Civil Engineering Departmental Seminar - Learning the hyperelastic constitutive relations from full-field data

Learning the hyperelastic constitutive relations from full-field data

Machine learning (ML)-based constitutive models have significantly enhanced the capacity to characterize the complex constitutive relations of materials, such as polycrystals, soft materials, etc. However, constructing such ML-based constitutive models, with the correct physical constraints remains a challenge, especially from experimentally measurable data. In this work, we propose a physical-augmented neural network (PANN) constitutive model that satisfies the objectivity, material symmetry (isotropic), polyconvexity, growth condition and stress-free condition by construction. With all these constraints in place, a hybrid finite element method-neural network (FEM-NN) optimization framework was developed to calibrate the PENN model based on the full-field displacement and external load data. Numerical and experimental data from isotropic hyperelastic materials were used to test the performance of the PANN model. Only a single uniaxial test is required for generating the training data. Results show that the PENN architecture can identify the unknown constitutive relationships of real-world materials with high accuracy and efficiency. The methods in this work is general and can be extended to a wide class of materials.