Viscoelastic bodies, mechanical models

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... 

A more common body is the plasto-viscoelastic, or Bingham body. Its mechanical model is shown in Figure 8-16C. When a stress is applied that is below the yield stress, the Bingham body reacts as an elastic body. At stress values beyond the yield stress, there are two components, one of which is constant and is represented by the friction ele-... 

Figure 8-16 Mechanical Models for a Plastic Body. (A) St. Venant body, (B) plasto-elastic body, and (C) plasto-viscoelastic or Bingham body.

The mechanical response of viscoelastic bodies such as polymers is poorly represented by either the spring or the dashpot. J. C. Maxwell suggested that a better approximation would result from a series combination of the spring and dashpot elements. Such a model, called a Maxwell element, is shown on the right in Figure 3-1. In describing tensile response with the Maxwell element, E, the instantaneous tensile modulus, characterizes the response of the spring while rjE, the viscosity of the liquid in the dashpot, defines the viscous... 

To illustrate this linear combination, various analogical models with no relationship with the molecular nature of the phenomena were proposed, identifying a polymer with a combination of springs and dashpots. The spring can be stfained without inertia and thus reflects a purely elastic mechanical behavior whereas dash-pots, which are pistons moving in cylinders filled with a viscous liquid, cannot respond instantaneously to a stress. These two elements were thus associated under various combinations to simulate the response of a viscoelastic body to a mechanical stress. 

In consideration of the clinical importance of being able to visualize any implant material within the body, radio-opaque hydrogels for NPR have been formulated [69]. Copolymers of iodobenzoyl-oxo-ethyl methacrylate (4IEMA) and hydrophilic PVP or hydroxylethyl methacrylate (HEMA) exhibit appropriate swelling characteristics, viscoelastic mechanical properties, and excellent cytocompatibility [69]. Moreover, inclusion of the covalently attached iodine molecules allowed for hydrogel visualization via X-ray in a porcine cadaveric spine model [69],... 

In order to derive some simple linear viscoelastic models, it is necessary to introduce the mechanical equivalents for a Newtonian and a Hookean body. 

The tissue has been modeled from a continuum mechanics point of view by Jfow and students (11,12,13). The model treats cartilage as a blphaslc material (the solid"organic matrix was assumed, for these purposes, to be one "phase" and the water the other). The "solid" organic matrix was further assumed to behave as a single Kelvln-Voigt body whose viscoelastic properties are attenuated by the frictional resistance to fluid flow from the tissue. Attempts were made to use this model to explain the load-strain and load dissipation properties of the tissue for the experimental configuration described In this paper (15),... 

Of course, viscoelasticity (response to an external mechanical excitation) and diffusion (response to thermal fluctuations) must have their origin in the same dynamical process at the molecular level, and any model proposed to explain one aspect must also consistently account for the other (as a consequence of the fluctuation dissipation theorem). The elaboration of such models has remained a challenge to polymer scientists for many years, and is indeed a complicated many-body problem. 

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