Shear modulus

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material Typical values ​​for
the shear modulus in G Pa
(at room temperature)
steel 79.3-81
copper 47
titanium 41.4
Glass 26.2
aluminum 25.5
magnesium 17th
Polyethylene 0.117
rubber 0.0003

Shear modulus of a special basic glass: Influences of the addition of selected glass components

The shear modulus (also slip modulus , G-modulus , shear modulus or torsion modulus ) is a material constant that provides information about the linear-elastic deformation of a component as a result of a shear force or shear stress . The SI unit is Newton per square meter (1 N / m² = 1  Pa ), i.e. the unit of mechanical stress . In material databases , the shear modulus is usually given in N / mm² (= MPa) or kN / mm² (= GPa).

In the context of the theory of elasticity , the shear modulus corresponds to the second Lamé constant and bears the symbol there .


The shear modulus describes the relationship between the shear stress and the tangent of the shear angle (slip):

A first approximation can be used for small angles ( small-angle approximation ).

This formula is analogous to Hooke's law for the 1-axis stress state :

When torsional stress of a component to its calculated torsional stiffness of the shear modulus and the torsional constant , which is related to the axis about which the body is twisted:

analogous to the determination of the tensile stiffness (from the product of the modulus of elasticity and cross-sectional area).

Relationship with other material constants

In an isotropic material the shear modulus is the elastic modulus  E , the Poisson's ratio  ν  (Poisson's ratio) and the bulk modulus  K in the following relationship:

For linear-elastic, non - auxetic material, the Poisson's number is greater than or equal to zero. The energy conservation results in the positive definiteness of the compression module and the modulus of elasticity . It follows that the Poisson's number is below 0.5. This results in the shear modulus of most materials in the linear-elastic range:

Auxetic materials are defined to have a negative Poisson's number, which only a few materials do. Since the shear modulus has a positive definite size due to the conservation of energy, the following applies to auxetic materials in the linear-elastic range:

Since the modulus of elasticity is also positive definite, the range of validity results for the Poisson's number

Conversion between the elastic constants

The module ... ... results from:
Compression module
modulus of elasticity
1. Lamé constant
Shear modulus or (2nd Lamé constant)
Poisson's number
Longitudinal module

See also

Web links

Individual evidence

  1. Crandall, Dahl, Lardner: An Introduction to the Mechanics of Solids . McGraw-Hill, Boston 1959.
  2. Eurocode 3: Steel construction. Retrieved May 7, 2020 .
  3. Calculation of the shear modulus of glasses (English).
  4. G. Mavko, T. Mukerji, J. Dvorkin: The Rock Physics Handbook . Cambridge University Press, 2003, ISBN 0-521-54344-4 (paperback).