Speaker
Description
The continuous development of increasingly complex materials necessitates the expansion of epistemic knowledge in materials modeling to enable comprehensive optimization in terms of cost and performance already during the virtual design phase. In parallel, modern experimental techniques and data-driven methodologies have advanced substantially, with machine learning offering unprecedented opportunities for extracting meaningful insights from extensive datasets. Such insights can guide the development of robust, physically interpretable models that improve both the predictive accuracy and the fundamental understanding of material behavior.
In this context, a novel data-driven approach for discovering constitutive laws governing isotropic hyperelastic materials is presented. Rather than relying solely on black-box models such as deep neural networks, a sparse regression technique is employed to identify a parsimonious, interpretable functional form for the strain energy density. By starting with a large library of candidate functions, the methodology systematically selects only those terms that contribute to an accurate and physically meaningful representation of the material response. This approach yields models that remain transparent and interpretable, thereby facilitating a deeper appreciation of the underlying mechanics and a more direct integration into established simulation frameworks.
The method leverages full-field displacement data acquired from experimental tests, e.g., via digital image correlation (DIC), which provide spatially resolved information on the deformation state. Global and local regularization strategies are employed by Bayesian inference to account for measurement noise, model uncertainties, and potential simplifications in the assumed constitutive structure. This probabilistic framework naturally incorporates uncertainty quantification, enabling assessed model confidence and guiding model refinement more effectively.
A critical step in the procedure is the calibration of the identified constitutive model. To achieve this, the experimentally measured displacements are directly coupled with the displacements of finite element simulations of the candidate material model. By iteratively adjusting model parameters, the discrepancies between the simulated and observed displacement fields are minimized. This inverse analysis approach, driven by Bayesian inference, not only provides optimal parameter estimates but also explicitly quantifies uncertainties arising from imperfect measurements or modeling assumptions.
The capabilities of the method are demonstrated through synthetic benchmark examples representing various isotropic hyperelastic materials.
