Shear modulus

Shear modulus is a material’s resistance to elastic shape change under shear stress, defined as shear stress divided by shear strain in the linear elastic range.

Shear stress: Shear stress is force per unit area acting parallel to a surface. It is the load in the numerator of the shear-modulus definition.
Young's modulus: Young's modulus measures stiffness under uniaxial tension or compression. It is another elastic stiffness, related to shear modulus for isotropic materials.
Dynamic mechanical analysis: Dynamic mechanical analysis measures a material’s response to oscillating mechanical loads. Its shear measurements can characterize frequency-dependent modulus.
Shear thinning: Shear thinning is a decrease in a fluid’s apparent viscosity as shear rate increases. It describes rate-dependent flow resistance, not elastic shear stiffness.
Shear strain: Shear strain measures angular distortion caused by tangential forces. It is the deformation in the denominator of the shear-modulus definition.
Bulk modulus: Bulk modulus measures resistance to uniform compression. Together with shear modulus, it describes isotropic elastic response.
Rheology: Rheology studies how materials deform and flow under applied forces. Shear modulus is a central measure for elastic behavior in soft and flowing materials.
Yield strength: Yield strength is the stress at which a material begins permanent deformation. It marks an elastic-limit threshold, whereas shear modulus describes elastic stiffness.
Hooke's law: Hooke's law states that, within an elastic range, deformation is proportional to applied force. The modulus is the proportionality linking shear stress and strain in the linear range.
Poisson's ratio: Poisson's ratio is the ratio of transverse strain to axial strain under uniaxial loading. It links shear modulus to Young's and bulk moduli in isotropic materials.

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