Parallel Elastic Component

The analytic validity of an abstract parallel elastic component rests on an assumption. On the basis of its presumed separate physical basis, it is ordinarily taken that the resistance to stretch present at rest is still there during activation. In short, it is in parallel with the filaments which generate active force. This assumption is especially attractive since the actin-myosin system has no demonstrable resistance to stretch in skeletal muscle. However, one should keep in mind, for example, that in smooth muscle cells there is an intracellular filament system which runs in parallel with the actin-myosin system, the intermediate filament system composed of an entirely different set of proteins, (vimentin, desmin, etc.), whose mechanical properties are essentially unknown. Moreover, as already mentioned, different smooth muscles have different extracellular volumes and different kinds of filaments between the cells. 

Fig. 14. Diagram of the parallel elastic component of vertebrate skeletal muscle sarcomere. Connectin filaments originating from the edges of the central bare zone of a thick (myosin) filament run through the thin (aclin) filament to the Z lines.

As was already discussed at length above, connectin is a very long, flexible elastic fllament linking the myosin filament to the Z lines in vertebrate skeletal muscle. Therefore, it is very plausible that connectin serves as the parallel elastic component in a myofibril (Fig. 14). The elastic nature of connectin filaments appears to make possible the passive tension generation when a myofibril is stretched beyond the overlap of the thick and thin filaments (Natori, 1954). It also explains why such overstretched myofibrils slowly return to the original state upon release (Natori, 1954). 

The use of a parallel plate plastimeter to determine both softness and recovery is a simple way of obtaining a measure of both the viscous and elastic components on deformation behaviour, albeit under conditions somewhat removed from those met during processing. An alternative approach is to measure the stress relaxation in a test piece and this was the basis of the Stress Relaxation Processibility Tester developed at RAPRA. 

The reaction of the arteriolar wall to changes in the blood pressure is considered to consist of a passive, elastic component in parallel with an active, muscular response. The elastic component is determined by the properties of the connective tissue, which consists mostly of collagen and elastin. The relation between strain e and elastic stress ae for homogeneous soft tissue may be described as [18] ... 

If / and /x are the effective step lengths (monomer length) for the random walks parallel and perpendicular to the ordering direction (in the isotropic phase / =/x= o)> respectively, and under the assumption that the deformation occurs without a change of volume, the following relation is obtained for the elastic component of the free energy in the nematic phase... 

With a blend or composite of sheats of both components arranged alternately in parallel, all components are subject to the same stress. The shear modulus analogously, the modulus of elasticity E, the viscosity 17, the... 

The most direct way to study arterial viscoelasticity is to determine the response of the test tissue to oscillatory stresses. If the arterial wall is conceived to be represented by a simple Kelvin-Voigt model consisting of a spring and a dashpot in parallel, the dynamic elastic component and the viscous component of a vessel can be expressed as... 

The viscoelastic properties of a polymeric material can be described by its reversible and irreversible responses to deformation. These can be identified most easily by dynamic mechanical analysis (DMA). Usually, the adhesive is placed between two parallel plates, one of which is oscillating sinusoidally, and the torque is measured. From the amplitude and the phase shift of the sinusoidal stress - strain curve, the elastic component, which is in phase, and the viscous component, which is 90° out of phase, can be derived [211, p. 158 if]. 

Various mathematical models that describe yielding behavior of metals can represent the hysteretic behavior of metallic dampers such as the standard Bouc-Wen model (Wen 1976). The standard Bouc-Wen model results from the parallel combination of an elastic component and an... 

Skeletal muscles are the only actuators in the human body. A skeletal muscle is composed of two types of structural components active contractile elements and inert compliant materials. The contractile elements are contained within the muscle fibers. The fibers vary in length from a few millimeters to more than 40 cm, and their width is between 1 and 150 im. Approximately, 85% of the mass of a muscle consists of the muscle fibers composed from sarcomeres, while the remaining 15% is largely composed of the connective tissue, which contains variable proportions of collagen, reticular, and elastic fibers. The connective tissues provide an arrangement of simple, spring-like elements (elastic components of the muscle) that exist both in series and in parallel with the contractile elements. 

Using the equilibrium equations of the elasticity theory enables one to determine the stress tensor component (Tjj normal to the plane of translumination. The other stress components can be determined using additional measurements or additional information. We assume that there exists a temperature field T, the so-called fictitious temperature, which causes a stress field, equal to the residual stress pattern. In this paper we formulate the boundary-value problem for determining all components of the residual stresses from the results of the translumination of the specimen in a system of parallel planes. Theory of the fictitious temperature has been successfully used in the case of plane strain [2]. The aim of this paper is to show how this method can be applied in the general case. 

In integrated photoelasticity it is impossible to achieve a complete reconstruction of stresses in samples by only illuminating a system of parallel planes and using equilibrium equations of the elasticity theory. Theory of the fictitious temperature field allows one to formulate a boundary-value problem which permits to determine all components of the stress tensor field in some cases. If the stress gradient in the axial direction is smooth enough, then perturbation method can be used for the solution of the inverse problem. As an example, distribution of stresses in a bow tie type fiber preforms is shown in Fig. 2 [2]. 

We commented above that the elastic and viscous effects are out of phase with each other by some angle 5 in a viscoelastic material. Since both vary periodically with the same frequency, stress and strain oscillate with t, as shown in Fig. 3.14a. The phase angle 5 measures the lag between the two waves. Another representation of this situation is shown in Fig. 3.14b, where stress and strain are represented by arrows of different lengths separated by an angle 5. Projections of either one onto the other can be expressed in terms of the sine and cosine of the phase angle. The bold arrows in Fig. 3.14b are the components of 7 parallel and perpendicular to a. Thus we can say that 7 cos 5 is the strain component in phase with the stress and 7 sin 6 is the component out of phase with the stress. We have previously observed that the elastic response is in phase with the stress and the viscous response is out of phase. Hence the ratio of... 

It has been shown that the anisotropy depends on the orientation of the diagonals of indentation relative to the axial direction 14). At least two well defined hardness values for draw ratios A. > 8 emerge. One value (maximum) can be derived from the indentation diagonal parallel to the fibre axis. The second one (minimum) is deduced from the diagonal perpendicular to it. The former value is, in fact, not a physical measure of hardness but responds to an instant elastic recovery of the fibrous network in the draw direction. The latter value defines the plastic component of the oriented material. 

In developing elastic tissue, the microfibrils are the first components to appear in the extracellular matrix. They are then thought to act as a scaffold for deposition, orientation, and assembly of tropoelastin monomers. They are 10—12 nm in diameter, and lie adjacent to cells producing elastin and parallel to the long axis of the developing elastin fiber (Cleary, 1987). 

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