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Continuum mechanics
About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.
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TL;DR: It is demonstrated that the breakdown of continuum mechanics can be understood as a result of the rough (multi-asperity) nature of the contact, and that roughness theories of friction can be applied at the nanoscale.
Abstract: Macroscopic laws of friction do not generally apply to nanoscale contacts. Although continuum mechanics models have been predicted to break down at the nanoscale, they continue to be applied for lack of a better theory. An understanding of how friction force depends on applied load and contact area at these scales is essential for the design of miniaturized devices with optimal mechanical performance. Here we use large-scale molecular dynamics simulations with realistic force fields to establish friction laws in dry nanoscale contacts. We show that friction force depends linearly on the number of atoms that chemically interact across the contact. By defining the contact area as being proportional to this number of interacting atoms, we show that the macroscopically observed linear relationship between friction force and contact area can be extended to the nanoscale. Our model predicts that as the adhesion between the contacting surfaces is reduced, a transition takes place from nonlinear to linear dependence of friction force on load. This transition is consistent with the results of several nanoscale friction experiments. We demonstrate that the breakdown of continuum mechanics can be understood as a result of the rough (multi-asperity) nature of the contact, and show that roughness theories of friction can be applied at the nanoscale.
802 citations
TL;DR: In this paper, finite element incremental formulations for non-linear static and dynamic analysis are reviewed and derived starting from continuum mechanics principles, and a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure.
Abstract: SUMMARY Starting from continuum mechanics principles, finite element incremental formulations for non-linear static and dynamic analysis are reviewed and derived. The aim in this paper is a consistent summary, comparison, and evaluation of the formulations which have been implemented in the search for the most effective procedure. The general formulations include large displacements, large strains and material non-linearities. For specific static and dynamic analyses in this paper, elastic, hyperelastic (rubber-like) and hypoelastic elastic-plastic materials are considered. The numerical solution of the continuum mechanics equations is achieved using isoparametric finite element discretization. The specific matrices which need be calculated in the formulations are presented and discussed. To demonstrate the applicability and the important differences in the formulations, the solution of static and dynamic problems involving large displacements and large strains are presented.
789 citations
Book•
01 Jan 1995
TL;DR: In this article, the authors describe the deformation and kinematics of a saturated porous medium, mass conservation, momentum balance, stress tensor, and linearized quasistatic evolution.
Abstract: Description of the Deformation and Kinematics of a Saturated Porous Medium, Mass Conservation. Momentum Balance, Stress Tensor. Thermodynamics of Open Continua. Linear Thermoporoelastic Behaviour. Poroplastic Behaviour. Hereditary Behaviours. Surfaces of Discontinuity. Linearized Quasistatic Evolutions in Thermoporoelasticity, Direct Methods of Resolution. Quasistatic Evolutions, Uniqueness of Solution, Numerical Methods of Resolution. Reactive Partially Saturated Porous Media. References. Index.
767 citations
TL;DR: In this paper, the basic properties of nonlinear Electromagnetic Solids are discussed. But they do not cover the properties of Elastic Ionic Crystals, Ferroelectrics and Ceramics.
Abstract: 1. Essential Properties of Electromagnetic Solids. 2. Elements of Continuum Mechanics. 3. General Equations of Nonlinear Electromagnetic Continua. 4. Elastic Dielectrics and Piezoelectricity. 5. Elastic Conductors. 6. Elastic Ferromagnets. 7. Elastic Ionic Crystals, Ferroelectrics and Ceramics. Appendices. Index.
765 citations
TL;DR: The advantages of a systematic application of the method of virtual power are exemplified by the study of continuous media with microstructure, and the equations of motion for the general micromorphic medium are established for the first time.
Abstract: The advantages of a systematic application of the method of virtual power are exemplified by the study of continuous media with microstructure. Results on micromorphic media of order one are easily found and the equations of motion for the general micromorphic medium are established for the first time. Various interesting special cases, which have been previously considered in the literature, may be derived upon imposing some convenient constraints. The paper ends with some comparisons with other related work.
763 citations