Interfacial width and shape fluctuations and extensions of the Gaussian model of capillary waves

Interfacial density fluctuations are studied at the level of the Gaussian model of capillary waves by means of density functional theory. We consider nonrigid fluctuations and arrive at exact Triezenberg-Zwanzig-type expressions for new interfacial coefficients. These include a width tension, a width rigidity, and other coefficients linked to both shape and width distortions. We find for these coefficients magnitudes of the same orders as those of their tangential counterparts. The corresponding capillary-wave model describes the effect of fluctuations when the density is slowly varying, and the recognition of the additional quantities and their roles may help in the understanding of ellipsometric studies near critical points.     

On the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids

It is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density. We derive the explicit form that the functional takes for a system of hard rods, and propose an approximate one for hard spheres. Attractive interactions are also considered in mean-field approximation. In all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated.     

Experimental and numerical analysis of fretting crack formation based on 3D X-FEM frictional contact fatigue crack model

Nowadays, numerical simulation of 3D fatigue crack growth is easily handled using the eXtended Finite Element Method coupled with level set techniques. The finite element mesh does not need to conform to the crack geometry. Most difficulties associated to complex mesh generation around the crack and the re-meshing steps during the possible propagation are hence avoided. A 3D two-scale frictional contact fatigue crack model developed within the X-FEM framework is presented in this article. It allows the use of a refined discretization of the crack interface independent from the underlying finite element mesh and adapted to the frictional contact crack scale. A stabilized three-field weak formulation is also proposed to avoid possible oscillations in the local solution linked to the LBB condition when tangential slip is occurring. Two basic three-dimensional numerical examples are presented. They aim at illustrating the capacities and the high level of accuracy of the proposed X-FEM model. Stress intensity factors are computed along the crack front. Finally an experimental 3D ball/plate fretting fatigue test with running conditions inducing crack nucleation and propagation is modeled. 3D crack shapes defined from actual experimental ones and fretting loading cycle are considered. This latter numerical simulation demonstrates the model ability to deal with challenging actual complex problems and the possibility to achieve tribological fatigue prediction at a design stage based on the fatigue crack modeling.