9 May 2024 | Georgios Kissas, Siddhartha Mishra, Eleni Chatzi, Laura De Lorenzis
The paper presents a novel approach to automatically discover constitutive laws for hyperelastic materials using formal grammars. The authors propose a symbolic regression pipeline that includes three main steps: library construction, pre-training, and data-driven discovery. The library of valid constitutive laws is generated using a formal grammar, which ensures that the derived expressions satisfy physical constraints. The pre-training step involves training a symbolic regression algorithm on the generated library, while the data-driven discovery step uses gradient-free optimization to find the best-fitting model from experimental data. The proposed method is evaluated on two tasks: automatically generating a library of valid constitutive laws for hyperelastic isotropic materials and discovering hyperelastic material models from displacement data with different noise levels. The results demonstrate the flexibility, efficiency, accuracy, robustness, and generalizability of the proposed methodology.The paper presents a novel approach to automatically discover constitutive laws for hyperelastic materials using formal grammars. The authors propose a symbolic regression pipeline that includes three main steps: library construction, pre-training, and data-driven discovery. The library of valid constitutive laws is generated using a formal grammar, which ensures that the derived expressions satisfy physical constraints. The pre-training step involves training a symbolic regression algorithm on the generated library, while the data-driven discovery step uses gradient-free optimization to find the best-fitting model from experimental data. The proposed method is evaluated on two tasks: automatically generating a library of valid constitutive laws for hyperelastic isotropic materials and discovering hyperelastic material models from displacement data with different noise levels. The results demonstrate the flexibility, efficiency, accuracy, robustness, and generalizability of the proposed methodology.