18.16 : 剪切应变

In a cubic element with a general state of stress, the shearing stresses can deform a cube into an oblique parallelepiped without affecting normal strains. The angular change under shearing stress is the shearing strain.

A cube, when subjected to only shearing stress, morphs into a rhomboid, highlighting the impact of shearing strain.

When the angle between the axes of the cube shrinks, the strain is deemed positive. The shearing stress-strain diagram follows Hooke's law, where the initial straight line indicates proportionality between shearing stress and strain.

The constant G in Hooke's law for shearing is termed the shear modulus or modulus of rigidity of the material. It is expressed in the same units as the shearing stress and is less than half but more than one-third of the modulus of elasticity.

For general stress conditions, a generalized Hooke's law is obtained using the shearing strain relations and Hook's law.

The constants in these relationships are determined experimentally, which can then be used to predict material deformations from various stress combinations.