All About Shear Modulus

Shear modulus, sometimes called the modulus of rigidity, is a fundamental material property that measures how stiff a material is when subjected to shear forces. In everyday terms, it describes how resistant a substance is to shape change when one part slides parallel to another. In this article, we’ll explain what shear modulus is, how it’s calculated, and how it compares with other elastic moduli, with real-world engineering examples to make it clear.

What is Shear Modulus?

In the diagram, the block is fixed at the bottom while a force F is applied parallel to the top surface. This force causes a horizontal displacement Δx, and the block deforms into a slanted shape. The tilt angle θ represents the shear strain (γ), which describes how much the shape has been distorted.

The shear stress (τ) is the applied force divided by the surface area A where the force acts:

τ = F / A

The shear strain (γ) is the ratio of the horizontal displacement to the height of the block:

γ = Δx / L (for small angles, θ ≈ γ in radians)

The shear modulus (G), sometimes denoted by μ or S, measures how resistant a material is to this type of distortion. It is defined as the ratio of shear stress to shear strain:

G = τ / γ = (F / A) / (Δx / L) = (F · L) / (A · Δx)

In the SI system, the unit of shear modulus is the pascal (Pa), which equals one newton per square meter (N/m²). Because the pascal is a very small unit, shear moduli for solid materials are usually very large. For this reason, engineers and scientists typically express G in gigapascals (GPa), where 1 GPa = 10⁹ Pa.

Shear Modulus Values

The table below shows typical shear modulus values for common materials:

These figures show how much materials differ in rigidity. Metals tend to have shear moduli in the tens of gigapascals. Ceramics and glass fall in a similar range, while concrete is somewhat lower. Plastics usually come in around 1 GPa or less. Even softer are rubber and elastomers, with shear moduli only in the megapascal range. At the very top, diamond reaches hundreds of gigapascals and is one of the stiffest known materials.

Materials with high shear modulus strongly resist being deformed or twisted. This is why steel and titanium alloys are essential in structures like bridges, buildings, and aircraft frames. Their stiffness keeps beams and fasteners from bending or shearing under heavy loads. Glass and ceramics, although brittle, benefit from having a relatively high modulus too. It helps them maintain precise shapes in applications such as lenses and semiconductor wafers. Diamond, with its very high shear modulus, undergoes almost no elastic strain even under large forces. This is why diamond cutting tools stay sharp.

On the other hand, materials with a low shear modulus are chosen when flexibility is an advantage. Rubber and other elastomers are used in vibration dampers, seals, and earthquake base isolators because their softness allows them to shear easily and absorb energy. Polymers such as polyethylene or nylon strike a balance between flexibility and strength, which is why they are widely used in lightweight structures and impact-resistant parts. Even natural materials like wood show strong directional differences: across the grain its shear modulus is much lower than along it, and builders need to account for this to avoid splitting under shear forces.

Shear Modulus Calculation

Different test methods can be used to determine the shear modulus G, and the choice depends on the material and whether you need a static or dynamic value. For metals and other isotropic solids, a common approach is a static torsion test on a rod or thin-walled tube; the slope of angle of twist versus applied torque gives G. ASTM E143 specifies a room-temperature procedure for structural materials.

For dynamic measurements, a torsion pendulum can be used: measure the oscillation period of a specimen–mass system and relate it to the (complex) shear modulus. ASTM D2236 is a legacy standard that describes this approach for plastics.

For fiber-reinforced composites, the in-plane shear modulus is obtained with V-notched methods such as ASTM D5379 (Iosipescu) and ASTM D7078 (V-notched rail shear). ASTM D4255 (rail shear) is also widely used for polymer-matrix composites.

Note that ASTM A938 is a torsion test for metallic wire intended to assess torsional performance (e.g., ductility); it is not a standard method for determining G.

Sometimes G is not measured directly but calculated from other data. For an isotropic material with Young’s modulus E and Poisson’s ratio ν,

Shear Modulus vs. Young’s Modulus vs. Bulk Modulus

These three constants capture the main ways a solid resists deformation: stretching, shearing, and squeezing. Young’s modulus (E) measures stiffness under tension or compression along a single axis. The shear modulus (G) describes resistance to shape change when layers of the material slide past one another. The bulk modulus (K) characterizes how strongly a material resists changes in volume under uniform pressure.

For many isotropic, linear-elastic solids, the three are linked by Poisson’s ratio (ν):

E = 2G(1 + ν) = 3K(1 – 2ν)

This relation is widely used but does not apply to anisotropic materials such as wood and composites, or to viscoelastic materials like polymers and rubbers, where time and temperature effects are important.

Typical values illustrate their differences. For steel, E ≈ 210 GPa and ν ≈ 0.30, giving G ≈ 81 GPa and K ≈ 170 GPa. Aluminum, with a lower E (~70 GPa), has a shear modulus in the mid-20s GPa range. Rubber, by contrast, is nearly incompressible (ν → 0.5): K becomes extremely large, while E and G remain small.

In practice, engineers use E when they need to know how stiff a bar or beam is under tension, compression, or bending. G is chosen when torsion, shear, or in-plane distortion matters, such as in shafts, adhesive layers, or thin webs. K is relevant when pressure causes volume changes, which is especially important in fluid systems, acoustics, or high-pressure vessels.

Applications of Shear Modulus

The role of shear modulus is best understood through practical engineering examples.

In civil and structural design, materials often face shear forces. Wind pushing on a skyscraper induces shear in the frame, and loads on a bridge cause shear within the beam cross-sections. Engineers rely on materials with sufficient shear stiffness to prevent excessive deformation or failure.

A classic case is the use of structural steel in tall buildings. Steel has a high shear modulus (~75–80 GPa), making it very rigid against shape change. Skyscrapers must withstand vertical loads, which involve Young’s modulus, as well as lateral loads like wind and earthquakes that create shear and torsional stresses. Steel’s high G helps the building resist swaying or twisting, keeping it stable.

Concrete beams illustrate the point as well. Plain concrete has a moderate shear modulus (~21 GPa) but is brittle, so steel reinforcement is added not only for tensile strength but also to improve shear capacity and prevent brittle shear failure. Bridges work similarly: under moving vehicles, beam sections experience shear. A high shear modulus ensures the bridge deflects mainly by bending, not by sliding between layers. Imagine a bridge built of rubber—with its very low G, it would distort badly under load.

Interestingly, low shear modulus can also be an advantage. Seismic base isolation systems use laminated rubber bearings under buildings. Rubber’s low G (0.001–0.01 GPa) allows the base to shear during an earthquake, decoupling ground motion from the structure above. The building rides out the quake more gently because the rubber absorbs the shear deformation. This shows that neither a high nor low shear modulus is inherently good or bad—it depends on whether the design calls for rigidity or flexibility.