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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),
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 .
Relations for other moduli are found in the (λ, G) row of the conversions table at the end of this article. Although the shear modulus, μ, must be positive, the Lamé's first parameter, λ, can be negative, in principle; however, for most materials it is also positive. The parameters are named after Gabriel Lamé.
The Young's modulus directly applies to cases of uniaxial stress; that is, tensile or compressive stress in one direction and no stress in the other directions. Young's modulus is also used in order to predict the deflection that will occur in a statically determinate beam when a load is applied at a point in between the beam's supports.
The slope of the initial, linear portion of this curve gives Young's modulus. Mathematically, Young's modulus E is calculated using the formula E=σ/ϵ, where σ is the stress and ϵ is the strain. Shear modulus (G) Initial structure: Start with a relaxed structure of the material. All atoms should be in a state of minimum energy with no ...
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:
Other moduli describe the material's response to other kinds of stress: the shear modulus describes the response to shear stress, and Young's modulus describes the response to normal (lengthwise stretching) stress. For a fluid, only the bulk modulus is meaningful.
In many materials, the relation between applied stress is directly proportional to the resulting strain (up to a certain limit), and a graph representing those two quantities is a straight line. The slope of this line is known as Young's modulus, or the "modulus of elasticity". The modulus of elasticity can be used to determine the stress ...