Data-driven Modeling of the Mechanical Behavior of Anisotropic Soft Biological Tissue

Constitutive models that describe the mechanical behavior of soft tissues have advanced greatly over the past few decades. These expert models are generalizable and require the calibration of a number of parameters to fit experimental data. However, inherent pitfalls stemming from the restriction to a specific functional form include poor fits to the data, non-uniqueness of fit, and high sensitivity to parameters. In this study we design and train fully connected neural networks as material models to replace or augment expert models. To guarantee objectivity, the neural network takes isochoric strain invariants as inputs, and outputs the value of strain energy and its derivatives with respect to the invariants. Convexity of the material model is enforced through the loss function. Direct prediction of the derivative functions -- rather than just predicting the energy -- serves two purposes: it provides flexibility during training, and it enables the calculation of the elasticity tensor through back-propagation. We showcase the ability of the neural network to learn the mechanical behavior of porcine and murine skin from biaxial test data. Crucially, we show that a multi-fidelity scheme which combines high fidelity experimental data with low fidelity analytical data yields the best performance. The neural network material model can then be interpreted as the best extension of an expert model: it learns the features that an expert has encoded in the analytical model while fitting the experimental data better. Finally, we implemented a general user material subroutine (UMAT) for the finite element software Abaqus and thereby make our advances available to the broader computational community. We expect that the methods and software generated in this work will broaden the use of data-driven constitutive models in biomedical applications.