An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed when a force is applied to it. The elastic modulus of an object is defined as the slope of its stress-strain curve: In physics, force is an influence that may cause a body to accelerate. ... Look up Slope in Wiktionary, the free dictionary. ... A stress-strain curve is a graph derived from measuring load (stress - σ) versus extension (strain - ε) for a sample of a material. ...

where λ is the elastic modulus; 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 caused by the stress to the original state of the object. Because stress is measured in pascals and strain is a unitless ratio, the units of λ are therefore pascals as well. An alternative definition is that the elastic modulus is the stress required to cause a sample of the material to double in length. This is not literally true for most materials because the value is far greater than the yield stress of the material or the point where elongation becomes nonlinear but some may find this definition more intuitive. Figure 1  Stress tensor A mature tree trunk may support a greater force than a fine steel wire but intuitively we feel that steel is stronger than wood. ... This article is about the deformation of materials. ... The pascal (symbol Pa) is the SI unit of pressure. ...

The concept of a constant elastic modulus is dependent on the assumption that the stress-strain curve is always linear. In reality, the curve is only linear within certain limits, because an object stretched or compressed too far will break, and an object under high pressure may undergo processes that will affect the stress-strain curve, such as chemical reactions or buckling. The word linear comes from the Latin word linearis, which means created by lines. ... In engineering, buckling is a failure mode characterised by a sudden failure of a structural member that is subjected to high compressive stresses where the actual compressive stresses at failure are smaller than the ultimate compressive stresses that the material is capable of withstanding. ...

There are three primary elastic moduli, each describing a different kind of deformation:

• The Young's modulus (E) describes tensile elasticity, 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. Because all other elastic moduli can be derived from Young's modulus, it is often referred to simply as the elastic modulus.
• The shear modulus or modulus of rigidity (G) 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's volume to deform when under pressure; 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.

This article is about a physical property. ... Elasticity has meanings in two different fields: In physics and mechanical engineering, the theory of elasticity describes how a solid object moves and deforms in response to external stress. ... Tensile stress (or tension) is the stress state leading to expansion; that is, the length of a material tends to increase in the tensile direction. ... In materials science, shear modulus S, sometimes referred to as the modulus of rigidity, is defined as the ratio of shear stress to the shear strain: S = shear stress/shear strain = (F/A)/Φ. Another commonly accepted symbol is G. Shear modulus is usually measured in ksi (kips per square... Shear stress is a stress state where the stress is parallel to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ... Shear strain is the components of a strain at a point that produce changes in shape of a body (distortion) without a volumetric change. ... The pitch drop experiment at the University of Queensland. ... The bulk modulus K of a fluid or solid is the inverse of the compressibility: where p is pressure and V is volume. ... Fluid Dynamics Compressibility (physics) is a measure of the relative volume change of fluid or solid as a response to a pressure (or mean stress) change: . For a gas the magnitude of the compressibility depends strongly on whether the process is adiabatic or isothermal, while this difference is small in...

Relationships between elastic moduli

For an isotropic elastic material the elastic moduli are related as follows: (ν is Poisson's ratio) When a sample of material is stretched in one direction, it tends to get thinner in the other two directions. ...

Also: E = K*L/A

See also

• Elastic limit
• Elasticity
• Tensile strength
• Young's modulus