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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.
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 ...
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} :
Direct integration is a structural analysis method for measuring internal shear, internal moment, rotation, and deflection of a beam. Positive directions for forces acting on an element. For a beam with an applied weight w ( x ) {\displaystyle w(x)} , taking downward to be positive, the internal shear force is given by taking the negative ...
The phenomenological equation which describes Harper–Dorn creep is = where ρ 0 is dislocation density (constant for Harper–Dorn creep), D v is the diffusivity through the volume of the material, G is the shear modulus and b is the Burgers vector, σ s, and n is the stress exponent which varies between 1 and 3.
As shown in the equations above, the use of the von Mises criterion as a yield criterion is only exactly applicable when the following material properties are isotropic, and the ratio of the shear yield strength to the tensile yield strength has the following value: [10]