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The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law: . Young's modulus E describes the material's strain response to uniaxial stress in the direction of this stress (like pulling on the ends of a wire or putting a weight on top of a column, with the wire getting longer and the column losing height),
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.
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.
[1] [2] Other names are elastic modulus tensor and stiffness tensor. Common symbols include C {\displaystyle \mathbf {C} } and Y {\displaystyle \mathbf {Y} } . The defining equation can be written as
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.
The book covers various subjects, including bearing and shear stress, experimental stress analysis, stress concentrations, material behavior, and stress and strain measurement. It also features expanded tables and cases, improved notations and figures within the tables, consistent table and equation numbering, and verification of correction ...
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 stress relaxation modulus () is the ratio of the stress remaining at time after a step strain was applied at time =: = (), which is the time-dependent generalization of Hooke's law . For visco-elastic solids, G ( t ) {\displaystyle G\left(t\right)} converges to the equilibrium shear modulus [ 4 ] G {\displaystyle G} :