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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: In this article, a simple model is constructed to predict the size dependence of the effective stiffness of the structural element, and the important length scale in the problem is identified to be the ratio of the surface elastic modulus to the elastic modulation of the bulk.
Abstract: Effective stiffness properties (D) of nanosized structural elements such as plates and beams differ from those predicted by standard continuum mechanics (Dc). These differences (D-Dc)/Dc depend on the size of the structural element. A simple model is constructed to predict this size dependence of the effective properties. The important length scale in the problem is identified to be the ratio of the surface elastic modulus to the elastic modulus of the bulk. In general, the non-dimensional difference in the elastic properties from continuum predictions (D-Dc)/Dc is found to scale as αS/Eh, where α is a constant which depends on the geometry of the structural element considered, S is a surface elastic constant, E is a bulk elastic modulus and h a length defining the size of the structural element. Thus, the quantity S/E is identified as a material length scale for elasticity of nanosized structures. The model is compared with direct atomistic simulations of nanoscale structures using the embedded atom method for FCC Al and the Stillinger-Weber model of Si. Excellent agreement between the simulations and the model is found.
1,648 citations
TL;DR: In this article, the authors derived the general solution of a wave equation describing the dynamics of two-layer viscoelastic polymer materials of arbitrary thickness deposited on solid (quartz) surfaces in a fluid environment.
Abstract: We have derived the general solution of a wave equation describing the dynamics of two-layer viscoelastic polymer materials of arbitrary thickness deposited on solid (quartz) surfaces in a fluid environment. Within the Voight model of viscoelastic element, we calculate the acoustic response of the system to an applied shear stress, i.e. we find the shift of the quartz generator resonance frequency and of the dissipation factor, and show that it strongly depends on the viscous loading of the adsorbed layers and on the shear storage and loss moduli of the overlayers. These results can readily be applied to quartz crystal acoustical measurements of the viscoelasticity of polymers which conserve their shape under the shear deformations and do not flow, and layered structures such as protein films adsorbed from solution onto the surface of self-assembled monolayers.
1,455 citations
01 Jan 1997
TL;DR: Panagiotopoulos, O.K.Carpinteri, B. Chiaia, R. Gorenflo, F. Mainardi, and R. Lenormand as mentioned in this paper.
Abstract: A. Carpinteri: Self-Similarity and Fractality in Microcrack Coalescence and Solid Rupture.- B. Chiaia: Experimental Determination of the Fractal Dimension of Microcrack Patterns and Fracture Surfaces.- P.D. Panagiotopoulos, O.K. Panagouli: Fractal Geometry in Contact Mechanics and Numerical Applications.- R. Lenormand: Fractals and Porous Media: from Pore to Geological Scales.- R. Gorenflo, F. Mainardi: Fractional Calculus: Integral and Differential Equations of Fractional Order.- R. Gorenflo: Fractional Calculus: some Numerical Methods.- F. Mainardi: Fractional Calculus: some Basic Problems in Continuum and Statistical Mechanics.
1,389 citations
TL;DR: In this paper, a continuum mechanics approach to two-phase flow is reviewed and an averaging procedure is applied to the exact equations of motion, and the nature of the resulting equations is studied.
Abstract: : A continuum mechanics approach to two-phase flow is reviewed. An averaging procedure is discussed and applied to the exact equations of motion. Constitutive equations are supplied and discussed for the stresses, pressure differences and the interfacial force. The nature of the resulting equations is studied. (Author)
1,347 citations
Book•
01 Jan 1987
TL;DR: In this article, the authors introduce the Continuum Approach to Earth Rheology from microphysics, which is based on the atomic basis of deformation, elasticity, strength, failure and plasticity.
Abstract: Preface. Introduction to the second edition. Introduction to the first edition. Part One: Rheology of Continua. 1. Continuum mechanics and rheology. 2. Stress, deformation and strain. 3. Elasticity. 4. Flow, strain rate and viscosity. 5. Strength, failure and plasticity. Part Two: The Continuum Approach to Earth Rheology. 6. The short timescale: seismological Earth models. 7. Temperature and heat transfer. 8. The long timescale: geodynamics and plate tectonics. Part Three: The Microphysical Approach to Earth Rheology. 9. The atomic basis of deformation. 10. Creep of polycrystals at high temperature and pressure. 11. Deformation maps and isomechanical groups. 12. Earth rheology from microphysics. References. Acknowledgements. Index.
1,342 citations