A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials

TL;DR

This paper introduces a neural operator-based hybrid model for multiscale simulation of rate-dependent materials, significantly reducing computational costs while maintaining accuracy by integrating physics-based microscale predictions with deep learning.

Contribution

The work presents a novel neural operator framework that combines data-driven and physics-based modeling for efficient multiscale simulation of viscoelastic materials.

Findings

Achieves less than 6% error in homogenized stress predictions

Provides approximately 100 times faster simulations than traditional methods

Successfully models time-dependent microscale behavior using internal variables

Abstract

The behavior of materials is influenced by a wide range of phenomena occurring across various time and length scales. To better understand the impact of microstructure on macroscopic response, multiscale modeling strategies are essential. Numerical methods, such as the $\text{FE}^2$ approach, account for micro-macro interactions to predict the global response in a concurrent manner. However, these methods are computationally intensive due to the repeated evaluations of the microscale. This challenge has led to the integration of deep learning techniques into computational homogenization frameworks to accelerate multiscale simulations. In this work, we employ neural operators to predict the microscale physics, resulting in a hybrid model that combines data-driven and physics-based approaches. This allows for physics-guided learning and provides flexibility for different materials and spatial discretizations. We apply this method to time-dependent solid mechanics problems involving viscoelastic material behavior, where the state is represented by internal variables only at the microscale. The constitutive relations of the microscale are incorporated into the model architecture and the internal variables are computed based on established physical principles. The results for homogenized stresses ($<6\%$ error) show that the approach is computationally efficient ($\sim 100 \times$ faster).