USE OF CONSTRUCTAL LAW TO PROOF THE MAXIMUM WORK “PRINCIPLE” FOR BOTH BULK PLASTICITY AND CONTACT SURFACE FRICTION. APPLICATION TO ANISOTROPIC TRIBOLOGICAL BEHAVIOUR

Abstract

Along this scientific article, it is propose to proof the Maximum Work “Principle” used by materials plasticity theory starting from a constrained optimisation problem based on Constructal Law developed by prof. Adrian BEJAN of DUKE University (USA). This law postulate that all finite-size system searche to flow more and more easily over the time and to evolve in those configurations or shape distributing their imperfections to minimize losses or dissipations and entropy variation. On the mechanical point view, if add the thermodynamics principles (energy conservation and system’s entropy evolution), starting from the first Newton law (describing equation of momentum balance and its equivalent form of virtual power principle), together with the natural tendency of all currents to flow from high to low values, it can be conclude that under external loadings, all material flow search to minimize the dissipated powers of both deformation and friction. So between all other virtual states corresponding to virtual mechanical variables values (stress, strain, strain rate) the real ones are those that minimize the total dissipated power. It is then obtained a minimization problem, which proofs mathematically that the Maximum Work “Principle”, applied to both bulk plastic deformations and surfaces frictions for all continuum media: solid, fluid, mushy state,…, is a consequence of Constructal Law. It is an original mathematical proof corresponding to plasticity mechanics and tribology never presented until now by previous scientific studies of other researchers. Following the obtained sub-sequent theorems of potential convexity and associated normal rule laws, it is then possible to describe the materials elastic-plastic flow and the surface friction in a more general framework for both isotropic or anisotropic rheological and tribological properties. The validation of an elliptic anisotropic formulation of Coulomb law to predict the static and kinetic friction coefficients, as a function of different sliding directions, it is develop using experimental data given by a Pin-on-Plane Tribometer in the case of anisotropic metal/isotropic polymer contact interfaces (AA20124-351 rolling thick plate/UHMWPE cylindrical pion). Furthermore, it is estimate the differences observed between the friction shear orientations and the sliding velocity directions proven in the case of anisotropic contact surface the dependency of friction coefficient also with sliding direction.