Abstract
On the behaviour of viscoelastic solids under multiaxial loads On the basis of modified Hooke's law for multiaxial stress in viscoelastic solids, threedimensional constitutive equations for strains have been derived. It is shown that after application or removal of triaxial static load, normal and shear strain components vary in course of time proportionally to each other and that in-phase stress components produce in-phase strain components. Harmonic out-of-phase stress as well as multiaxial periodic and stationary random stresses are also considered. The matrix of dynamical flexibility of viscoelastic materials is determined which depends on three material constants (Young modulus, Poisson's ratio and coefficient of viscous damping of normal strain) and load circular frequency.
Highlights
Deformation of solids is accompanied by internal friction [1]
The anelastic strain, which occurs during long-time creep, is basically the same as that which occurs during vibratory load, and in both cases the anelastic behaviour can be expressed in the same terms [2]
The vector of complex amplitudes of n-th terms of the stress components: The matrix of dynamical flexibility of the homogeneous, isotropic viscoelastic material has been determined which depends on three material constants (Young modulus, Poisson’s ratio, coefficient of viscous damping of normal strain) and load circular frequency
Summary
Deformation of solids is accompanied by internal friction [1]. even in the region below the proportionality limit metals are not perfectly elastic [2]. It is obvious that: creep recovery at a given time, following partial or complete unloading from a given prior load of a given duration, is proportional to the stress decrement after creep recovery, deformation should cease and the dimensions should remain constant. As the relaxation modulus is known, the stress response can be determined under any strain loading condition through a convolution integral. The aim of the present paper is to derive three-dimensional constitutive equations for strains by means of the modified Hooke’s law for multiaxial stress in viscoelastic solids [4] because its simplicity in the case of homogeneous isotropic materials may be advantageous
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