The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying the full-field heterogeneous elastic properties of soft materials using traditional computational and engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in using data-driven models to learn full-field mechanical responses such as displacement and strain from experimental or synthetic data. However, research studies on inferring the full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, we propose a physics-informed machine learning approach to identify the elastic modulus distribution in nonlinear, large deformation hyperelastic materials. We evaluate the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) on inferring the heterogeneous material parameter maps across three nonlinear materials with structural complexity that closely resemble real tissue patterns, such as brain tissue and tricuspid valve tissue. Our improved PINN architecture accurately estimates the full-field elastic properties of three hyperelastic constitutive models, with relative errors of less than 5% across all examples. This research has significant potential for advancing our understanding of micromechanical behaviors in biological materials, impacting future innovations in engineering and medicine.

翻译：生物组织的异质微力学特性在医学与工程领域具有深远意义。然而，由于局部应力场估算困难，利用传统计算与工程方法识别软材料全域异质弹性属性面临根本性挑战。近年来，基于数据驱动模型从实验或合成数据学习全域力学响应（如位移和应变）的研究日益增多。但针对更具挑战性的材料全域弹性属性推断问题，尤其是大变形超弹性材料的相关研究仍十分匮乏。本文提出一种物理信息机器学习方法，用于识别非线性大变形超弹性材料的弹性模量分布。我们评估了物理信息神经网络（PINNs）在推断三类结构复杂度接近真实组织（如脑组织与三尖瓣组织）的非线性材料异质参数图谱时的预测精度与计算效率。改进的PINN架构能准确估计三种超弹性本构模型的全域弹性属性，在所有测试实例中相对误差均低于5%。该研究对深化理解生物材料微力学行为具有重要潜力，并将影响未来工程与医学领域的创新。