Strain Hooke’s law

Modulus of elasticity Most materials, including plastics and metals, have deformation proportional to their loads below the proportional limit. Since stress is proportional to load and strain to deformation, this implies that stress is proportional to strain. Hooke s Law, developed in 1676, follows that this straight line (Fig. 2-2) of proportionality is calculated as ... 

Hint 3 Assume that the fabric is perfectly elastic so that stress is proportional to strain (Hooke s law). 

Syntactic foams manufactured from hollow glass or silica microspheres and an epoxide, phenolic or other matrix resin represent a class of lightweight structural materials used for buoyancy purposes, insulation and packaging. The effect of silanes on the mechanical properties of syntactic foams at a nominal density of 0.35 g/cm3 is shown in Tables 14-16. The Proportional Limit is defined as the greatest stress which the foam is capable of sustaining without any deviation from proportionality of stress to strain (Hooke s Law). 

Generalized Stress-Strain Hooke s Law for Isotropic Solids 162... 

GENERALIZED STRESS-STRAIN HOOKE S LAW FOR ISOTROPIC SOLIDS... 

Stress (ct) is the resistance to strain. Figure 2.5 shows a typical stress-strain curve for a material. For a material whose stress-strain curve is similar to that of figure 2.5, the relationship between stress and strain is linear for small values of strain. Hooke s law applies to this linear region and is expressed as... 

Determine V t). Hint 1 The pressure difference between the inside and the outside of the balloon must be balanced by the stress in the fabric of the balloon so that AP = 2n Rha, where h is the thickness of the fabric and a is the stress. Hint 2 assume the density of the fabric is constant so that AnR h = AnR ho. Hint 3 Assume the fabric is perfectly elastic so that stress is proportional to strain (Hooke s law). Hint 4 The ideal gas law applies. 

We usually assume that elasticity (how stress is related to strain) is linear. The assumption is that strains are small so that stresses are linearly related to strains (Hooke s law). We then think of the crystal as a continuum (a struc-... 

In the description of the basics of thermomechanical analysis in the first part of this section the mechanical properties were assumed to result from perfect elasticity, i.e., the stress is direcdy proportional to the strain and independent of the rate of strain. Hooke s law expresses this relationship with a constant modulus as sketched at the top of Fig. 4.157 for the example of tensile stress and strain. 

Proportional Limit. The greatest stress which a material is capable of sustaining without deviation from proportionality of stress and strain (Hooke s law). It is expressed in force per unit area, usually in pounds per square inch. 

We usually assume that elasticity (how stress is related to strain) is linear. The assumption is that strains are small so that stresses are linearly related to strains (Hooke s law). We then think of the crystal as a continuum (a structureless sponge ) with two independent elastic constants (for example, p, the shear modulus, and v Poisson s ratio At the core of the dislocation, the strains are too large for this assumption to be valid so we exclude this region from our calculation and replace it by a fudge factor involving r, the core radius (not ideal because it assumes nothing varies across the core and we do not know what is). One consequence of linear elasticity is that when... 

In contrast to liquids, solids have an elastic response to applied stress or strain, at least for small deformations. An elastic object is one that returns to its original shape if the force is removed. At low strains, the stress is proportional to strain (Hooke s law) and independent of the deformation rate. 

For most metallic materials, elastic deformation persists only to strains of about 0.005. As the material is deformed beyond this point, the stress is no longer proportional to strain (Hooke s law. Equation 6.5, ceases to be valid), and permanent, nonrecoverable, or plastic deformation occurs. Figure 6.10a plots schematically the tensile stress-strain behavior into the plastic region for a typical metal. The transition from elastic to plastic is a gradual one for most metals some curvature results at the onset of plastic deformation, which increases more rapidly with rising stress. 

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