EAAI Journal 2026 Journal Article
Biaxial tensile test meets unsupervised learning: a novel strategy for accurate constitutive modeling
- Zhihao Wang
- Dominique Guines
- Xingrong Chu
- Lionel Leotoing
- Wenke Wang
With the rapid advancements in forming processes and materials engineering, the demand for precise constitutive modeling has grown significantly, and machine learning techniques have shown great potential in this field, offering more flexible and efficient solutions. This study proposes a new unsupervised learning approach combining an artificial neural network (ANN) with the finite element (FE) method to learn thermo-viscoplastic constitutive relations from indirect data. The ANN maps the strain, temperature and strain rate to flow stress of AA6061 sheets and is implemented into finite element analysis via a user material subroutine that adopts the Yld2000-3d yield surface and associated flow rule assumptions. The unsupervised learning approach eliminates the need for flow stress computation, relying instead on strain and global force measurements provided by fifteen biaxial tensile tests that use a dedicated cruciform specimen at different temperatures and strain rates. These indirect data contain rich information about material constitutive relations and enable ANN constitutive modeling in complex scenarios. A novel symbolic differentiation approximation method is developed to address the challenge of the gradient computation of a loss function that contains strains from FE solutions. The method is applicable to general FE framework, offers robust and efficient convergence, and is user-friendly to implement. Additionally, a continual training strategy with weighted gradients by gradually introducing new dataset is adopted to balance multiple datasets and mitigate catastrophic forgetting. Finally, validations through thermal equi-biaxial stretching and shear tests demonstrate that the trained ANN model can accurately predict constitutive relations and reasonably extrapolate to large strain levels.