Poisson coefficient

In order to calculate the value of the elastic modules in the local area of the studied material one should use the tabular values ps of density and of Poisson coefficient (v), or their quantity, determined by one of the certain standard methods ... 

It should be noted that at isothropic behaviour the shear stress equals G - (1/3)E when the ratio of the cross-sectional compression to the longitudinal extension (Poisson coefficient) is 0.5. 

It is also necessary to mention that certain configurations of bonds (local regions) can possess unusual properties—in particular, a negative Poisson coefficient vp < 0. Thus, for example, the chain of bonds shown in Fig. 52, when stretched out, not only lengthens but also thickens. If such a configuration constitutes the principal contribution to the macroscopic properties of the system, then the Poisson coefficient may be negative. 

Thus we can conclude that by making an appropriate choice for the structure of a random medium representing the inhomogeneous medium (the coordination number Z), we can obtain a material with a negative Poisson coefficient far from the percolation threshold. 

Figure 52. Lattice modulus with negative Poisson coefficient (a) lattice with coordination number N = 3 (b) a chain of bonds.

Once Klc was detennined, the fracture energy, GIc, was calculated with Youngs modulus and the Poisson coefficient, which were determined experimentally for every formulation following usual procedures. 

The cantilever deflection, Az, generated by a surface stress change, Act, (due to a biorecognition process, for example) depends on the microcantilevers dimensions (length L and thickness h) and its material s properties (Young s modulus E and Poisson coefficient v) following the Stoney s equation ... 

The Lame Ao, Go and the Poisson coefficients of intact rock are used as well as crack concentration v = N(a y This appears at the integration of the displacement jump over the... 

In the case of dilatant cracks we have the two equations for the Young modulus = 2(1 -I- v)G and the Poisson coefficient ... 

In Figure 4 the graphs of shear modulus G and the Poisson coefficient v are plotted for growing concentrations of cracks V. Curve 1 shows the decrease of G with growth of V. Curve 2 shows the practical constancy of the Poisson coefficient under changes of V. 

The use of fractal analysis makes it possible to relate molecular parameters to characteristics of supermolecular structure of polymers. Figure 11.12 illustrates the linear correlation between D and df [dj was estimated from Equation (11.27)] for epoxy polymers. When the molecular mobility is suppressed (D = 1), the structure of the polymer has the fractal dimension df = 2.5, which corresponds to p. = 0.25. The given value of the Poisson coefficient corresponds to the boundary of ideally brittle structure at p< 0.25, the polymer is collapsed without viscoelastic or plastic dissipation of energy [3]. This is fnlly consistent with the Kansch conclnsion [117] stating that any increase in the molecular mobility enhances dissipation of the mechanical energy supplied from the outside and, as a conseqnence, increases plasticity of the polymer. When D = 2 the df value is equal to 3, which corresponds to p = 0.5, typical of the rubbery state. 

From the other hand, determining of Y via the volumetric modulus E = 2P by the ratio (Eq. 60), we will again obtain the relationship by Eq. (62) t)q)e, comparing of which with the Eq. (110), we will obtain the expression for the Poisson coefficient in the well-known form Eq. (63). So, the Poisson coefficient both for the linear chains and for the polymeric stars in diluted and concentrated solutions is the universal function only on the Euclidian space. 

Due to the inherent symmetry of as-produced textile fabrics, woven composite plates are orthotropic. Their stiffness can be represented by engineering constants Young s modules shear modules Gy and Poisson coefficients py, ij= 1,...,3. If the reinforcement is deformed during production of the composite, or if the preform is net shaped, or for some knitted performs, then the assumption of orthotropy does not necessarily apply and the full stiffness matrix has to be introduced. 

The ratio of the lateral compression (w j, or Uyy) to the longitudinal tension is called the Poisson coefficient... 

Moreover, under the conditions of the same uniaxial stretching, the Poisson coefficient that reduces ASi to zero and iiicr< ascs AHi, predominates. This can also be directly... 

Figure 11 Influence of the Poisson coefficient on the first four eigenfrequencies.

---