Mechanics of Elasticity

The upshot of all this is that the mechanics of elastic and plastic types of deformation spans a spectrum from the uncompromising and highly general rational... 

Contact mechanics of elastic solids with interfaces in non-equilibrium... 

J. H. Weiner. Statistical Mechanics of Elasticity. New York Wiley, 1983. 

This coacervation process forms the basis for the self-assembly, which takes place prior to the crosslinking. The assembly of tropoelastin is based on an ordering process, in which the polypeptides are converted from a state with little order to a more structured conformation [8]. The insoluble elastic fiber is formed via the enzymatic crosslinking of tropoelastin (described in Sect. 2.1). Various models have been proposed to explain the mechanism of elasticity of the elastin fibers. 

The main models are described in a review by Vrhovski and Weiss [8]. For ideal elastomers in the extended mode, all the energy resides on the backbone and can therefore be recovered upon relaxation [18]. Generally, it is believed that the mechanism of elasticity is entropy-driven, thus the stretching decreases the entropy of the system and the recoil is then induced by a spontaneous return to the maximal level of entropy [8]. 

Similar to the symmetrical disturbances, here again both mechanism of elasticity (equilibrium and dynamic) are important. The film deformation under the effect of various external non-local factors has been considered in [28]. 

The mechanism of the equilibrium elasticity acts until it is possible to provide a surfactant re-partition between the exterior and interior of the film. In a NBF such a repartition is not possible and this mechanism of elasticity ceases to act. The elasticity properties of bilayer films, in which the hydrodynamic and adsorption processes are characterised with normal time of relaxation, are due to Marangoni effect in the insoluble adsorption layers. That is why stable foams with black films are very sensitive to different local disturbances (heating, vibration, etc.). 

For Vo below the second threshold denoted by Vq, the kinetic friction is zero in the limit of quasi-static sliding that is, for sliding velocity v Q. That is, for Vo < Vq" the kinetic friction behaves like a viscous drag. For Vo > the dynamics is determined by the Prandtl Tomlinson-like mechanism of elastic instability, which leads to a finite kinetic friction. The threshold amplitude Vq increases with k and is always larger than zero. Therefore, in the commensurate case, vanishing kinetic friction does not imply vanishing static friction just like in the PT model. The FKT model for Vj, < Vo < is an example of a dry-friction system that behaves dynamically like a viscous fluid under shear even though the static friction is not zero. 

Statistical Mechanics of Elasticity by J. H. Weiner, John Wiley Sons, New York New York, 1983. Weiner s book has a number of interesting and useful insights into the meeting point between continuum mechanics and microscopic theories. 

Marangoni and Gibbs elasticity. The mechanism of elastic action of the adsorption layer can be represented as follows. Any deformation of the surface accompanying, for example, an increase in its area decreases the quantity of adsorbed surfactants per unit area. This decreases the surface pressure of surfactant molecules and hence increases the surface tension that counteracts further elongation of the surface. If the concentration of surfactants in the adsorption layer is small, then the two-dimensional gas of surfactant molecules is governed by the equation of state... 

As described above for elastin and resilin, the ability of elastomeric proteins to exhibit elasticity relies on the molecular movement, stmctural folding, and conformational freedom of individual components so that they can instantaneously respond to the applied force within a cross-linked network to distribute the stress throughout the system. Stretching initially will interrupt interactions between the loops such as hydrophobic interactions, hydrogen bonding, and electrostatic interactions, while at higher extensions a decrease in conformational entropy will be prevalent. To date, different models are proposed to explain the mechanisms of elasticity for resilin, based on the knowledge from elasticity models that have been proposed for elastin. 

As shown in Table 3, in aqueous solution these short resilin-like peptides adopt a mixture of PPII stmcture, unordered conformations, and p-tums, while in Ttifluoroethanol (TFE) primarily type-11 p tums populate the conformational space. These findings are consistent with what Andersen has predicted and are also very similar to other elastomeric proteins studied. Interestingly, coacervation, a common phenomenon in elastin and abductin (in which a protein-rich phase is formed when the temperature is raised), has not been observed in resilin-like polypeptides (RLPs). This is almost certainly due to the inaeased hydrophilicity of resilin, which is soluble in water under all relevant experimental conditions. As mentioned above, additional spectroscopic studies on extended RLPs, as well as manipulations of RLP sequences via the introduction of different amino acid analogs and evaluation of corresponding conformational changes, would be useful to elucidate the mechanism of elasticity of resilin. 

Painter, E. V. Mechanics of Elastic Performance of Textile Materials, Part VIII Graphical Analysis of Fabric Geometry. Tex. Res. J., 153-169 (1952). 

D.W. Urry and T.M. Parker, Mechanics of Elastin Molecular Mechanism of Biological Elasticity and its Relevance to Contraction. J. Muscle Res. Cell Motil., 23,541-557,2002. Special Issue, Mechanics of Elastic Biomolecules. H. Granzier, M. Kellermayer, W. Linke, Editors. 

Early reviews are available on the development of the molecular conformation of the tetrapep-tide, pentapeptide, and hexapeptide repeating sequences of elastin and on the mechanism of elasticity of the basic elastic-contractile model protein. These may be sought for historical background. Recent reviews of the mechanism of elasticity and its relation to contractility may be examined for a more... 

This mechanism of elasticity provides a common groundwork of explanation for the elasticity of all chain molecules regardless of composition and structure as long as there exists an internal chain motion that becomes decreased on deformation. For this reason, it too is a consilient mechanism. To delineate this consilient mechanism for elasticity from the consilient mechanism for hydrophobic association, as treated extensively in this volume, it will be referred to as the elastic consilient mechanism. 

Historically, the question of mechanism of elasticity has been one of evaluating the relative contributions of three different proposed mechanisms (1) the random chain network (classic rubber elasticity) theory, - (2) the solvent entropy theory, and (3) the damping of internal chain dynamics on extension. Ttie first is due to the Flory school the second was initiated by Weis-Fogh and Andersen, and the third is due to the present author and coworkers of the last quarter century. 

D.W. Urry, C.M. Venkatachalam, M.M. Long, and K.U. Prasad, Dynamic p-Spirals and A Librational Entropy Mechanism of Elasticity. ... 

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