Inelasticity effects

As loading stresses approach or exceed the shear strength of a solid, inelastic effects are to be expected, and details of the behavior have been readily observed with modern, time-resolving measurement techniques. There are many observations of these behaviors. 

Shear-stress-shear-strain curves typical of fiber-reinforced epoxy resins are quite nonlinear, but all other stress-strain curves are essentially linear. Hahn and Tsai [6-48] analyzed lamina behavior with this nonlinear deformation behavior. Hahn [6-49] extended the analysis to laminate behavior. Inelastic effects in micromechanics analyses were examined by Adams [6-50]. Jones and Morgan [6-51] developed an approach to treat nonlinearities in all stress-strain curves for a lamina of a metal-matrix or carbon-carbon composite material. Morgan and Jones extended the lamina analysis to laminate deformation analysis [6-52] and then to buckling of laminated plates [6-53]. 

Chen Y-C, Zwolak M, Di Ventra M (2005) Inelastic effects on the transport properties of alkanethiols. Nano Lett 5(4) 621-624... 

During last years many new methods were developed to describe transport at finite voltage, with focus on correlation and inelastic effects, in particular in the cases when Coulomb blockade, Kondo effect and vibronic effects take place. 

The most comprehensive description of the tunneling problem is based either on a self-consistent solution of the Lippman-Schwinger equation [3] or on the non-equilibrium Green s function approach [4-8]. Inelastic effects within e.g. a molecule-surface interface can be included by considering multiple electron paths from the vacuum into the surface substrate [9], The current between two leads with the chemical potentials /ja and hb is given by the energy integral ... 

When a tunneling calculation is undertaken, many simplifications render the task easier than a complete transport calculation such as the one of [32]. Let us take the formulation by Caroli et al. [16] using the change induced by the vibration in the spectral function of the lead. In this description, the current and thus the conductance are proportional to the density of states (spectral function) of the leads (here tip and substrate). This is tantamount to using some perturbational scheme on the electron transmission amplitude between tip and substrate. This is what Bardeen s transfer Hamiltonian achieves. The main advantage of this approximation is that one can use the electronic structure calculated by some standard way, for example plane-wave codes, and use perturbation theory to account for the inelastic effect. In [33], a careful description of the Bardeen approximation in the context of inelastic tunneling is given, and how the equivalent of Tersoff and Hamann theory [34,35] of the STM is obtained in the inelastic case. 

This suggests that the rotational excitation may be associated entirely with the extended transition state rather than the presence of a molecular well with a different orientation in the exit channel. In summary, N2 recombination from Cu(l 11) follows a very similar pattern of energy release to that of H2 on the same surface, albeit with a much larger energy release. Desorption is dominated by N2 repulsion from the surface with little evidence for inelastic effects. 

Inelastic effects are exploited in the rapidly developing technique of high resolution electron energy loss spectroscopy (ELS or EELS) which permits identification of adsorbed molecules or molecular fragments by their vibrational spectra. Thus the method has much in common with the infrared spectroscopy of surfaces and, not surprisingly, the classic case of CO adsorption has received attention on Ni(lOO) and on stepped Ni and Pt surfaces. Other recent investigations of interest include H2 on organic species on Ni and Pt, and the observation of... 

As with metals, diffraction experiments using covalent crystals have proved difficult also. In this case the open structure should produce pronounced corrugation but with Si(lll) broad scattering distributions, showing no significant structure, were observedit is probable that inelastic effects are important in these systems. Very recently, however, high-quality patterns have been published by Cardillo and Becker... 

Fig. 8. Schematic of a molecular motor activated by intramolecular vibration energy relaxation of manifold A towards the rotor part of the motor. The rotor is positioned on an axis connected to reservoir 1 kept at a temperature T. Vibration manifold A is represented here by a simple molecular spring that can be excited by light or by the inelastic effect of a tunneling current passing through the molecular spring. Without such an excitation, manifold A is statistically populated by reservoir 1. A specific choice of a molecular structure equivalent to the spring may avoid its complete thermalization, for example by filtering the thermal noise giving rise to a unidirectional rotary motion...

The measurements of T and by LIE for diatomic ions (particularly N2 ) drifting in He have revealed no cooling due to inelastic effects, but Tef in those studies (<600 K) was far too low to populate the first excited vibrational state of N2. It is tempting to ascribe the small increase of inelastic effect from Cl or NO to N02 and NOs (Figure 2.19c) to the inelastic energy loss via excitation of ion vibrations growing as they get softer and their number increases, but that would be an overinterpretation of scarce data. 

Nonlinear fracture mecbanics is largely concerned with inelastic effects. 

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