Homogenization with the Quasistatic Tresca Friction Law: Qualitative and Quantitative Results

Abstract

Modeling of frictional contacts is crucial for investigating mechanical perforances 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 the author’s 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.

Keywords

Homogenization / Frictional contact mechanics / Quasistatic Tresca friction law

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