  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.
