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An
elastic modulus, or
modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically (i.e. non-permanently) when a force is applied to it. The elastic modulus of an object is defined as the slope of its
stress-strain curve in the elastic deformation region:
\lambda \ \stackrel{\text{def-->{=}\ \frac {\text{stress--> {\text{strain-->
where λ is the elastic modulus; stress (physics) is the force causing the deformation divided by the area to which the force is applied; and strain (materials science) is the ratio of the change caused by the stress to the original state of the object. If stress is measured in
pascal (unit)s, and since strain is a unitless ratio, then the units of λ are 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.
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 (physics), 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 \mu) 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.
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.
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.
See also
External links
- Free database of engineering properties for over 63,000 materials
es:Constante elásticaja:弾性率
simple:Elastic modulusuk:Модулі пружності
An
elastic modulus, or
modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically (i.e. non-permanently) when a
force is applied to it. The elastic modulus of an object is defined as the
slope of its stress-strain curve in the elastic deformation region:
\lambda \ \stackrel{\text{def-->{=}\ \frac {\text{stress--> {\text{strain-->
where λ is the elastic modulus; stress (physics) is the force causing the deformation divided by the area to which the force is applied; and
strain (materials science) is the ratio of the change caused by the stress to the original state of the object. If stress is measured in pascal (unit)s, and since strain is a unitless ratio, then the units of λ are 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.
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 (physics), 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 \mu) 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.
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.
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.
See also
External links
- Free database of engineering properties for over 63,000 materials
es:Constante elásticaja:弾性率simple:Elastic modulus
uk:Модулі пружності
Elastic modulus - Wikipedia, the free encyclopedia
An elastic modulus, or modulus of elasticity, is the mathematical description of an object or substance's tendency to be deformed elastically (i.e., non-permanently) when a force ...
Young's modulus - Wikipedia, the free encyclopedia
In solid mechanics, Young's modulus (E) is a measure of the stiffness of a material. It is also known as the Young modulus, modulus of elasticity, elastic modulus (though the Young ...
THE ELASTIC MODULUS
1 M J Reece MAE 1103 THE ELASTIC MODULUS LECTURE 2 M J Reece MAE 1103 THE ELASTIC MODULI The modulus measures the resistance of a material to elastic deformation . In simple terms ...
Elastic Modulus Measurement
ndt, panametrics - ndt, non-destructive test equipment, ultrasonic transducers, used ndt equipment, ultrasonic sensors, non destructive testing, measuring thickness, nondestructive ...
Lloyd Instruments - elastic modulus
The ratio of stress, within the proportional limit, to the corresponding strain
Cardiff ePrints Caerdydd - Evaluation of elastic modulus of materials ...
Results of Mossakovskii's analysis for the elastic, adhesive (no-slip) contact between a rigid, axisymmetric punch and an isotropic, elastic half-space are developed in order to ...
Lloyd Instruments - elastic modulus
The ratio of stress, within the proportional limit, to the corresponding strain
e-Prints Soton - Increases in the elastic modulus of trabecular bone ...
Increases in the elastic modulus of trabecular bone tissue leads to more rapid perforation of trabeculae in osteoporotic bone; Mulvihill, B., McNamara, L.M. and Prendergast, P.J ...
elastic modulus definition of elastic modulus in the Free Online ...
elastic modulus or elastic constant. In materials science and physical metallurgy, any of various numbers that quantify the response of a material to elastic or springy deflection.
elastic modulus - definition of elastic modulus by the Free Online ...
Thesaurus Legend: Synonyms Related Words Antonyms. Noun: 1. elastic modulus - (physics) the ratio of the applied stress to the change in shape of an elastic body
