We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) framework to efficiently solve the heterogenized formulation through parsimonious model selection using sparsity-promoting priors and Monte Carlo Markov Chain sampling. We utilize experimentally observable 3D surface displacement and boundary-averaged force data generated from Finite Element simulations of non-equi-biaxial tension tests on heterogeneous specimens. The framework broadly consists of two steps -- residual force-based segmentation, and constitutive parameter identification. We validate and demonstrate the ability of the proposed framework to segment the domain, and characterize the constituent materials on various types of thin square heterogeneous domains. We validate of the framework's ability to segment and characterize materials with various levels of displacement noises and non-native mesh discretizations, i.e, using different meshes for the forward FE simulations and the inverse EUCLID problem. This demonstrates Hetero-EUCLID framework's applicability in Digital Image/Volume Correlation-based experimental scenarios. Furthermore, the proposed framework performs successful segmentation and material characterizations based on data from a single experiment, thereby making it viable for rapid, interpretable model discovery in domains such as aerospace and defense composites and for characterization of selective tissue stiffening in medical conditions such as fibroatheroma, atherosclerosis, or cancer.

翻译：本文提出一种名为Hetero-EUCLID的计算框架，用于实现异构材料所有组分完整超弹性行为的表征，该框架包含材料区域分割与参数识别两大功能。本研究基于贝叶斯-EUCLID（高效无监督本构定律识别与发现）框架，通过采用稀疏先验的简约模型选择与马尔可夫链蒙特卡罗采样方法，高效求解异构化表述问题。我们利用有限元模拟对异构试样进行非等双轴拉伸试验所产生的实验可观测三维表面位移数据与边界平均力数据。该框架主要包含两个步骤——基于残余力的区域分割和本构参数识别。我们在多种类型的薄板方形异构域上验证并展示了该框架实现区域分割及组分材料表征的能力。我们验证了该框架在不同位移噪声水平及非原生网格离散化（即正向有限元模拟与逆向EUCLID问题采用不同网格）条件下的材料分割与表征能力，这证明了Hetero-EUCLID框架在基于数字图像/体积相关技术的实验场景中的适用性。此外，所提框架能够基于单次实验数据成功实现材料分割与表征，这使其在航空航天与国防复合材料等领域具有快速、可解释模型发现的实用价值，并可用于医学领域（如纤维粥样斑块、动脉粥样硬化或癌症）选择性组织硬化现象的表征研究。