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. Stress is the internal distribution of force per unit area that balances and reacts to external loads applied to a body. ... This article is about the deformation of materials. ... The pascal (symbol: Pa) is the SI derived unit of pressure or stress (also: Youngs modulus and tensile strength). ...

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. ...

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 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. It is often referred to simply as the elastic modulus.
• The shear modulus or modulus of rigidity (G or μ) 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.

Three other elastic moduli are Poisson's ratio, Lamé's first parameter, and P-wave modulus. In solid mechanics, Youngs modulus (E) is a measure of the stiffness of a given material. ... 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 a strain that acts parallel to the face of a material that it is acting on. ... Viscosity is a measure of the resistance of a fluid to deform under shear stress. ... The bulk modulus (K) of a substance essentially measures the substances resistance to uniform compression. ... 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... Figure 1: Rectangular specimen subject to compression, with Poissons ratio circa 0. ...

Homogeneous and isotropic (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. Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ...

Inviscid fluids are special in that they can not support shear stress, meaning that the shear modulus is always zero. This also implies that Young's modulus is always zero. In solid mechanics, Youngs modulus (E) is a measure of the stiffness of a given material. ...

See also

• Stiffness
• Elastic limit
• Elasticity
• Tensile strength
• Elastic wave

Stiffness is the resistance of an elastic body to deflection or deformation by an applied force. ... The elastic limit is the maximum stress a material can undergo at which all strains are recoverable. ... Elasticity is a branch of physics which studies the properties of elastic materials. ... Tensile strength , or measures the force required to pull something such as rope, wire, or a structural beam to the point where it breaks. ... An elastic wave is a mechanical wave. ...