On Surrogate Duality and Competition Between Entropy and Potential Energy in the Finite Element Model of Elastic Contact Mechanics

The competition between entropy and energy that usually occurs in thermodynamics - an increase in one usually leads to a decrease in the other - was also shown to hold in static-elastic contact mechanics in our previous work on solving contact problems with an iterative algorithm. In this paper, we first present a theoretical analysis of the surrogate duality of the optimization model of contact problems, propose several propositions characterizing the surrogate duality, and identify the condition under which the fractional objective function of the surrogate dual problem is quasi concave. Second, we further clarify the correspondence between the concepts of statistical physics and the finite element model of contact problems so that the concepts of statistical physics can be more cleanly used to solve contact problems. Third, we provide examples to calculate the contact force with an improved iterative algorithm based on the quasi concavity that more clearly verifies the competition between entropy and potential energy, and the competition shows strong negentropy behavior: potential energy increases while entropy decreases throughout the iterative process.