含准静态Tresca摩擦定律的均匀化：定性与定量结果
Homogenization with quasistatic Tresca's friction law: qualitative and quantitative results
AI总结：
该研究针对含强非均匀系数与准静态Tresca摩擦定律的线弹性系统，在H-收敛和小ε-周期框架下开展均匀化研究，得到定性收敛结论与H¹范数定量误差估计，并通过数值实验验证收敛速率。
摘要：
摩擦接触建模对于研究复合材料在不同服役环境下的力学性能至关重要。本文考虑一类具有强非均匀系数和准静态Tresca摩擦定律的线弹性系统，在H-收敛和小ε-周期性框架下研究其均匀化理论。定性结果基于H-收敛，证明原振荡解将弱收敛至均匀化解；定量结果则给出了周期均匀化问题在H¹范数下的渐近误差估计。本文还设计了若干数值实验，以验证定量分析中的收敛速率。
英文摘要：
Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments. The paper considers a linear elasticity system with strongly heterogeneous coefficients and quasistatic Tresca friction law, and studies the homogenization theories under the frameworks of H-convergence and small $ε$-periodicity. The qualitative result is based on H-convergence, which shows the original oscillating solutions will converge weakly to the homogenized solution, while our quantitative result provides an estimate of asymptotic errors in $H^1$-norm for the periodic homogenization. This paper also designs several numerical experiments to validate the convergence rates in the quantitative analysis.
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