The discovery of constitutive laws for complex materials has historically faced a dichotomy between high-fidelity data-driven approaches, which demand prohibitive full-field experimental data, and traditional engineering fitting, which often yields numerically unstable models outside calibration regimes. In this work, we propose an Engineering-Oriented Symbolic Regression (EO-SR) framework that bridges this gap by leveraging Large Language Models (LLMs) as "Physics-Informed Agents." Unlike unconstrained symbolic regression, our framework utilizes an LLM Agent to zero-shot synthesize executable physical constraints -- specifically thermodynamic consistency and frame indifference -- transforming the search process from mathematical curve-fitting into a physics-governed discovery engine. We validate this approach on the hyperelastic modeling of rubber-like materials using standard Treloar datasets. The framework autonomously identifies a novel hybrid constitutive law that combines a Mooney-Rivlin linear base with a rational locking term. This discovered model not only achieves high predictive accuracy across multi-axial deformation modes (including zero-shot prediction of pure shear) but also guarantees unconditional convexity. Finite element validation demonstrates that while industry-standard models (e.g., Ogden N=3) fail due to numerical singularities under severe transverse compression, the EO-SR-discovered model maintains robust convergence. This study establishes a generalized, low-barrier pathway for discovering simulation-ready constitutive closures that satisfy both data accuracy and rigorous physical laws.

翻译：复杂材料本构律的发现长期面临两难困境：一方面，高保真数据驱动方法要求难以承受的全场实验数据；另一方面，传统工程拟合方法在校准范围外往往生成数值不稳定的模型。本文提出工程导向符号回归（EO-SR）框架，通过将大语言模型（LLM）作为"物理信息智能体"来弥合这一鸿沟。与无约束符号回归不同，该框架利用LLM智能体零样本合成可执行的物理约束（热力学一致性与框架无关性），将搜索过程从数学曲线拟合转变为物理驱动的发现引擎。我们使用标准Treloar数据集对橡胶类材料的超弹性建模验证了该方法。该框架自主识别出结合Mooney-Rivlin线性基与有理锁紧项的新型混合本构律。发现模型不仅在多轴变形模式下（包括纯剪切零样本预测）实现高预测精度，还保证了无条件凸性。有限元验证表明，当工业标准模型（如Ogden N=3）因严重横向压缩下的数值奇异性而失效时，EO-SR发现的模型仍保持稳健收敛。本研究为发现同时满足数据精度与严格物理定律的仿真就绪本构闭合方程，建立了一条通用低门槛路径。