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

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 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.