Continuum mechanics

About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.

Physics of lubricated impact of a sphere on a plate in a narrow continuum to gaps of molecular dimensions

Abstract: This paper investigates the phenomenon of lubricated impact dynamics of ellipsoidal bodies upon semi-infinite elastic solids, giving rise to Hertzian contact conditions. The analysis conforms to the numerical predictions and experimental findings of others, when the physics of motion of the lubricant can be described through Newtonian continuum mechanics, with the dominant viscous action embodied in the transient solution of Reynolds' equation. The equivalence of squeeze film action under impacting conditions with that of a converging gap in pure entraining motion is shown. This concept is extended to study the accelerative nature of the lubricant film surface, and its concordance with Reynolds' assumption through use of a relativistic frame of reference and hyperbolic geometry. When the investigation is extended to the case of ultra-thin film conjunctions of the order of a few to several molecular diameters of the intervening fluid layer, the physics of fluid film motion through impact involves more complex kinetic interactions. These include the effect of structural force of solvation, as well as that of a meniscus force, formed in such narrow conjunctions. The former, through active dispersion, tends to promote a structureless environment, whilst the latter through wetting action encourages the formation of a coherent film. This paper shows the interplay between these competing kinetics.

Theoretical modeling of the Casimir force-induced instability in freestanding nanowires with circular cross-section

Abstract: The Casimir force can induce instability and adhesion in freestanding nanostructures. Previous research efforts in this area have exclusively focused on modeling the instability in structures with planar or rectangular cross-section, while, to the best knowledge of the authors, no attention has been paid to investigate this phenomenon for nanowires with circular cross-section. In this study, effects of the Casimir force on the instability and adhesion of freestanding Cylinder–Plate and Cylinder–Cylinder geometries are investigated, which are commonly encountered in real nanodevices. To compute the Casimir force, two approaches, i.e. the proximity force approximation (PFA) for small separations and Dirichlet asymptotic approximation (scattering theory) for large separations, are considered. A continuum mechanics theory is employed, in conjunction with the Euler-beam model, to obtain constitutive equations of the systems. The governing nonlinear constitutive equations of the nanostructures are solved using two different approaches, i.e. the analytical modified Adomian decomposition (MAD) and the numerical finite difference method (FDM). The detachment length and minimum gap, both of which prevent the Casimir force-induced adhesion, are computed for both configurations.

Symmetry classes for even-order tensors

Abstract: The purpose of this article is to give a complete and general answer to the recurrent problem in continuum mechanics of the determination of the number and the type of symmetry classes of an even-order tensor space. This kind of investigation was initiated for the space of elasticity tensors. Since then, different authors solved this problem for other kinds of physics such as photoelectricity, piezoelectricity, flexoelectricity, and strain-gradient elasticity. All the aforementioned problems were treated by the same computational method. Although being effective, this method suffers the drawback not to provide general results. And, furthermore, its complexity increases with the tensorial order. In the present contribution, we provide general theorems that directly give the sought results for any even-order constitutive tensor. As an illustration of this method, and for the first time, the symmetry classes of all even-order tensors of Mindlin second strain-gradient elasticity are provided.

A Hygroelastic Self-consistent Model for Fiber-reinforced Composites

Abstract: Stress analyses are performed in unidirectional fiber-reinforced composites, exposed to ambient fluid, by extending a classical self-consistent model to hygroelastic solicitations. Constitutive laws are given for the macroscopic elastic properties and Coefficients of Moisture Expansion (CME) by considering a jump in moisture content between the fiber and the matrix. Inverse forms for the unknown CME of the constituent matrix are proposed. The macroscopic (ply) and local (fiber and matrix) internal stress states are evaluated for various moisture content ratios between the matrix and the ply. The macroscopic stresses are calculated by using continuum mechanics formalisms and the local stresses are deduced from the scale transition model.

Nonlinear Elliptic Equations

Abstract: Methods of the calculus of variations applied to problems in geometry and classical continuum mechanics often lead to elliptic PDE that are not linear. We discuss a number of examples and some of the developments that have arisen to treat such problems.