Model-driven identification framework for optimal constitutive modeling from kinematics and rheological arrangement

Abstract

Soft materials such as biological tissues or magnetorheological elastomers present complex mechanical behaviors that include large deformations, numerous nonlinearities, time- or even external field (magnetic)-dependent responses. The description of their constitutive modeling is challenging and often time-consuming. Numerical algorithms to automatically calibrate model parameters have provided invaluable tools to help this purpose. However, these are mostly limited to the fitting of a set of pre-defined parameters associated with the model used. In this work, we go a step further by developing a machine learning framework capable of automatically identifying not only such model parameters but also the optimal kinematics and rheological model. To this end, we present a multiphysics model-driven framework that optimally selects the most suitable model kinematics, its rheological components and their arrangement for a given set of experimental curves. Subsequently, it calibrates all the material constants belonging to such a model, independent of its complexity. We demonstrate the versatility and capabilities of this framework with examples on hyperelastic, viscohyperelastic and magneto-viscohyperelastic materials. The present work opens new routes to not only fit model parameters but to identify the constitutive ingredients and underlying mechanisms needed to describe nonlinear responses of soft active materials.