Physics informed neural networks for continuum micromechanics [article]

Alexander Henkes, Henning Wessels, Rolf Mahnken
2021 arXiv   pre-print
Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial differential equations. Due to the global approximation, physics informed neural networks have difficulties in displaying localized effects and strong non-linear solutions by optimization. In this work we consider material non-linearities invoked by material
more » ... ties 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 able to accurately resolve nonlinear stress, displacement and energy fields in heterogeneous microstructures obtained from real-world μCT-scans.
arXiv:2110.07374v1 fatcat:mbqrelv3jzc67luqxacvcsy54u