Boundary Element Methods for Steady-State Thermal-Mechanical Problems of Counterformal Contact

This paper presents a concise boundary integral equation framework for relating the thermal-mechanical surface load (the three traction components and the normal heat flux) to the thermal-mechanical response (the three quasi-static displacement components and the steady-state temperature). This uncoupled thermoelastic framework allows the simultaneous calculation of displacement and temperature—without subsurface discretization—because it is based on classical Green’s functions for displacement and for temperature and on newly derived Green’s functions for thermoelastic displacement. In general, the boundary element method (BEM) can be applied with this framework to finite geometry problems of steady-state thermal-mechanical contact. Here, example calculations are performed for counterformal contact problems, which can be modeled as contact on a halfspace. A linear element BEM is developed and compared with the constant element BEM for speed and accuracy. The linear element BEM uses newly derived influence coefficients for constant loads over an arbitrary triangular element, and these closed form expressions are used to improve the accuracy of the numerical algorithm. The constant element BEM uses the discrete convolution fast Fourier transform (DC-FFT) algorithm, which is based on influence coefficients for constant loads over rectangular elements. The quasi-static surface displacements and the steady-state surface temperature are calculated from an applied semi-ellipsoidal pressure with accompanying frictional heating effects. The surface thermal-mechanical behavior of the counterformal contact is shown in graphs vs. the radius, and the deviations from axisymmetry are highlighted.