非均质结构动态非线性湿热-力学耦合问题的高效高阶多尺度方法及其收敛性估计
Efficient higher-order multi-scale method and its convergence estimate for dynamic nonlinear hygro-thermo-mechanical coupling problems of heterogeneous structures
AI总结：
本文提出高阶多尺度（HOMS）框架，构建含高阶修正项的多尺度渐近模型，推导误差估计并开发两阶段数值算法，经二维、三维实验验证其精度高、鲁棒性好且计算开销低。
AI中文摘要：
本文提出了一种新型高阶多尺度（HOMS）计算框架，用于高效、高精度、低成本地模拟非均质结构中的非线性湿热-力学（H-T-M）耦合问题。所研究模型的固有非线性主要源于温度或湿度相关的材料属性，该模型还考虑了放热、耗湿化学反应（如水化作用）引发的温度相关内热源及湿度汇项。本文主要贡献如下：其一，结合多尺度渐近方法与泰勒级数展开，为空间高度非均质的非均质结构非线性H-T-M耦合问题构建了包含高阶修正项的高精度多尺度渐近模型；其二，推导了多尺度渐近解的逐点及积分意义下的严格误差估计，从理论上证明了所提HOMS方法的必要性与优越性；其三，基于有限差分法与有限元法，开发了兼具离线与在线阶段的高效两阶段数值算法，并对其收敛性进行了严格证明；最后，开展了二维及三维数值实验以评估所提HOMS方法的计算性能，结果表明其具有优异的数值精度与鲁棒性，且计算开销较低。
英文摘要：
This paper presents a novel higher-order multi-scale (HOMS) computational framework for efficient, high-accuracy, and low-cost simulation of nonlinear hygro-thermo-mechanical (H-T-M) coupling problems in heterogeneous structures. The inherent nonlinearity in the investigated model stems primarily from temperature- or moisture-dependent material properties, and this model also accounts for temperature-dependent internal heat source and moisture sink terms induced by exothermic, moisture-consuming chemical reactions (e.g., hydration). The main contributions of this work are as follows. First, a high-accuracy multi-scale asymptotic model incorporating higher-order correction terms is constructed for nonlinear H-T-M coupling problems in heterogeneous structures with highly spatial inhomogeneity, using the multi-scale asymptotic approach together with Taylor series expansions. Second, rigorous error estimates in both point-wise and integral senses are derived for the multi-scale asymptotic solutions, which theoretically demonstrate the necessity and superiority of the proposed HOMS method. Third, an efficient two-stage numerical algorithm with off-line and on-line stages is developed, based on finite difference and finite element methods, and its convergence is also proved rigorously. Finally, two- and three-dimensional numerical experiments are performed to assess the computational performance of the proposed HOMS approach, showing excellent numerical accuracy and robustness with low computational overhead.
