Speaker
Description
The behavior of materials is influenced by a variety of phenomena that take place across diverse time and length scales. Multiscale modeling strategies are required to have a better understanding of the effect of the microstructure on the macroscopic response. Numerical approaches, such as the FE2 method, consider the macro-micro interaction to predict a global response in a concurrent manner. However, such methods are computationally expensive due to the repeated evaluation of the micro-scale. This limitation has motivated the integration of deep learning methods into a computational homogenization framework to accelerate multi-scale simulations. One such approach is to use a neural network-based surrogate model to replace the micro-scale analysis. Such models are purely data-driven and are faster without compromising accuracy. However, the state of the micro-scale is not available when using a substitutive surrogate model and incorporating known physical relations of the microstructure such as the equilibrium conditions is not feasible.
In this contribution, we use neural operators to predict the micro-scale physics resulting in a combination of data-driven and physics-based hybrid model. This enables physics-guided learning and is flexible for different materials and spatial discretization. The applied multiscale FE$^2$ simulations are based on periodic homogenization theory and consist of a representative volume element (RVE) at each Gauss integration point of the macro-scale. We approximate the solutions of RVE by constructing a physics-informed operator network. Homogenized stresses and strains are then computed using conventional finite element methods and the consistent tangent matrix is computed via automatic differentiation.
We apply the proposed approach as two variants to time-dependent problems in solid mechanics considering viscoelastic material behavior, where the state is represented as internal variables only at the micro-scale. In the first variant, the internal variables are computed based on known physics whereas in the second variant, the internal variables are learnt from data. The results of homogenized stresses and strains from both these methods are analyzed. Additionally, we demonstrate that integrating cutting-edge high-performance computing tools and just-in-time compilation can significantly accelerate performance, achieving speed gains by multiple orders of magnitude.
