Continuous Matter

4 Key excerpts on "Continuous Matter"

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  eBook - ePub

  Understanding Physics

  • Michael M. Mansfield, Colm O'Sullivan(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  10 Continuum mechanics: mechanical properties of materials: microscopic models of matter

  AIMS

  • to describe mechanical properties of materials through models in which the materials involved are considered to be continuous throughout the bulk matter
  • to explain the elastic nature of solids and the general properties of fluids
  • to develop a simple model of gases at low pressure (called the kinetic theory of gases) which is based on their microscopic composition; to see how this model may be modified when the effect of the range of molecular forces and/or molecular size is taken into consideration
  • to discuss microscopic models of liquids and solids which give further insight into their mechanical properties

  10.1 Dynamics of continuous media

  While we know from discussions in Chapter 1 that matter in bulk is formed from large collections of particles such as atoms or molecules, attempts to describe the macroscopic properties of materials on this basis can be difficult and non‐productive. Our everyday experience of matter, in any event, is of continuous media; a block of metal appears continuous throughout, the air in the room shows no obvious evidence of being anything other than a continuous substance filling the room. Accordingly, we will begin our study of the properties of materials with a model in which matter is assumed to be continuous. Later in this chapter we shall see how many general properties, described at the macroscopic level, may be explained from a microscopic viewpoint; microscopic theories often give us insight into both the basic nature of these properties and the fundamental interatomic or intermolecular forces.

  Materials seem to fall naturally into two broad categories – solids and fluids. Solids generally retain their shape under the influence of external forces, although they may show temporary distortions while such forces are applied. Fluids, as the name implies, are materials which can flow and are usually divided into two subcategories, liquids and gases. In the laboratory, a liquid settles to the bottom of the vessel into which it is poured – its volume does not change – while a gas, on the other hand, expands to fill the whole container to which it is confined. These broad categories of different states of matter are not quite as clear‐cut as implied above; matter can also appear in other forms, such as vitreous (glassy) materials or plasmas (ionised gases), which do not fit into the simple categories of solids, liquids or gases.

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  eBook - PDF

  Continuum Mechanics

  Elasticity, Plasticity, Viscoelasticity

  • Ellis H. Dill(Author)
  • 2006(Publication Date)
  • CRC Press

    (Publisher)

  1 1 Fundamentals of Continuum Mechanics 1.1 MATERIAL MODELS This book deals with large-scale mechanics of materials. Although matter is com-posed of minute discrete particles acting upon each other in some de fi nite way, engineering applications typically deal with the gross in fl uence of the presence of the material in some region of space that would contain an extremely large number of such particles. The effect of an individual particle is not detectable and experiments can be interpreted by a theory that ignores the existence of discrete particles and instead imagines matter to consist of a smooth distribution of material, in fi nitely divisible into smaller and smaller portions, each composed of smoothly distributed material. Such a hypothetical material is referred to as a continuous medium. In continuum theories, a body is a set of elements that are in one-to-one corre-spondence with the points of a region of Euclidean three-space at each instant of time. This region is called the con fi guration of the body. Associated with the body are certain physical entities, such as mass and energy, which are smoothly distributed over the body. Discontinuous changes in these entities are allowed at isolated points, lines, or surfaces. Such discontinuities may be interpreted as a fracture surface, a shock wave, a vortex sheet, etc.; they divide the material into parts that may each be treated as a continuum. The material may be satisfactorily treated as a continuum when the distance between the real physical particles is very small compared to the characteristic dimensions of the problem. Thus, the continuum theory will apply to gases, liquids, and solids in most instances. Such classical theories as aerodynamics, fl uid mechan-ics, elasticity, viscoelasticity, and plasticity are special branches of continuum mechanics. On the other hand, the kinetic theory of gases is not a continuum theory.

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  Physics of Continuous Matter

  Exotic and Everyday Phenomena in the Macroscopic World

  • B. Lautrup(Author)
  • 2011(Publication Date)
  • CRC Press

    (Publisher)

  The microscopic world impinges upon the macroscopic almost only through material con-stants, such as coefficients of elasticity and viscosity, characterizing the interactions between macroscopic amounts of matter. It is, of course, an important task for the physics of materi-als to derive the values of these constants, but this task lies outside the realm of continuum physics. It is nevertheless sometimes instructive to make simple models of the underlying atomic or molecular structure in order to obtain an understanding of the origin of macroscopic phenomena and of the limits to the continuum description. This chapter paints in broad outline the transition from molecules to Continuous Matter, or mathematically speaking from point particles to fields. It is emphasized that the macro-scopic continuum description must necessarily be statistical in nature, but that random statis-tical fluctuations are strongly suppressed by the enormity of the number of molecules in any macroscopic material object. The modern fields of nanophysics and biophysics straddle the border between the continuum and particle descriptions of matter, resulting in numerous new phenomena outside the scope of classical continuum physics. These topics will not be covered here. The central theme of this book is the recasting of Newton’s laws for point particles into a systematic theory of Continuous Matter, and the application of this theory to the wealth of exotic and everyday phenomena in the macroscopic material world. 2 PHYSICS OF Continuous Matter Figure 1.1. How Continuous Matter really looks at the atomic scale. Noise-filtered image of freshly cleaved Mica obtained by atomic force microscopy, approximately 225 Angstrom on a side. This gran-ularity of matter is ignored in continuum physics. (Source: Mark J. Waner, PhD dissertation, Michigan State University, 1998. With permission.) 1.1 Molecules H 2 H 2 C H 2 O H 2 O ! O 2 The quantitative meaning of a chemical formula.

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  Introduction to Nanoscience

  • Gabor L. Hornyak, Joydeep Dutta, H.F. Tibbals, Anil Rao(Authors)
  • 2008(Publication Date)
  • CRC Press

    (Publisher)

  Indeed, a good intuitive understanding of quantum mechanics is a prerequisite for a thorough understanding of chemistry, physics, and materials science. Why? Because nanotechnology is all about a finite number of atoms or molecules that together are the basic building blocks of everything and so small that they are inherently quantum mechanical. For example, within an atom or molecule, negatively charged electrons are trapped in the neighborhood of one or more (positively charged) atomic nuclei because of the attraction the electrons have for the nuclei and repulsions for other electrons. These electrons only have certain energies that correspond to the 1s, 2p, etc. orbitals we learned in freshman chemistry. For some nanomaterials, electrons can also be trapped and exhibit only certain allowed energies. Following this chapter, we present a special chapter about nanothermodynamics. We adhere to strict thermodynamic topics and hope to shed light on the energetic relationships of nanoscale materials: Are those relationships worthy of form-ing the foundation of a new discipline called nanothermodynamics? You decide! 7.0 M ATERIAL C ONTINUUM The concept of “continuum” (from the Latin continuus, meaning “uninterrupted”) is ingrained in everything surrounding us. The definition of a continuum is a continuous extent, or whole, no part of which can be distinguished from neigh-boring parts except by arbitrary division. Many examples of common continua exist around us—those of language, mathematics, mechanics, time, radiation, and others. The matter–energy con-tinuum implies that all matter and all energy are convertible through E = mc 2 . The material continuum implies that there is a smooth transition from the bulk world into the quantum domain. This statement is completely true in the sense that all materials are made of atoms and molecules and that nanomaterials simply have progressively fewer of them.

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