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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. Material properties are most often characterized by a set of numerical parameters called moduli.
The bulk modulus or or ) of a ... for these materials one additional elastic modulus, for example the shear modulus, ... (first part of the table) and for 2D ...
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
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).
This fact follows from the symmetry of the stress and strain tensors, together with the requirement that the stress derives from an elastic energy potential. For isotropic materials, the elasticity tensor has just two independent components, which can be chosen to be the bulk modulus and shear modulus. [3]
Bulk modulus: Ratio of pressure to volumetric compression (GPa) or ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume; Coefficient of restitution: The ratio of the final to initial relative velocity between two objects after they collide. Range: 0–1, 1 for perfectly elastic collision.
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.
In the isotropic case, the stiffness tensor may be written: [citation needed] = + (+) where is the Kronecker delta, K is the bulk modulus (or incompressibility), and is the shear modulus (or rigidity), two elastic moduli. If the medium is inhomogeneous, the isotropic model is sensible if either the medium is piecewise-constant or weakly ...