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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),
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. They have the same dimension as stress and are usually given in SI unit of stress [Pa].
The Poisson's ratio of a stable, isotropic, linear elastic material must be between −1.0 and +0.5 because of the requirement for Young's modulus, the shear modulus and bulk modulus to have positive values. [3] Most materials have Poisson's ratio values ranging between 0.0 and 0.5.
Shear stress vs. shear strain curve: Plot the calculated shear stress against the applied shear strain for each increment.The slope of the stress-strain curve in its linear region provides the shear modulus, G=τ/γ, where τ is the shear stress and γ is the applied shear strain. Bulk modulus (K) Initial structure: Start with a relaxed ...
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:
Material properties are most often characterized by a set of numerical parameters called moduli. 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 .
Homogeneous isotropic linear elastic materials have their elastic properties uniquely determined by any two moduli among these; thus, given any two, any other of the elastic moduli can be calculated according to these formulas, provided both for 3D materials (first part of the table) and for 2D materials (second part). 3D formulae
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.