A numerical-modelling method is developed to investigate the stress of the static-equilibrium state of the two-dimensional frictional contact problem achieved through a quasistatic process of increasing loading. The problem of relative tangential displacement between particles on the two contact surfaces is addressed. This scheme relies on solving each of the two contact solids in turn and iterating back and forth. The solutions for the two elastic bodies are connected through the surface traction and surface deformation. The contact surface is approximated by a cubic spline, and friction is modelled using the classical Coulomb friction law. Variational inequalities and finite-element methods are used to implement this scheme and are solved by an optimization method. In addition, the distinction between Cauchy stress and PiolaKirchoff stress is taken into account and discussed. A numerical investigation is conducted into the stress dependence on the loading conditions and geometries of the solids. The results from the numerical examples deviate from Hertz theory and previous reports. Stress is shown to be sensitive to the loading distribution and geometry of contact solids. Therefore, it suggests that an accurate analysis of the dry frictional contact problem requires a refined knowledge of the loading conditions and the total geometry of both solids. PACS Nos.: 03.40D, 46.30P, 62.20P
Frictional contact problem with wear for electro-viscoelastic
materials with long memory
