Modification of Hookes law for multiaxial stress in viscoelastic solids

On the basis of Hooke’s law for multiaxial stress in elastic solids, similar relationships for viscoelastic materials are considered. It is assumed that the material is homogeneous and isotropic, and that the Kelvin-Voigt’s model is applicable to normal strain components. An analogous model is also taken for shear strain components. It is shown that the ratio of coefficients of viscous damping of normal and shear strain components is equal to the ratio of Young modulus and shear modulus. As a result, the modified Hooke’s law for multiaxial stress in viscoelastic materials has been formulated which includes three material constants: Young modulus, Poisson’s ratio and coefficient of viscous damping of normal strain.