 100, D-33098 Paderborn, Germany

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2022年 / 393卷

关键词：

Physics informed neural networks; Micromechanics; Adaptivity; Domain decomposition; mu CT -scans; Heterogeneous materials; DEEP LEARNING FRAMEWORK;

D O I：

10.1016/j.cma.2022.114790

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

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.

引用

页数：22