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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]
The elastic properties can be well-characterized by the Young's modulus, Poisson's ratio, Bulk modulus, and Shear modulus or they may be described by the Lamé parameters. Young's modulus [ edit ]
E i is the Young's modulus along axis i; G ij is the shear modulus in direction j on the plane whose normal is in direction i; ν ij is the Poisson ratio that corresponds to a contraction in direction j when an extension is applied in direction i. The Poisson ratio of an orthotropic material is different in each direction (x, y and z). However ...
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.
G is the modulus of rigidity (shear modulus) of the material J is the torsional constant. Inverting the previous relation, we can define two quantities; the torsional rigidity, = with SI units N⋅m 2 /rad. And the torsional stiffness,
Pure shear stress is related to pure shear strain, denoted γ, by the equation [3] =, where G is the shear modulus of the isotropic material, given by = (+). Here, E is Young's modulus and ν is Poisson's ratio .
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.
The bulk modulus (which is usually positive) can be formally defined by the equation =, where is pressure, is the initial volume of the substance, and / denotes the derivative of pressure with respect to volume.