Soft biological tissues exhibit a tendency to maintain a preferred state of tensile stress, known as tensional homeostasis, which is restored even after external mechanical stimuli. This macroscopic behavior can be described using the theory of kinematic growth, where the deformation gradient is multiplicatively decomposed into an elastic part and a part related to growth and remodeling. Recently, the concept of homeostatic surfaces was introduced to define the state of homeostasis and the evolution equations for inelastic deformations. However, 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. In this work, we extend our inelastic Constitutive Artificial Neural Networks (iCANNs) by incorporating kinematic growth and homeostatic surfaces to discover the scalar model equations, namely the Helmholtz free energy and the pseudo potential. The latter describes the state of homeostasis in a smeared sense. 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.

翻译：软组织表现出维持特定拉伸应力状态的倾向，即张力稳态，即使在外部机械刺激后仍能恢复。这种宏观行为可通过运动生长理论进行描述，其中变形梯度被乘法分解为弹性部分和与生长重构相关的部分。近期引入的稳态曲面概念可用于定义稳态状态及非弹性变形的演化方程。然而，无论针对何种具体的非弹性现象，要准确捕捉非弹性材料宏观行为的最佳模型和材料参数识别，通常需要大量专业知识、耗时且易出错。为应对这一挑战，内置物理机制的机器学习算法展现出巨大潜力。本研究通过整合运动生长理论和稳态曲面，扩展了非弹性本构人工神经网络（iCANNs），以发现标量模型方程——即亥姆霍兹自由能和伪势函数。后者以弥散形式描述稳态状态。我们评估了所提出网络在材料点层面从实验获取的组织等效数据中学习的能力，检验其在训练区间外的预测准确性，并讨论其在结构层面应用时的现有局限性。相关源代码、数据、案例及对应材料子程序的实现已通过 https://doi.org/10.5281/zenodo.13946282 公开。