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

arXiv: https://arxiv.org/abs/2107.05388 · HTML: https://mlsanity.com/paper/2107.05388/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jul 2021.

## Built on by (most cited first, 14 of 14)

- [Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations](https://mlsanity.com/paper/2110.03774/) (2021)
- [A Physics-Guided Neural Operator Learning Approach to Model Biological Tissues from Digital Image Correlation Measurements](https://mlsanity.com/paper/2204.00205/) (2022)
- [Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations](https://mlsanity.com/paper/2302.03598/) (2023)
- [Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review](https://mlsanity.com/paper/2303.07647/) (2023)
- [Enhancing Mechanical Metamodels with a Generative Model-Based Augmented Training Dataset](https://mlsanity.com/paper/2203.04183/) (2022)
- [Generative Hyperelasticity with Physics-Informed Probabilistic Diffusion Fields](https://mlsanity.com/paper/2310.03745/) (2023)
- [Heterogeneous Peridynamic Neural Operators: Discover Biotissue Constitutive Law and Microstructure From Digital Image Correlation Measurements](https://mlsanity.com/paper/2403.18597/) (2024)
- [A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains](https://mlsanity.com/paper/2510.04187/) (2025)
- [Physics-Informed Machine Learning in Biomedical Science and Engineering](https://mlsanity.com/paper/2510.05433/) (2025)
- [COMMET: orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updates](https://mlsanity.com/paper/2510.00884/) (2025)
- [Automating modeling in mechanics: LLMs as designers of physics-constrained neural networks for constitutive modeling of materials](https://mlsanity.com/paper/2512.01735/) (2025)
- [Exploring hyperelastic material model discovery for human brain cortex: multivariate analysis vs. artificial neural network approaches](https://mlsanity.com/paper/2310.10762/) (2023)
- [LLM-driven design of physics-constrained constitutive models: two agents are better than one](https://mlsanity.com/paper/2605.23754/) (2026)
- [CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data](https://mlsanity.com/paper/2606.14565/) (2026)

## Abstract (arXiv)

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.