Size-dependent thermomechanical contact analysis via boundary element formulation

We are currently in a new era of space exploration. Space agencies of several countries have been developing and conducting an unprecedented number of missions in the solar system and its other planets, and the stellar spaces beyond. Spacecraft and its payload structures including their mechanisms used for human and robotic space missions are operating in extreme thermal environments, which can potentially damage mission critical components and jeopardize mission success. It is well-known that high-quality predictions of contact stress are vital to achieve the optimal payload structure and mechanism structural designs. It is also widely recognized that the well-established predictive methodology is one of the essential approaches to accurately address contact analysis and fracture mechanics, which are crucial for spacecraft and payload structure design and development. In this paper, a boundary element method is developed to examine two-dimensional size-dependent thermomechanical contact problems of isotropic solids, where size-dependency is described by one characteristic material length scale parameter l and the thermal effect is quantified by the classical thermal expansion coefficient a and conductivity k. A Newton-based algorithm is employed to achieve convergence of the resulting nonlinear problem. This formulation is then used to solve a prototype thermomechanical frictionless contact problem to validate the robustness of the numerical implementation and to examine size-dependent response. The computational study shows that for a given contact half-width a both the total contact load and heat flux increase significantly with the inclusion of couple stresses. Furthermore, the stress and heat flux distributions deviate dramatically from those in classical thermomechanics in the vicinity of the contacting areas. Interestingly, the results also show that the location of maximum effective stress may in fact occur directly on the contacting surface. This may be very important in failure analysis, for example, when faced with potential surface pitting fatigue.