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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 .
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:
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.
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 two parameters together constitute a parameterization of the elastic moduli for homogeneous isotropic media, popular in mathematical literature, and are thus related to the other elastic moduli; for instance, the bulk modulus can be expressed as K = λ + 2 / 3 μ. Relations for other moduli are found in the (λ, G) row of the ...
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 ...