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Elastic constants are specific parameters that quantify the stiffness of a material in response to applied stresses and are fundamental in defining the elastic properties of materials. These constants form the elements of the stiffness matrix in tensor notation, which relates stress to strain through linear equations in anisotropic materials.
If the material is isotropic, the linearized stress–strain relationship is called Hooke's law, which is often presumed to apply up to the elastic limit for most metals or crystalline materials whereas nonlinear elasticity is generally required to model large deformations of rubbery materials even in the elastic range.
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
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.
Other geometric properties used in design include: area for tension and shear, radius of gyration for compression, and second moment of area and polar second moment of area for stiffness. Any relationship between these properties is highly dependent on the shape in question. There are two types of section modulus, elastic and plastic:
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
In materials science, a general rule of mixtures is a weighted mean used to predict various properties of a composite material. [1] [2] [3] It provides a theoretical upper- and lower-bound on properties such as the elastic modulus, ultimate tensile strength, thermal conductivity, and electrical conductivity. [3]
The elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. [ 1 ] [ 2 ] Other names are elastic modulus tensor and stiffness tensor . Common symbols include C {\displaystyle \mathbf {C} } and Y {\displaystyle \mathbf {Y} } .