Shear modulus

The shear modulus (also shear modulus, G - modulus, shear modulus or modulus of torsion ) is a material constant, which provides information on the linear-elastic deformation of a component due to a shear force or shear stress. The SI unit is Newton per square meter ( 1 N / m² = 1 Pa ), ie the unit of voltage. In material databases of the shear modulus is usually expressed in N / mm ² ( = MPa) or GPa.

In the context of elasticity theory corresponds to the shear modulus of the second Lamé constants and there carries the symbol.

Definition

The shear modulus is the ratio between the shear stress and the tangent of the shear angle ( slip ):

For small angles can be set to a first approximation ( small angle approximation ).

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

In torsion of a component is calculated from the shear modulus, its torsional stiffness and the torsional moment, which is based on the axis around which the body is twisted:

Analogous to the determination of the axial stiffness ( the product of the elastic modulus and cross-sectional area ).

Context of other material constants

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

For linear-elastic, non- auxetic material, the Poisson's ratio is in the range Thus, for the shear modulus of most materials:

In the special case of linear elastic auxetic materials, the Poisson's ratio has the scope of this result for the shear modulus: