Glossary term
Shear Modulus
The elastic material stiffness that relates shear stress to shear strain in torsion, shear loading, and wave propagation.
Definition
quantityShear modulus is the elastic stiffness that relates shear stress to shear strain in the linear elastic range.
Shear modulus, usually denoted G, describes resistance to shape change at nearly constant volume. It is used in torsion, shafts, beams, vibration, finite element models, elastomers, composites, adhesives, and viscoelastic materials where shear deformation contributes to stiffness or dynamic response.
In the linear elastic range, shear modulus is defined by:
where \tau is shear stress and \gamma is engineering shear strain. A high shear modulus means the material resists angular distortion; a low shear modulus means it deforms easily in shear.
For an isotropic linear elastic material, shear modulus is related to Young’s modulus E and Poisson’s ratio \nu by:
This relation is not valid for anisotropic materials, layered composites, cracked materials, or nonlinear viscoelastic behaviour unless the assumptions behind isotropic elasticity are satisfied.
Engineering use
Shear modulus appears directly in torsion. For a circular shaft, the angle of twist is governed by torque, shaft length, polar moment of inertia, and G. It also affects beam deflection, shear deformation in short or deep members, wave speed, vibration modes, elastomer mounts, adhesive joints, and finite element material cards.
Materials can have different effective shear modulus depending on temperature, strain rate, frequency, moisture, cure state, ageing, and direction. Elastomers and polymers often require a dynamic or frequency-dependent shear modulus rather than a single static value.
Common mistakes
A common mistake is deriving G from E and Poisson’s ratio for a material that is not isotropic or linear. Another is using a room-temperature static value for a hot, cold, cyclic, or high-rate condition. A strong shear-modulus review states test method, strain range, temperature, frequency or loading rate, material direction, linearity assumption, and whether the value is secant, tangent, storage, or design modulus.