Energy of deformation

Chapter 8 Nominal and True Stress and Strain, Energy of Deformation... 

Hence, from Eqs. (68) and (69) one can conclude that the change in volume due to torsion does not contribute to the free energy of deformation, that torsion is accompanied by a decrease in volume and that this volume decrease is a parabolic function of the twisting angle. 

According to the models, the free energy of deformation and the stress in the network with constrained chains contains an additive contribution to that describing... 

The free energy of deformation in the sliplink model is57)... 

Free energy of deformation of solids ftee enthalpy... 

Theoretical calculations on 3,4-benzophenanthrene (3) and tetrabenzo-naphthalene (4) indicate that the potential energy of deformation arising from out-of-plane bending and ring-angle distortion is of the same order, but that the combined effect of both is much smaller than either separately. 

Several attempts have been made to explain theoretically the effects of flow on the phase behavior of polymer solutions [112,115-118,123,124]. This has been done by modification of the mean-field free energy. The key point is to include properly the elastic energy of deformation produced by flow. A more rigorous approach originates from Helfand et al. [125, 126] and Onuki [127, 128] who proposed hydrodynamic theories for the dynamics of concentration fluctuations in the presence of flow coupled with a linear stability analysis. 

To understand elastic mechanical properties, the discussion of the storage of energy of deformation provides a powerful approach. Dynamic mechanical measurements at higher strain on filled silicone elastomers show that the energy of deformation may be related to an entropic and an enthalpic part. The entropic part is mainly due to the restriction of the conformational space of the polymer chain by the presence of the solid silica particles. Whereas the enthalpic part of the energy of deformation is related to... 

It was shown above that the number of adsorption junctions as well as their strength strongly depends both on temperature and the type of Aerosil surface. Therefore, an analysis of the temperature dependence of the modulus and the energy of deformation can be of use for understanding the role of chain adsorption in these properties. 

Using formula (13.148), one can demonstrate that function W describes the potential energy of deformations, i.e. the work performed by the external stresses and volume forces in order to produce the given deformations in the elastic body. Indeed, if the body, affected by those forces, changes from its initial state of rest (in the absence of deformations) into a new state of rest under deformations, then, as seen from (13.148), it appears that... 

The total free energy of deformation per unit volume is the sum of Wi and W2. For large N, the entanglement contribution to network elasticity becomes... 

High static and dynamic flexibility of the polysiloxane chain, associated with a very low energy barrier to rotation around their skeletal bonds and a low energy of deformation of the SiOSi bond angle, make the polymer soluble in many solvents. The catalyst attached to such a mobile polymer chain, which can adopt many conformations, is available for the interaction with reactants in a... 

For a confined powder which is composed of the particles the response to the application of stress follows the steps discussed above. That is, before the transmission of stress to an individual particle in the body of the powder is the same as if it were directly stressed, the particles have to rearrange to allow multiple points of inter-particulate contact and approach the Tully dense" state (relative to the individual particles). This results in a lag in the stress-strain prorile however the yield point and energy of deformation should remain close to that of the individual particle property once corrected for the number of particles in the powder. A schematic stress-strain prorile for a particle and for a powder made up of the particles is illustrated in Figure 2A. Figure 2B shows the same plots normalized. 

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