张拉稳态的自动化模型发现：生长与重塑中的本构机器学习
Automated Model Discovery for Tensional Homeostasis: Constitutive Machine Learning in Growth and Remodeling
AI总结：
本研究扩展非弹性本构人工神经网络，结合运动学生长与稳态表面，自动发现张拉稳态的标量模型方程，并在材料点级别验证其学习与预测能力。
摘要：
软组织生物组织表现出维持优选拉伸应力状态的趋势，即张拉稳态，即使在外部机械刺激后也能恢复。这种宏观行为可以用运动学生长理论来描述，其中变形梯度被乘法分解为弹性部分和与生长及重塑相关的部分。最近，引入了稳态表面的概念来定义稳态状态以及非弹性变形的演化方程。然而，无论具体的非弹性现象如何，识别最优模型和材料参数以准确捕捉非弹性材料的宏观行为，只能凭借显著的专业知识完成，且通常耗时且容易出错。为应对这一挑战，内置物理的机器学习算法提供了巨大潜力。在本工作中，我们通过纳入运动学生长和稳态表面来扩展我们的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。后者以弥散方式描述稳态状态。我们评估了所提出网络从材料点级别的实验组织等效数据中学习的能力，评估了其在训练范围之外的预测准确性，并讨论了其在结构级别应用时的当前局限性。我们的源代码、数据、示例以及相应材料子程序的实现已在 https://doi.org/10.5281/zenodo.13946282 公开提供。
英文摘要：
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.
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