Small deformations, elastic behavior under

Under small deformations rubbers are linearly elastic solids. Because of high modulus of bulk compression (about 2000 MN/m ) compared with the shear modulus G (about 0.2-5 MN/m ), they may be regarded as relatively incompressible. The elastic behavior under small strains can thus be described by a single elastic constant G. Poisson s ratio is effectively 1/2, and Young s modulus E is given by 3G, to good approximation. 

As normally prepared, molecular networks comprise chains of a wide distribution of molecular lengths. Numerically, small chain lengths tend to predominate. The effect of this diversity on the elastic behavior of networks, particularly under large deformations, is not known. A related problem concerns the elasticity of short chains. They are inevitably non-Gaussian in character and the analysis of their conformational statistics is likely to be difficult. Nevertheless, it seems necessary to carry out this analysis to be able to treat real networks in an appropriate way. 

The word vixt oeUislic encompasses many fluids that exhibit both elasticity (solidlike behavior) and flow (liquid-like behavior) when sheared. Most concentrated pastes, emulsions, and gels are viscoelastic. Under small deformations, viscoelastic fluids literally behave as elastic solids under higher deformations they flow as liquids. 

Let us examine a structured system under the condition of uniform shear at constant temperature, T, and constant shear stress, t, which, in this case, acts as pressure, p. The behavior of such a system can be described using the thermodynamic potential (per unit volume), elastic deformations, which are very small at these low stresses, and focusing only on the elastic deformations associated with the change in particle configuration, we may state that U = const, S = S = 2(8), where is independent of the deformation e, and S2 = 2(8) is the configuration component of the entropy. Furthermore, e = 0 and 2= 0 at t = 0. 

For the meehanieal eonstitutive law, a linear elastic behavior of the gel is assumed - whieh is true for small deformations as it normally oeeurs, e.g., under eleelrieal stimulation. In diis ease, die relationship is expressed by the generalized Hooke s law... 

A plastic material is defined as one that does not undergo a permanent deformation until a certain yield stress has been exceeded. A perfectly plastic body showing no elasticity would have the stress-strain behavior depicted in Figure 8-15. Under influence of a small stress, no deformation occurs when the stress is increased, the material will suddenly start to flow at applied stress a(t (the yield stress). The material will then continue to flow at the same stress until this is removed the material retains its total deformation. In reality, few bodies are perfectly plastic rather, they are plasto-elastic or plasto-viscoelastic. The mechanical model used to represent a plastic body, also called a St. Venant body, is a friction element. The... 

Generally, the structure of the polymer-particle complex can be found from the minimization of free energy that includes the polymer-particle interaction energy, entropies of nonadsorbed monomer units and imits localized at the surface of the particle, and typically, for the system under consideration, the elastic deformation of crosslinked macromolecule. Such theoretical analysis, following the lines of [234,235], can explain the specific behavior of P(T,a) observed for the envelopes with different niunbers of crosslinks j [ 57 ]. According to [235], when the number of crosslinks is small enough, nj all jimc-... 

Ductile properties such as crack pattern and deformations prefiguring the nearing failure are important characteristics regarding the fracture behavior of structural concrete members. The tests demonstrated that in general TRC members have a distinctive ductile behavior although the stress-strain-behavior of the fabrics is linear-elastic until a brittle tensile failure. While the deformations under service loads (SLS) are rather small, the load-bearing behavior of the specimens is characterized by a distinctive stabilized crack pattern as well as high deformations in ultimate limit state (ULS) of L/30 - L/20. 

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