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Encyclopedia > Shear modulus
Shear strain
Shear strain

In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is defined as the ratio of shear stress to the shear strain:[1] The Materials Science Tetrahedron, which often also includes Characterization at the center Materials science or Materials Engineering is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. ... Shear stress is a stress state where the stress is parallel or tangential to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ... Shear strain is a strain that acts parallel to the face of a material that it is acting on. ...

G  stackrel{mathrm{def}}{=} frac {sigma_{xy}} {epsilon_{xy}} = frac{F/A}{Delta x/h} = frac{F h}{Delta x A}

where

sigma_{xy} = F/A , = shear stress;
F is the force which acts
A is the area on which the force acts
epsilon_{xy} = Delta x/h = tan theta , = shear strain;
Δx is the transverse displacement
h is the initial length (labelled I in the diagram opposite)

Shear modulus is usually measured in GPa (gigapascals) or ksi (thousands of pounds per square inch). For other uses, see Pascal. ...

Material Typical values for
shear modulus (GPa)
(at room temperature)
Diamond[2] 478.
Steel[3] 79.3
Copper[3] 63.4
Titanium[3] 41.4
Glass[3] 26.2
Aluminium[3] 25.5
Polyethylene[3] 0.117
Rubber[4] 0.0006

Contents

Look up giga- in Wiktionary, the free dictionary. ... For other uses, see Pascal. ... This article is about the mineral. ... For other uses, see Steel (disambiguation). ... For other uses, see Copper (disambiguation). ... General Name, symbol, number titanium, Ti, 22 Chemical series transition metals Group, period, block 4, 4, d Appearance silvery metallic Standard atomic weight 47. ... This article is about the material. ... Aluminum redirects here. ... This article does not cite any references or sources. ... This does not cite any references or sources. ...

Explanation

The shear modulus is one of several quantities for measuring the strength of materials. All of them arise in the generalized Hooke's law: Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...

  • Young's modulus describes the material's response to linear strain (like pulling on the ends of a wire),
  • the bulk modulus describes the material's response to uniform pressure, and
  • the shear modulus describes the material's response to shearing strains.

The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force (such as friction). In the case of an object that's shaped like a rectangular prism, it will deform into a parallelepiped. Anisotropic materials such as wood and paper exhibit differing material response to stress or strain when tested in different directions. In this case, when the deformation is small enough so that the deformation is linear, the elastic moduli, including the shear modulus, will then be a tensor, rather than a single scalar value. In solid mechanics, Youngs modulus (E) is a measure of the stiffness of a given material. ... The bulk modulus (K) of a substance essentially measures the substances resistance to uniform compression. ... This article is about pressure in the physical sciences. ... In geometry, a parallelepiped (now usually pronounced , traditionally[1] in accordance with its etymology in Greek παραλληλ-επίπεδον, a body having parallel planes) is a three-dimensional figure like a cube, except that its faces are not squares but parallelograms. ... This article is being considered for deletion in accordance with Wikipedias deletion policy. ... For other uses, see Wood (disambiguation). ... For other uses, see Paper (disambiguation). ...

Influences of selected glass component additions on the shear modulus of a specific base glass.[5]

This article is about the material. ...

Waves

In homogeneous and isotropic solids, there are two kinds of waves, pressure waves and shear waves. The velocity of a shear wave, (vs) is controlled by the shear modulus, Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ... Plane P-wave Representation of the propagation of a P-wave on a 2d grid (empirical shape) One of the two types of elastic body waves (named because they travel through the body of the Earth) that are produced by earthquakes and recorded by seismometers. ... A type of seismic wave, the S-wave moves in a shear or transverse wave, so motion is perpendicular to the direction of wave propagation. ...

v_s = sqrt{frac {G} {rho} }

where

G is the shear modulus
ρ is the solid's density.

For other uses, see Density (disambiguation). ...

See also

Shear stress is a stress state where the stress is parallel or tangential to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ... Shear strain is a strain that acts parallel to the face of a material that it is acting on. ... Shear strength in engineering is a term used to describe the strength of a material or component against the type of yield or structural failure where the material or component fails in shear. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ... // The impulse excitation technique is a nondestructive test method that uses natural frequency, dimensions and mass of a test-piece to determine Youngs modulus, Shear modulus, Poissons ratio and damping coefficient. ...

References

  1. ^ International Union of Pure and Applied Chemistry. "shear modulus, G". Compendium of Chemical Terminology Internet edition.
  2. ^ McSkimin, H.J.; Andreatch, P. (1972). "". J. Appl. Phys. 43: 2944-2948. 
  3. ^ a b c d e f Crandall, Dahl, Lardner (1959). An Introduction to the Mechanics of Solids. McGraw-Hill. 
  4. ^ Spanos, Pete (November 2003). "Cure system effect on low temperature dynamic shear modulus of natural rubber". Rubber World. 
  5. ^ Shear modulus calculation of glasses
Conversion formulas
Homogeneous isotropic linear elastic materials have their elastic properties uniquely determined by any two moduli among these, thus given any two, any other of the elastic moduli can be calculated according to these formulas.
(lambda,,mu) (E,,mu) (K,,lambda) (K,,mu) (lambda,,nu) (mu,,nu) (E,,nu) (K,, nu) (K,,E) (M,,mu)
K=, lambda+ frac{2mu}{3} frac{Emu}{3(3mu-E)} lambdafrac{1+nu}{3nu} frac{2mu(1+nu)}{3(1-2nu)} frac{E}{3(1-2nu)} M - frac{8mu}{3}
E=, mufrac{3lambda + 2mu}{lambda + mu} 9Kfrac{K-lambda}{3K-lambda} frac{9Kmu}{3K+mu} frac{lambda(1+nu)(1-2nu)}{nu} 2mu(1+nu), 3K(1-2nu), mufrac{3M-4mu}{M-mu}
lambda=, mufrac{E-2mu}{3mu-E} K-frac{2mu}{3} frac{2 mu nu}{1-2nu} frac{Enu}{(1+nu)(1-2nu)} frac{3Knu}{1+nu} frac{3K(3K-E)}{9K-E} M - 2mu,
mu=, 3frac{K-lambda}{2} lambdafrac{1-2nu}{2nu} frac{E}{2+2nu} 3Kfrac{1-2nu}{2+2nu} frac{3KE}{9K-E}
nu=, frac{lambda}{2(lambda + mu)} frac{E}{2mu}-1 frac{lambda}{3K-lambda} frac{3K-2mu}{2(3K+mu)} frac{3K-E}{6K} frac{M - 2mu}{2M - 3mu}
M=, lambda+2mu, mufrac{4mu-E}{3mu-E} 3K-2lambda, K+frac{4mu}{3} lambda frac{1-nu}{nu} mufrac{2-2nu}{1-2nu} Efrac{1-nu}{(1+nu)(1-2nu)} 3Kfrac{1-nu}{1+nu} 3Kfrac{3K+E}{9K-E}
IUPAC logo The International Union of Pure and Applied Chemistry (IUPAC) (Pronounced as eye-you-pack) is an international non-governmental organization established in 1919 devoted to the advancement of chemistry. ... Compendium of Chemical Terminology (ISBN 0-86542-684-8) is a book published by IUPAC containing internationally accepted definitions for terms in chemistry. ... An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substances tendency to be deformed when a force is applied to it. ... Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ... The bulk modulus (K) of a substance essentially measures the substances resistance to uniform compression. ... In solid mechanics, Youngs modulus (E) is a measure of the stiffness of a given material. ... In linear elasticity, the Lamé parameters are the two parameters λ, also called Lamés first parameter. ... Figure 1: Rectangular specimen subject to compression, with Poissons ratio circa 0. ... In linear elasticity, the P-wave modulus is one of the elastic moduli available to describe isotropic homogeneous materials. ...

  Results from FactBites:
 
Shear modulus - Wikipedia, the free encyclopedia (210 words)
Shear modulus is usually measured in ksi (thousands of pounds per square inch) or GPa (gigapascals).
The shear modulus is one of several quantities for measuring the strength of materials.
Young's modulus describes the material's response to linear strain (like pulling on the ends of a wire), the bulk modulus describes the material's response to uniform pressure, and the shear modulus describes the material's response to shearing strains.
  More results at FactBites »

 
 

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