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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 symmetry of the stress and strain tensors implies that not all the six Poisson's ratios in the equation are independent.
Conversion formulae 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).
2 Poisson's ratio. 3 Bulk modulus. 4 Shear modulus. 5 References. 6 See also. Toggle the table of contents. Elastic properties of the elements (data page) 1 language.
where is the flexural modulus (in Pa), is the second moment of area (in m 4), is the transverse displacement of the beam at x, and () is the bending moment at x. The flexural rigidity (stiffness) of the beam is therefore related to both E {\displaystyle E} , a material property, and I {\displaystyle I} , the physical geometry of the beam.
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.
Defining equation SI unit Dimension Temperature gradient: No standard symbol K⋅m −1: ΘL −1: Thermal conduction rate, thermal current, thermal/heat flux, thermal power transfer P = / W ML 2 T −3: Thermal intensity I = / W⋅m −2
Several attempts have been made to develop approximations to the Zoeppritz equations, such as Bortfeld's (1961) and Aki & Richards’ (1980), [4] but the most successful of these is the Shuey's, which assumes Poisson's ratio to be the elastic property most directly related to the angular dependence of the reflection coefficient.
Conversion formulae 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).