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

Changqing Ye; Eric T. Chung; Junzhi Cui

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arXiv · 2204.09253

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

Changqing Ye·Eric T. Chung·Junzhi Cui

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Abstract

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 $\epsilon$-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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Changqing Ye, Eric T. Chung, Junzhi Cui. 2022-04-20. Homogenization with quasistatic Tresca's friction law: qualitative and quantitative results. https://arxiv.org/abs/2204.09253

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