The International Information Center for Structural Engineers

Friday, 21 June 2019 01:00cat

The constants of linear elasticity and their correlations

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Elastic Constants and Their Relationships, Source: Elastic Constants and Their Relationships, Source:

The constants and their correlations that are used to determine the behavior of an elastic material are presented below.

Elasticity is one of the theories that use mathematical forms to describe how a material behaves when subjected to stress. In elasticity theory, the ratio of the applied stresses to the strains produced is considered constant and when the stress is removed, the material re-gains its original shape. It consists a widely used and simple approach that is adequate for a large amount of applications, including construction industry. The constants that are used by the elasticity theory are the following:

Young's Modulus

Young's modulus or modulus of elasticity is the elastic constant that defines the ratio between applied compressive or tensile stress and the generated strain within the elastic limits of a body (meaning that elastic behavior can be attributed to a certain stress-strain range of the material). Young's modulus is denoted as E and is usually measured in MPa.

Shear Modulus

The shear modulus or modulus of rigidity is the ratio of shear stress applied to a body to the generated shear deformation. Shear modulus is measured in MPa and is usually denoted as G.

Bulk Modulus

If an elastic material is uniformly compressed, the ratio of the direct stress and the volumetric strain is constant and is called bulk modulus. Basically, the bulk modulus shows how resistant to compression a material is. Its measurement unit is MPa and it is denoted as K.

Poisson's Ratio

Poisson's ratio describes the extent of Poisson effect, the condition in which a body tends to expand perpendicular to the direction of compression. As a consequence, when a material is subjected to tensile stresses it will compress in the opposite direction. It is the ratio of the lateral strain to the longitudinal strain and is symbolized by the Greek letter "µ". For most materials used in construction industry the Poisson's ratio ranges between 0.25 and 0.33.

Correlation between Elastic Properties

According to the mathematical formulas of the elasticity theory, the following correlations of the aforementioned elastic properties derive:

  • E=2*G*(1+μ)
  • Ε=3*Κ*(1-2*μ)
  • Ε=9*Κ*G/(3*K+G)
  • μ=(3*K-2*G)/(6*K+2*G)




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