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.

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