熱觸發型自修復高分子材料因具備自我修復裂縫之能力，於生醫領域與結構健康維護上極具潛力，而熱膨脹係數 (coefficient of thermal expansion, CTE) 為驅動高分子流動與裂縫閉合之關鍵參數。然而，本研究探討之深共熔溶劑 (deep eutectic solvent, DES) 離子凝膠於室溫下力學模數偏低，傳統接觸式量測易因接觸導致試體非預期變形，難以取得可靠之 CTE 數據。
為突破此限制，本研究結合非接觸光學影像與有限元素法 (Finite Element Method, FEM)，建構數值反演 (inverse calibration) 框架。研究先建構基於時溫疊加原理之廣義馬克士威黏彈模型，隨後對受限於模具之凝膠試體進行加熱原位觀測，以實驗位移為基準於 Abaqus 中反覆迭代識別 CTE，並於俯視角雙軸拘束與側視角單側膨脹兩組配置下交叉比對。
結果顯示，兩種觀測配置反演之 CTE 在量級與形式上存在差異：俯視角於雙軸拘束下得乘冪函數 α(T) = 0.0245 × T^(-1.621)，將 24 小時預測誤差由 89% 降至 4–12%；側視角於半自由邊界下得等效 CTE 為 9.3 × 10⁻³ °C⁻¹，與實驗吻合度達 99.98%。此數量級差異表明，反演所得之 CTE 並非材料純粹之熱力學常數，而是反映幾何拘束、重力耦合與高溫黏性流動共同作用之表觀等效參數。
此外，針對修復後重新拉伸之大變形分析需求，並克服 FEM 於參數反演與大變形模擬之限制，本研究開發結合再生核質點法 (Reproducing Kernel Particle Method, RKPM) 與神經網路之混合求解器 (RKPM-NN)，於線彈性與線性黏彈性等基準例題中皆達到與傳統方法相近之精度，為後續自修復材料完整熱-力耦合模擬與自動化參數反算奠定方法學基礎。

Thermally triggered self-healing polymers, capable of autonomously healing cracks, hold substantial promise for biomedical applications and structural health maintenance. The coefficient of thermal expansion (CTE) plays a pivotal role in driving polymer flow and crack closure. However, the deep eutectic solvent (DES) ionogel investigated in this study exhibits a low mechanical modulus at room temperature, rendering conventional contact-based measurements prone to specimen deformation and precluding reliable CTE acquisition.
To overcome this limitation, this study integrates non-contact optical imaging with the finite element method (FEM) to establish an inverse identification framework. A generalized Maxwell viscoelastic model based on the time-temperature superposition principle was first constructed. In-situ heating observations were then conducted on mold-confined specimens, and the CTE was iteratively identified in Abaqus using experimental displacements as reference, with cross-validation between a top-view biaxially constrained setup and a side-view unilaterally expanding setup.
The results indicate that the CTE values inverted from the two observation configurations differ in magnitude and form. Under biaxial constraint, the top-view configuration yielded a power-law function α(T) = 0.0245 × T^(-1.621), reducing the 24-hour prediction error from 89% to 4–12%. Under a semi-free boundary, the side-view configuration yielded an equivalent CTE of 9.3 × 10⁻³ °C⁻¹, with 99.98% agreement against the experiment. This order-of-magnitude difference indicates that the identified CTE is not an intrinsic thermodynamic constant of the material, but rather an apparent equivalent parameter reflecting the combined effects of geometric constraints, gravitational coupling, and high-temperature viscous flow.
Furthermore, to address large-deformation analysis after healing and to circumvent the limitations of FEM in parameter inversion, a hybrid solver (RKPM-NN) combining the reproducing kernel particle method (RKPM) with neural networks was developed. Validated against linear elastic and viscoelastic benchmarks with accuracy comparable to conventional methods, the solver establishes a methodological foundation for fully coupled thermo-mechanical simulation of self-healing materials and automated parameter identification.

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