elastic modulus (rus. модуль упругости otherwise модуль Юнга) — a ratio between stress and strain in an object.

### Description

Deformation of an object under elastic compression, extension or shear is determined only by the strength of stresses applied to the object and does not depend on the sequence in which such stresses are applied. Elastic strain of an object is reversible: the object will return to its initial state as soon as the applied stress is removed. In the domain of small deformations, the stress to strain ratio is a linear function (linear elasticity state).

In a simple case of tensile deformation, a sample’s elongation in the direction of extension is directly proportional to the force applied to the object. The ratio of the sample’s elongation and the force applied to the sample divided by the area of the sample’s base is known as the Young modulus (E) of a given material. The Poisson ratio ( ) is defined as a negative of the ratio of strain in the direction perpendicular to the tension or compression axis to the strain along this axis resulting from simple tension or compression, and is also used to describe the behaviour of a linear solid body. An incompressible body will have a Poisson ratio of 0.5. The following ratios are also used: shear modulus or modulus of rigidity (G or ), bulk modulus of elasticity or modulus of volume elasticity (K), and longitudinal modulus (M). Any two parameters of those listed above will suffice for a comprehensive description of the behaviour of an isotropic linear solid body. In a general case of linear elasticity of an anisotropic body, strain is defined by a second-rank tensor, the deformation tensor, whose relation to the values of mechanical stress that are defined by the stress tensor may be determined based on the elasticity tensor, a fourth-rank tensor containing 21 independent ratios.

### Illustrations

#### Authors

• Goryacheva Irina G.
• Shpenеv Alexey G.

#### Sources

1. Chernykh K.F. Nonlinear elasticity // Mathematical modeling of systems and processes (in Russian). 2001. №9. 177–185 pp.
2. Landau L. D., Lifshic E.M. Course of Theoretical Physics. V. VII. The theory of elasticity (in Russian). — Мoscow: Nauka, 1987. — 248 pp.