Abstract
Modification of Hooke's 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.
Highlights
For the purpose of solving physical problems considered in the present paper, it is assumed that an engineering detail is made of a homogeneous isotropic metal and loaded below the yield point
If a load is suddenly applied and maintained constant, a small amount of “creep” will always be observed [1]. This creep is due to anelastic strain which may arise from any of several sources, such as the presence of grain boundaries, twin boundaries, or slip bands, the diffusion of interstitial solute atoms and the phenomenon of magnetostriction
Where σ are the normal stress components and τ are the shear stress components on three orthogonal planes passing through the point
Summary
HOOKE’S LAWFor the purpose of solving physical problems considered in the present paper, it is assumed that an engineering detail is made of a homogeneous isotropic metal and loaded below the yield point. The elastic behaviour of a particular homogeneous, isotropic metal at a given temperature is completely defined by the Young modulus and the Poisson’s ratio [1, 2]. The Kelvin-Voigt′s model is applied to viscoelastic materials under three-dimensional loads. Where σ are the normal stress components and τ are the shear stress components on three orthogonal planes passing through the point.
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