This work presents a two-stage physics-informed, data-driven constitutive modeling framework for hyperelastic soft materials undergoing progressive damage and failure. The framework is grounded in the concept of hyperelasticity with energy limiters and employs Gaussian Process Regression (GPR) to separately learn the intact (undamaged) elastic response and damage evolution directly from data. In Stage I, GPR models learn the intact hyperelastic response through volumetric and isochoric response functions (or only the isochoric response under incompressibility), ensuring energetic consistency of the intact response and satisfaction of fundamental principles such as material frame indifference and balance of angular momentum. In Stage II, damage is modeled via a separate GPR model that learns the mapping between the intact strain energy density predicted by Stage I models and a stress-reduction factor governing damage and failure, with monotonicity, non-negativity, and complete-failure constraints enforced through penalty-based optimization to ensure thermodynamic admissibility. Validation on synthetic datasets, including benchmarking against analytical constitutive models and competing data-driven approaches, demonstrates high in-distribution accuracy under uniaxial tension and robust generalization from limited training data to compression and shear modes not used during training. Application to experimental brain tissue data demonstrates the practical applicability of the framework and enables inference of damage evolution and critical failure energy. Overall, the proposed framework combines the physical consistency, interpretability, and generalizability of analytical models with the flexibility, predictive accuracy, and automation of machine learning, offering a powerful approach for modeling failure in soft materials under limited experimental data.

翻译：本研究提出了一种两阶段物理信息数据驱动本构建模框架，用于描述经历渐进损伤与失效的超弹性软材料。该框架基于带能量限制器的超弹性理论，并采用高斯过程回归（GPR）直接从数据中分别学习完整（未损伤）弹性响应与损伤演化。在第一阶段，GPR模型通过体积响应函数与等容响应函数（或在不可压缩条件下仅通过等容响应函数）学习完整的超弹性响应，确保完整响应的能量一致性并满足材料标架无差异性与角动量平衡等基本原理。在第二阶段，损伤通过独立的GPR模型进行建模，该模型学习第一阶段模型预测的完整应变能密度与控制损伤失效的应力折减因子之间的映射关系；通过基于惩罚项的优化强制执行单调性、非负性及完全失效约束，以确保热力学相容性。在合成数据集上的验证（包括与解析本构模型及现有数据驱动方法的基准测试）表明，该框架在单轴拉伸下具有较高的分布内精度，并能从有限训练数据稳健地泛化至训练未使用的压缩与剪切模式。在脑组织实验数据中的应用验证了框架的实际适用性，并可推断损伤演化与临界失效能量。总体而言，所提框架融合了解析模型的物理一致性、可解释性与泛化能力，以及机器学习的灵活性、预测精度与自动化优势，为在有限实验数据下建模软材料失效提供了一种强有力的方法。