Strain/stress elastic

Considering a fiber or thread of nylon-66, which is an unoriented glassy polymer, its modulus of elasticity is about 2,000 MPa (300,000 psi). Above the Tg its elastic modulus drops even lower, because small stresses will readily straighten the kinked molecular chains. However, once it is extended and has its molecules oriented in the direction of the stress, larger stresses are required to produce added strain. The elastic modulus increases. 

The analysis of propagating acoustic waves in an elastic medium allows its characterization by means of strain-stress relationships. The stress ay is defined as the ratio of an external force F parallel to a direction i (x,y or z) to a surface S perpendicular to the direction j. 

Other Transducers. Ultrasound also has been used for the measurement of force, vibration, acceleration, interface location, position changes, differentiation between the composition of differing materials, grain size in metals, and evaluation of stress and strain and elasticity in materials. Sonic devices can used to detect gas leaks, and to count discrete parts by means of an interrupted sound beam. Frequently, an ultrasonic device can be applied where photoelectric derices are used. Particularly tn situations where light-sensitive materials are being processed (hence presence of light must be avoided), ultrasonic devices may be the detectors of choice. 

Figure H3.3.4 Mechanical models are often used to model the response of foods in creep or stress relaxation experiments. The models are combinations of elastic (spring) and viscous (dashpot) elements. The stiffness of each spring is represent by its compliance (J= strain/stress), and the viscosity of each dashpot is represent by a Newtonian viscosity (ri). The form of the arrangement is often named after the person who originally proposed the model. The model shown is called a Burgers model. Each element in the middle—i.e., a spring and dashpot arranged in parallel—is called a Kelvin-Voigt unit.

The basis for the above-mentioned model47) was provided by Maxwell s nonlinear model obtained in general form in Ref. 48). Flere the total strain was divided into irreversible strain and elastic strain X, Stress a and velocity of irreversible strain ep were determined from the elastic strain. In Ref. 48) a number of functions a (a.) and ep(X) were defined more specifically. Beside that, Maxwell s nonlinear models were connected in parallel. Note that in case of one Maxwell s element X = a23), but in case of several elements connected in parallel this is not true and a is determined from the solution of the respective problem. In case of the uniaxial extension the model of Ref.47) takes the following form ... 

Abstract When subjected to a mechanical loading, the solid phase of a saturated porous medium undergoes a dissolution due to strain-stress concentration effects along the fluid-solid interface. Through a micromechanical analysis, the mechanical affinity is shown to be the driving force of the local dissolution. For cracked porous media, the elastic free energy is a dominant component of this driving force. This allows to predict dissolution-induced creep in such materials. 

All materials undergo a deformation, either noticeable or unnoticeable, whenever they are subjected to an external force. The deformation can be elastic, plastic, elastomeric, or viscoelastic. When an external force is applied on a body, the displacement of points of the body relative to neighboring points is measured as strain and the strength of the force applied to the local point is measured as stress. Elastic deformation such as rubber band stretch is recovered when the stress, or external force, is removed. Plastic deformation such as a dent on a metal car body is permanent and is not recoverable with the removal of the deforming stresses. 

Elastic materials strain instantaneously when stretched and just as quickly return to their original state once the stress is removed. Viscoelastic materials have elements of both of these properties and, as such, exhibit time dependent strain. Whereas elasticity is usually the result of bond stretching along crystallographic planes in an ordered solid, viscoelasticity is the result of the diffusion of atoms or molecules inside of an amorphous material [3-6],... 

Because all tissues are viscoelastic this means that their mechanical properties are time dependent and their behavior is characterized both by properties of elastic solids and those of viscous liquids. The classic method to characterize a viscoelastic material is to observe the decay of the stress required to hold a sample at a fixed strain (stress relaxation) or by the increasing strain required to hold a sample at a fixed stress (creep) as diagrammed in Figure 7.1 and explained further in Figure 7.2. Viscoelastic materials undergo processes that both store (elastic) and dissipate (viscous)... 

Figure 7.10. Stress-strain curve for skin. Total stress-strain curves (open boxes) were obtained by collecting all the initial, instantaneous, force measurements at increasing time intervals and then dividing by the initial cross-sectional area and multiplying by 1.0 + the strain. The elastic stress-strain curve (closed diamonds) was obtained by collecting all the force measurements at equilibrium and then dividing by the initial cross-sectional area and multiplying by 1.0 + the strain. The viscous component curve (closed squares) was obtained from the difference between the total and the elastic stresses.

In a typical indentation experiment the indenter is pressed onto the surface under investigation and the load is successively increased up to a certain maximum load. In the so-called compliance approach both load and indenter displacement are recorded and plotted as a load-displacement curve, the so-called compliance curve. If the experiment is exclusively run in the compressive load regime, the curve is also referred to as the load-penetration curve. Upon loading, elastic deformations occur succeeded by plastic ones. Upon releasing the imposed stress, elastic strain recovers immediately. 

In Fig. 5.4a and b, the initial creep rate of each phase (Eqn. (7)) is represented by the intersection of the monolithic creep curve for that phase and the elastic stress and strain (vertical line). After initial loading, the total strain rate (elastic + creep) of each phase, which remains equal to the total strain rate of the composite (for compatibility), decreases. The only exception arises if ki 0 = 2,0 (= c,o), so that ec 0 = c ss (see Fig. 5.4c). In this instance, the initial condition matches the steady-state condition—the composite strain rate remains unchanged. The applied stress for this condition is given by... 

Write the constitutive relations for the medium to relate stress to strain, assuming elastic linearity (Hooke s Law) ... 

Stress-Strain Relations for Viscoelastic Materials. The viscoelastic behaviour of an elastomer varies with temperature, pressure, and rate of strain. This elastic behaviour varies when stresses are repeatedly reversed. Hence any single mathematical model can only be expected to approximate the elastic behaviour of actual substances under limited conditions 2J. ... 

Generalized Strain-Stress Relationships for Ideal Elastic Systems 170... 

GENERALIZED STRAIN-STRESS RELATIONSHIPS FOR IDEAL ELASTIC SYSTEMS... 

The same parameters can also be determined by applying a constant shear stress to the interface and measuring the resulting shear strain as a function of time (see fig. 3.40), so-called interfacial creep tests. At t = 0, a shear stress is suddenly applied, and kept constant thereafter. For ideally viscous monolayers a steady increase of the shear strain with t will be observed, while for an elastic material the observed strain will be instantaneous and constcmt in time. For a viscoelastic material, as in fig. 3.40, there is first am Instantaneous increase AB in the strain, the elastic response followed by a delayed elastic response BC and a viscous... 

Hooke s law. When a load is applied to any elastic body so that the body is deformed or strained, then the resulting stress (the tendency of the body to resume its normal condition) is proportional to the strain. Stress is measured in units of force per unit area, strain is the extent of the deformation. For example, when a bar of metal is subjected to a stretching load, the extent of the increase in length of the bar is directly proportional to the force per unit area, i.e., to the stretching load or stress. In general Hooke s law applies only up to a certain stress called the yield strength. 

Consider a cylindrical rod of cross-sectional area A stressed elastically in tension by a force F (Fig. 16-3). There is a stress (x, = FjA in the y direction but none in the x or z directions. (This stress is the only normal stress acting there are also shear stresses present, but these are not directly measurable by x-ray diffraction.) The stress Oy produces a strain , in the y direction given by... 

The stress state, where the stress can be both applied and residual, and the associated strain influence many different material properties, which is especially important in engineering and technological applications. The residual stress and strain can be advantageous or, on the contrary, can provoke a faster failure of machine parts or other manufactured materials. There are different methods to determine the strain and stress in materials mechanical, acoustical, optical and the diffraction of X-ray and neutrons. The diffraction method is applicable for crystalline materials and is based on the measurements of the elastic strain effects on the diffraction lines. There are two kinds of such effects, a peak shift and a peak broadening. The strain modifies the interplanar distances d. In a polycrystalline specimen a peak shift is produced if the average of the interplanar distance modifications on the crystallites in reflection is different from zero. If the dispersion of interplanar distance modifications is different from zero, then a peak broadening occurs. The effect of the strain on the peak breadth is described in Chapter 13. Here we deal only with the peak shift effect caused by the macroscopic, or Type I strain/stress. There is a substantial amount of literature on this subject. The comprehensive... 

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