Parallel-elastic element

FIGURE 48.3 The Hill model of muscle separates the artive properties of muscle into a contractile element, in series with a purely elastic element. The properties of the passive muscle are represented by the parallel elastic element. 

Muscles provide two kinds of forces, active and passive, which compose a mnscles total force. Though actin and myosin ratching mechanism mnscles will provide the active force while with the help of non contractile element the muscle will provide passive forces, muscles are called as parallel elastic element that contribntes to its passive forces. In 1922 A.V. Hill(Hill 1970) first noted that activated muscles produce more force when held isometrically ( at a length fixed) then when they shorten. 

In addition to actin and myosin, other proteins are found in the two sets of filaments. Tropomyosin and a complex of three subunits collectively called troponin are present in the thin filaments and play an important role in the regulation of muscle contraction. Although the proteins constituting the M and the Z bands have not been fully characterized, they include a-actinin and desmin as well as the enzyme creatine kinase, together with other proteins. A continuous elastic network of proteins, such as connectin, surround the actin and myosin filaments, providing muscle with a parallel passive elastic element. Actin forms the backbone of the thin filaments [4]. The thin... 

Numerous attempts have been made to fit simplified mechanical models to the two behavior patterns described by Eq. (6). One can picture the elastic element as a spring-anayed network parallel with the viscous element to give essentially a (Kelvin) solid with retarded elastic behavior, wherein ... 

Another approach that has physical merit is to model the behavior of viscoelastic materials as a series of springs (elastic elements) and dashpots (viscous elements) either in series or parallel (see Figure 8.1). If the spring and dashpot are in series, which is described as a Maxwell mechanical element, the stress in the element is constant and independent of the time and the strain increases with time. 

Butter, and other unctuous materials, may be qualitatively described by a modified Bingham body (Elliott and Ganz, 1971 Elliott and Green, 1972), which consists of viscous, plastic and elastic elements in series. The stress-strain behavior for the model proposed by Elliot and Ganz (1971) is shown in Figure 7.12B. Diener and Heldman (1968) proposed a more complex model to describe how butter behaves when a low level of strain is applied. The model consists of plastic and viscous elements in parallel, coupled in series with a viscous element in parallel with a combination of a viscous and an elastic element. Figure 7.12C shows the stress-strain curve for... 

Let us now introduce a non-linear element. The model that describes internal residual stresses involves a parallel combination of elastic element and dry friction (Fig. IX-12). If the applied stress, x, exceeds the yield... 

Figure 16.4 illustrates the mechanical components of the oculomotor plant for horizontal eye movements, the lateral and medial rectus muscle, and the eyeball. The agonist muscle is modeled as a parallel combination of an active state tension generator Fag> viscosity element Bag> and elastic element TlT) connected to a series elastic element Rse- The antagonist muscle is similarly modeled as a parallel combination of an active state tension generator Tant> viscosity element Rant> and elastic element TlT) connected to a series elastic element Rse- The eyeball is modeled as a sphere with moment of inertia /p, connected to viscosity element Bp and elastic element Kp. The passive elasticity of each muscle is included in spring Kp for ease in analysis. Each of the elements defined in the oculomotor plant is ideal and linear. 

The early observations of Bagge et al. [1977] led them to suggest that the neutrophil behaves as a simple viscoelastic solid with a Maxwell element (an elastic and viscous element in series) in parallel with an elastic element. This elastic element in the model was thought to pull the unstressed cell into its spherical shape. Subsequently, Evans and Kukan [1984] and Evans and Yeung [1989] showed that the cells flow continuously into a pipette, with no apparent approach to a static limit, when a constant suction pressure was applied. Thus, the cytoplasm of the neutrophil should be treated as a liquid rather than a solid, and its surface has a persistent cortical tension that causes the cell to assume a spherical shape. 

Parallel finite element computations have been developed for a number of years mostly for elastic solids and structures. The static domain decomposition (DD) methodology is currently used almost exclusively for decomposing such elastic finite element domains in subdomains. This subdivision has two main purposes, namely (a) to distribute element computations to CPUs in an even manner and (b) to distribute system of equations evenly to CPUs for maximum efficiency in solution process. 

The elastic-plastic parallel finite element computational problem... 

In this paper, an algorithm, named the Plastic Domain Decomposition (PDD), for parallel elastic-plastic finite element computations was presented. Presented was also a parallel scalability study, that shows how PDD scales quite well with increase in a number of compute nodes. More importantly, presented details of PDD reveal that scalability is assured for inhomogeneous, multiple generation parallel computer architecture, which represents majority of currently available parallel computers. 

The Voigt-Kelvin model consists of an elastic element and a viscous element coupled in parallel (Fig. 5.23). The following constitutive equations are obtained by solving the differential equation ... 

Interestingly, one can prove that Eq. 20 is the relaxation function of N Maxwell s elements in parallel, i.e., a set of N parallel elastic springs Ri each one connected in series with a viscous dash-pot D( = Rfle (see Fig. 8). Accordingly, the reaction force can be expressed as (Palmeri et al. 2003 Adhikari and Wagner 2004)... 

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