A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911015489241088 |
|---|---|
| author | Jeyaraj, Dhananjeyan Eivazi, Hamidreza Tröger, Jendrik-Alexander Wittek, Stefan Hartmann, Stefan Rausch, Andreas |
| author_facet | Jeyaraj, Dhananjeyan Eivazi, Hamidreza Tröger, Jendrik-Alexander Wittek, Stefan Hartmann, Stefan Rausch, Andreas |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16918 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials Jeyaraj, Dhananjeyan Eivazi, Hamidreza Tröger, Jendrik-Alexander Wittek, Stefan Hartmann, Stefan Rausch, Andreas Computational Physics Computational Engineering, Finance, and Science Machine Learning 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). |
| title | A Neural Operator based Hybrid Microscale Model for Multiscale Simulation of Rate-Dependent Materials |
| topic | Computational Physics Computational Engineering, Finance, and Science Machine Learning |
| url | https://arxiv.org/abs/2506.16918 |