Automated model discovery for tensional homeostasis: Constitutive machine learning in growth and remodeling

We present a built-in physics neural network architecture, known as inelastic Constitutive Artificial Neural Network (iCANN), to discover the inelastic phenomenon of tensional homeostasis. In this course, identifying the optimal model and material parameters to accurately capture the macroscopic behavior of inelastic materials can only be accomplished with significant expertise, is often time-consuming, and prone to error, regardless of the specific inelastic phenomenon. To address this challenge, built-in physics machine learning algorithms offer significant potential. We introduce the incorporation of kinematic growth and homeostatic surfaces into the iCANN to discover the Helmholtz free energy and the pseudo potential. The latter describes the state of homeostasis in a smeared sense. To this end, we additionally propose a novel design of the corresponding feed-forward network in terms of principal stresses. We evaluate the ability of the proposed network to learn from experimentally obtained tissue equivalent data at the material point level, assess its predictive accuracy beyond the training regime, and discuss its current limitations when applied at the structural level. Our source code, data, examples, and an implementation of the corresponding material subroutine are made accessible to the public at https://doi.org/10.5281/zenodo.13946282.