A neural operator-based hybrid microscale model for the multiscale simulation of rate-dependent materials

• Hybrid microscale model using operator learning and physical principles. • Accounting for rate-dependent nonlinear viscoelasticity at the microscale. • The hybrid model is ∼ 100 × faster than the finite element solver per microscale evaluation. 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 the macroscopic response, multiscale modeling strategies are essential. Numerical methods, such as the FE 2 -approach, account for micro-macro interactions to predict the global response in a concurrent manner. However, these methods are computationally intensive because of the repeated evaluations of the discretized 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 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 relationships at the microscale are incorporated into the model architecture and the internal variables are computed on the basis of established physical principles. The results for homogenized stresses ( < 6 % error) show that the approach is computationally efficient ( ∼ 100 × faster).