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E 1 and E 2 are the Young's moduli in the 1- and 2-direction and G 12 is the in-plane shear modulus. v 12 is the major Poisson's ratio and v 21 is the minor Poisson's ratio. The flexibility matrix [S] is symmetric. The minor Poisson's ratio can hence be found if E 1, E 2 and v 12 are known.
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 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 modulus of elasticity can be used to determine the stress–strain relationship in the linear-elastic portion of the stress–strain curve. The linear-elastic region is either below the yield point, or if a yield point is not easily identified on the stress–strain plot it is defined to be between 0 and 0.2% strain, and is defined as the ...
The bulk modulus is an extension of Young's modulus to three dimensions. Flexural modulus ( E flex ) describes the object's tendency to flex when acted upon by a moment . Two other elastic moduli are Lamé's first parameter , λ, and P-wave modulus , M , as used in table of modulus comparisons given below references.
[1]: 58 For example, low-carbon steel generally exhibits a very linear stress–strain relationship up to a well-defined yield point. The linear portion of the curve is the elastic region, and the slope of this region is the modulus of elasticity or Young's modulus. Plastic flow initiates at the upper yield point and continues at the lower ...
where is the volume fraction of the fibers in the composite (and is the volume fraction of the matrix).. If it is assumed that the composite material behaves as a linear-elastic material, i.e., abiding Hooke's law = for some elastic modulus of the composite and some strain of the composite , then equations 1 and 2 can be combined to give
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),