Solids macroscopic/microscopic length scales

A traditional explanation of solid friction, which is mainly employed in engineering sciences, is based on plastic deformation.12 Typical surfaces are rough on microscopic length scales, as indicated in Figure 3. As a result, intimate mechanical contact between macroscopic solids occurs only at isolated points, typically at a small fraction of the apparent area of contact. 

Figure 6.1 Illustration of microscopic and macroscopic length scales in gases, liquids, and solids.

Quantum mechanics is the theory that captures the particle-wave duality of matter. Quantum mechanics applies in the microscopic realm, that is, at length scales and at time scales relevant to subatomic particles like electrons and nuclei. It is the most successful physical theory it has been verified by every experiment performed to check its validity. It is iso the most counter-intuitive physical theory, since its premises are at variance with our everyday experience, which is based on macroscopic observations that obey the laws of classical physics. When the properties of physical objects (such as solids, clusters and molecules) are studied at a resolution at which the atomic degrees of freedom are explicitly involved, the use of quantum mechanics becomes necessary. 

While an explicit treatment of the microscopic, atomistic degrees of freedom is necessary when a locally realistic approach is required, on a macroscopic level the continuum framework is perfectly adequate when the relevant characteristics are scalar, vector, or tensor fields (e.g., displacement fields for mechanical properties). A combination of the two levels of description would be useful [29,30]. Here we focus on the deformation of solids The elastic mechanics of homogeneous materials is well understood on the atomistic scale and the continuum theory correctly describes it. Inelastic deformation and inhomogeneous materials, however, require techniques that bridge length and time scales. 

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