The preservation of cultural heritage is increasingly transitioning towards data-driven predictive maintenance and "Digital Twin" construction. However, the mechanical constitutive models required for high-fidelity simulations remain fragmented across decades of unstructured scientific literature, creating a "Data Silo" that hinders conservation engineering. To address this, we present an automated, two-stage agentic framework leveraging Large Language Models (LLMs) to extract mechanical constitutive equations, calibrated parameters, and metadata from PDF documents. The workflow employs a resource-efficient "Gatekeeper" agent for relevance filtering and a high-capability "Analyst" agent for fine-grained extraction, featuring a novel Context-Aware Symbolic Grounding mechanism to resolve mathematical ambiguities. Applied to a corpus of over 2,000 research papers, the system successfully isolated 113 core documents and constructed a structured database containing 185 constitutive model instances and over 450 calibrated parameters. The extraction precision reached 80.4\%, establishing a highly efficient "Human-in-the-loop" workflow that reduces manual data curation time by approximately 90\%. We demonstrate the system's utility through a web-based Knowledge Retrieval Platform, which enables rapid parameter discovery for computational modeling. This work transforms scattered literature into a queryable digital asset, laying the data foundation for the "Digital Material Twin" of built heritage.