Physics informed neural networks for continuum micromechanics
This work addresses a domain-specific problem in continuum micromechanics for researchers and engineers dealing with material inhomogeneities, representing an incremental improvement over existing methods.
The paper tackled the challenge of modeling material nonlinearities and sharp phase interfaces in heterogeneous microstructures using physics-informed neural networks, which struggle with localized effects. By employing adaptive training strategies and domain decomposition, the method accurately resolved nonlinear stress, displacement, and energy fields in real-world μCT-scans.
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 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 able to accurately resolve nonlinear stress, displacement and energy fields in heterogeneous microstructures obtained from real-world $μ$CT-scans.