Work of deformation

Parsegian, V. A., Fuller, N., and Rand, R. P. (1979). Measured work of deformation and repulsion of lecithin bilayers, Proc. 

The most common cause of it is the neglect of 3-dimensional effects as compared with those in two dimensions. Thus, all stresses in a loaded wire or ribbon are disregarded in the shrinkage method, Section III. 1. The work of deformation leading to rupture is a bulk effect which does not receive its due consideration in the calculation of fracture energy, Section III.3. Bulk deformations associated with thermal etching, Section III.4, demand more attention than was alloted to them by many scientists. The method of bubbles, Section III.5, is invalid both because of the above neglect (that is, that of the volume stresses around the bubble) and because of another popular error, namely an erroneous treatment of capillary pressure Pc. 

Gordon et al (Ref 14a), as quoted from Cook s book (Ref 17, p 271), discussed in detail the Trauzl Test and showed that the work of deformation did not vary linearly with the weight (or energy) of the expl, but instead the volume of expansion (vm) was related to the weight of expl chge (w) by the equation ... 

Rubber deformation occurs at nearly constant volume. The work of deformation dW is equal to the free energy dF at constant volume ... 

Rusanov, A.I. (1975). Theory of elastically of the wetting deformed bodies. 2. Equihbrium conditions and work of deformation with a finite contact angle. Colloid J. USSR, 37, 614-22. 

Because crack-tip plastic deformation would accompany crack growth, the work of deformation would contribute to the work of crack growth, or the fracture toughness (Kc or Gc) of the material. As such, Kc or Gc would vary as a function of thickness to reflect the changing constraint on crack-tip plastic deformation. Indeed, experimental observations show that the typical variation in fracture toughness with thickness (or B/ry) for a single material would be shown by the schematic diagram in Fig. 4.3. 

Mechanical equilibrium is established when small reductions in free energy due to formation of adhesive contact just balance small increases in mechanical work of deformation of the vesicle (8,11). Tnis variational statement leads to a direct relation between the free energy potential for adhesion and the suction pressure applied to tne adherent vesicle,... 

The work of deformation is stored, in this case, as heat energy. 

Insertion of this current chain length into eq. (6.43) gives the work of deformation... 

Most companies now use ethylidene norbornene as termonomer. EPT rubbers contain 15 double bonds per 1000 carbon atoms, whereas 1,4-cw-poly (butadiene) and l,4-cw-poly(isoprene) contain about 250 and 200 double bonds per 1000 carbons atoms, respectively. Consequently, EPT rubbers are much more stable to ozone than are the polydienes. Because of this, 20%-25% of EPR is added to NR or SBR to make tire walls. While 100% EPR tires can be used for automobiles, the work of deformation is too large for 100% EPR tires for trucks Too much heat is developed and the elasticity decreases. 

Under deformation, sections of chains between the network points are stretched. In a good approximation, elastomers do not change their volume under strain (Av = 0). Hence, the work of deformation (stretching) of a specimen is due only to the action of the applied force,/ According to 1st and 2nd Law of Thermodynamics, it might be separated in an energetic and entropic contribution ... 

Swelling Equilibrium Studies of Elastomeric Network Structures The elementary work of deformation of the swollen network is dW = f,dLv... 

The Equation of State for a Single Polymer Chain. The variation in the Helmholtz free energy is the negative of the work of deformation in isothermal elongation... 

The deformation of a system involves changes in the position, relative to the local frame, of portions of the system boundary. At a small surface element r of the boundary, the work of deformation is given in general by the expression ... 

As discussed above in Section II.A, the local work of deformation per unit surface can be written as ... 

This expression, which represents the work of deformation or elastically stored free energy per unit volume, completely defines the elastic properties of the rubber providing the eight assumptions made are valid. It will be noted that the chain length na does not appear in this equation nor are any details of the molecular structure of the rubber required. 

Since the Helmholtz free energy is the work function and the work of deformation is / dL (where L = a Li), as shown in the second equality, the elastic force may be obtained by differentiating Eq. (1.12), giving... 

A typical stress-strain isotherm obtained for a strip of cross-linked natural rubber as described above is shown in Fig. 1.11 [ 1-3]. The units for the force are generally newtons, and the curves obtained are usually checked for reversibility. In this type of representation, the area under the curve is frequently of considerable interest since it is proportional to the work of deformation w = / / dL. Its value up to the rupture point is thus a measure of the toughness of the material. 

Energy Stored, Energy Dissipated, and Work of Deformation in Transient Loading... 

The total work of deformation in tests such as those described above has two contributions, corresponding to the stored elastic energy and the energy dissipated as heat (assuming isothermal conditions). These can be formulated as allows for deformation in simple extension, the usual geometry for practical test procedures. 

For deformation at constant rate of tensile strain, e, the total work of deformation per unit volume is... 

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