Data-driven modeling of the mechanical behavior of anisotropic soft biological tissue

Closed-form constitutive models are currently the standard approach for describing soft tissues’ mechanical behavior. However, there are inherent pitfalls to this approach. For example, explicit functional forms can lead to poor fits, non-uniqueness of those fits, and exaggerated sensitivity to parameters. Here we overcome some of these problems by designing deep neural networks (DNN) to replace such explicit expert models. One challenge of using DNNs in this context is the enforcement of stress-objectivity. We meet this challenge by training our DNN to predict the strain energy and its derivatives from (pseudo)-invariants. Thereby, we can also enforce polyconvexity through physics-informed constraints on the strain-energy and its derivatives in the loss function. Direct prediction of both energy and derivative functions also enables the computation of the elasticity tensor needed for a finite element implementation. Then, we showcase the DNN’s ability by learning the anisotropic mechanical behavior of porcine and murine skin from biaxial test data. Through this example, we find that a multi-fidelity scheme that combines high fidelity experimental data with a low fidelity analytical approximation yields the best performance. Finally, we conduct finite element simulations of tissue expansion using our DNN model to illustrate the potential of data-driven approaches such as ours in medical device design. Also, we expect that the open data and software stemming from this work will broaden the use of data-driven constitutive models in soft tissue mechanics.