Homogenization with quasistatic Tresca's friction law: qualitative and quantitative results

04/20/2022

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by   Changqing Ye, et al.

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The problems of frictional contacts are the key to the investigation of mechanical performances of composite materials under varying service environments. The paper considers a linear elasticity system with strongly heterogeneous coefficients and quasistatic Tresca's friction law, and we study 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 the H^1 norm for the periodic homogenization. We also design several numerical experiments to validate the convergence rates in the quantitative analysis.