Hooke's law

For elastic deformations the normal stress is directly proportional to strain. The ratio of axial stress/strain is a constant. This constant is known as Young's modulus or modulus of elasticity E. Young's modulus is directly proportional to the axial stress and inversely proportional to the axial strain.

For three-dimensional stress state the formulas include more than one stress component. The expressions for isotropic elastic body include three elastic constants of material: modulus of elasticity E, Poisson's ratio m and shear modulus G. The elastic constants are characteristics of the material. They do not depend on the shape or size of the specimen.

The shear modulus G can be expressed by the first two elastic constants. There are only two constants that are independent parameters for an isotropic material.

Poisson's ratio m characterizes transverse deformation under axial tension or compression. It is a dimensionless parameter. For m=0.3, axial tension of 10% corresponds to a transverse compression of 3%.

The expressions show another form of the Hooke's law. Normal stress sx depends on all three linear components of strain e_x, e_y and e_z.

Volume expansion e characterizes an increase of an element size, not a change of its shape. It depends on the linear strains only. The volume expansion e can be defined by the elastic constants of the material E, m and the sum of the normal stresses s_x, s_y and s_y.