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Shear strain. In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: [1]
Elastic properties describe the reversible deformation (elastic response) of a material to an applied stress. They are a subset of the material properties that provide a quantitative description of the characteristics of a material, like its strength. Material properties are most often characterized by a set of numerical parameters called moduli.
The shear modulus or modulus of rigidity (G or Lamé second parameter) describes an object's tendency to shear (the deformation of shape at constant volume) when acted upon by opposing forces; it is defined as shear stress over shear strain. The shear modulus is part of the derivation of viscosity.
In the isotropic case, the stiffness tensor may be written: [citation needed] = + (+) where is the Kronecker delta, K is the bulk modulus (or incompressibility), and is the shear modulus (or rigidity), two elastic moduli. If the medium is inhomogeneous, the isotropic model is sensible if either the medium is piecewise-constant or weakly ...
Other names are sometimes employed for one or both parameters, depending on context. For example, the parameter μ is referred to in fluid dynamics as the dynamic viscosity of a fluid (not expressed in the same units); whereas in the context of elasticity, μ is called the shear modulus, [2]: p.333 and is sometimes denoted by G instead of μ.
Isotropic elastic properties can be found by IET using the above described empirical formulas for the Young's modulus E, the shear modulus G and Poisson's ratio v. For isotropic materials the relation between strains and stresses in any point of flat sheets is given by the flexibility matrix [S] in the following expression:
where is the shear modulus, which can be determined by experiments. From experiments it is known that for rubbery materials under moderate straining up to 30–70%, the Neo-Hookean model usually fits the material behaviour with sufficient accuracy.
For instance, Young's modulus applies to extension/compression of a body, whereas the shear modulus applies to its shear. [1] Young's modulus and shear modulus are only for solids, whereas the bulk modulus is for solids, liquids, and gases. The elasticity of materials is described by a stress–strain curve, which shows the relation between ...