Elastic spring force

A reasonable approximation for the force between two adjacent particles is given by the so-called FENE (finitely extendable non-linear elastic) spring force law (Bird et al. 1987a)... 

The second term of Eq. (3-26) is the elastic spring force, F. The form assumed,... 

Figure 3.18 Elastic spring force versus molecular extension for the Warner spring, for the freely jointed chain (which is described by the inverse Langevin function), and for the linear spring. (From Tanner, copyright 1985 by Oxford University Press, Inc. Used by permission of Oxford University Press, Inc.)...

Figure Bl.20.1. Direct force measurement via deflection of an elastic spring—essential design features of a direct force measurement apparatus.

The resistance to plastic flow can be schematically illustrated by dashpots with characteristic viscosities. The resistance to deformations within the elastic regions can be characterized by elastic springs and spring force constants. In real fibers, in contrast to ideal fibers, the mechanical behavior is best characterized by simultaneous elastic and plastic deformations. Materials that undergo simultaneous elastic and plastic effects are said to be viscoelastic. Several models describing viscoelasticity in terms of springs and dashpots in various series and parallel combinations have been proposed. The concepts of elasticity, plasticity, and viscoelasticity have been the subjects of several excellent reviews (21,22). 

Substituting Eq. (12) into Eq. (11) permits us to derive the Hookean spring force law, well-known in the classical theory of rubber elasticity ... 

An elastic spring tethers the two beads together and exerts a force on the beads tends to restore the system to its equilibrium coil-like shape. If the spring is taken to e a force constant, K (l R ), the spring force is... 

Other modifications to the elastic dumbbell have been considered, such as the concept of internal viscosity, where an additional spring force proportional to the rate of... 

In order to incorporate both tendencies, Lazare, Sundheim, and Gregor developed an improved model, where the elastic and electrostatic interactions were included. In this model, the resin was regarded as a set of charged planar capacitors, with the plates interconnected by elastic springs (Figure 7.24) [126], The balance between forces is attained when the elastic forces provided by the polymeric resin stabilize the dissolution propensity. 

The motion of a mass suspended from an elastic spring of force constant kH satisfying Hooke s law. 

Due to its structure, a pilus has an intricate force response that differs from that of a single bond as well as those of many other types of biopolymer. As illustrated in Fig. 18.2b, a force-vs.-elongation response of a single pilus can be seen as composed of three regions Region /, in which the response is basically linear, like that of a normal (elastic) spring Region II, in which the... 

Such circuits are constructed on the basis of three elementary units a spring, a dashpot and a slider, which are sketched in fig. 3.50. Following computer language, we call these pictures icons. Icon (a) mimics a purely elastic spring, icon (b) the purely viscous movement of a piston in a viscous liquid. The slider (c) represents a system with a yield stress, i.e. where a minimum force is required to achieve flow. Here, we shall only consider icons (a) and (b). In mechanical models we construct circuits consisting of a number of springs and a number of dashpots, arranged in such a way that the experimental observations are optimally accounted for. The two simplest circuits are sketched in fig. 3.51a and b. 

The force to hold chain ends separated by a general vector R is linear in R, like a simple elastic spring ... 

The Maxwell model comprises an elastic spring (of modulus G) in series with a dashpot containing a purely viscous liquid (of viscosity T ) (12,15,18). Following application of an external force to this system, the stress in the spring is equal to that in the dashpot and, furthermore, the total strain in the system (jtotal) is the sum of the strain in the spring (ys) and that in the dashpot (yd). 

Recall that F = -d /dx. The first term in Eq. (50) is the true force and the second term is known as the spring force. If k is too large the elastic band becomes stiff and the final path will not converge to the MEP. Instead, the elastic band path will cut comers. If k is too small, the images begin to slide down the path to the two minima wells. 

Fig. 5.9 (Chapter 5) depicts in its entirety the force or pressure diagram of a typical cycle of high-pressure agglomeration as a function of time. The effect of the two phenomena that are responsible for most problems associated with this technology, expansion of compressed air and/or elastic spring back, are shown to occur after having reached and take some time. The more important changes caused by these phenomena, however, are an increase in volume and porosity (Fig. 5.9) and the potential lowering of the product s structural integrity. In the best case, they will (only) lead to reduced strength, which may be corrected by a suitable post-treatment (e.g., coating.

---