An elastic modulus (also known as modulus of elasticity) is the unit of measurement of an object's or substance's resistance to being deformed elastically (i.e., non-permanently) when a stress is applied to it. The elastic modulus of an object is defined as the slope of its

stress–strain curve In engineering and materials science, a stress–strain curve for a material gives the relationship between stress and strain. It is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and ...

in the elastic deformation region: A stiffer material will have a higher elastic modulus. An elastic modulus has the form: :

\delta \ \stackrel\  \frac

where stress is the force causing the deformation divided by the area to which the force is applied and strain is the ratio of the change in some parameter caused by the deformation to the original value of the parameter. Since strain is a dimensionless quantity, the units of

\delta

will be the same as the units of stress. Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined. The three primary ones are: # '' Young's modulus'' (E) describes tensile and compressive

elasticity Elasticity often refers to: *Elasticity (physics), continuum mechanics of bodies that deform reversibly under stress Elasticity may also refer to: Information technology * Elasticity (data store), the flexibility of the data model and the cl ...

, or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of tensile stress to

tensile strain In physics, deformation is the continuum mechanics transformation of a body from a ''reference'' configuration to a ''current'' configuration. A configuration is a set containing the positions of all particles of the body. A deformation can ...

. It is often referred to simply as the ''elastic modulus''. # The '' shear modulus'' or ''modulus of rigidity'' (G or

\mu \,

Lamé second parameter) describes an object's tendency to shear (the deformation of shape at constant volume) when acted upon by opposing forces; it is defined as shear stress over shear strain. The shear modulus is part of the derivation of viscosity. # The '' bulk modulus'' (K) describes volumetric elasticity, or the tendency of an object to deform in all directions when uniformly loaded in all directions; it is defined as volumetric stress over volumetric strain, and is the inverse of compressibility. The bulk modulus is an extension of Young's modulus to three dimensions. 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. Homogeneous and

isotropic Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...

(similar in all directions) materials (solids) have their (linear) elastic properties fully described by two elastic moduli, and one may choose any pair. Given a pair of elastic moduli, all other elastic moduli can be calculated according to formulas in the table below at the end of page.

Inviscid fluids The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inter ...

are special in that they cannot support shear stress, meaning that the shear modulus is always zero. This also implies that Young's modulus for this group is always zero. In some texts, the modulus of elasticity is referred to as the ''elastic constant'', while the inverse quantity is referred to as ''elastic modulus''.

See also

References

Further reading