Mechanics

2000, No. 4

V.I. Astafev, Y.N. Radayev

V.I. Astafev, A.M. Lokoschenko

TO THE 70^th ANNIVERSARY OF S.A. SHESTERIKOV

E.N. Kozhevnikov, E.V. Afanaseva

SOUND ARSORBTION IN ELASTIC MEDIA WITH CAVITIES FILLED BY VISCOUS LIQUIDS

Energy dissipaition in sound wave propagating in solid media with liquid pores is determined on the base of scattered wave field analysis. It is proposed that energy loss is determined by viscous waves propagating from solid-liquid boundary into liquid pores. Imaginary part of Yung modulus and sound attenuation coeficient are found under neglection of multiple wave scattering.

Y.N. Radayev

NON-LINEAR ELASTICITY AS A FIELD THEORY

Non-linear elasticity is considered from the physical viewpoint as a field theory. First, field equations and constitutive relations of finite-strain elasticity in their canonical forms are derived in a conventional way. In view of practical application to fracture, special attention is paid to to the construction and immediate consequences of the canonical equations of energy and pseudomomentum balance, thus demonstrating the wealth of the framework, and allowing readily introduce Eshelby`s stress tensor, the path-independent integral and Eshelby`s force, acting on an elastic inhomogeneity. Then the field-theoretic concept is used in order to define the tensors of non-linear elasticity and reveal their natural co-ordinate representation. The variational formulation and Noether`s theorem are chosen to derive conservation laws and additional path-independent integrals. Inverse-motion description and variational symmetries of the Hamiltonian action are shown provide a true field theory of non-linear inhomogeneous elasticity.

Y.E. Senitskii

THEOREM OF EXPANSION ON CHARACTERISTIC VECTOR-FUNCTIONS IN DYNAMIC THEORY OF ELASTICITY

Using the Gobert inquality we give the proof of fundamental theorem stating that linear differential operators of dynamic theory of elasticity generate extended-orthogonal systems of characteristic vector-functions, but corresponding to them complete spectral expansions are the only ones and possess mean square converge in the metric of spase L₂. The results are correct for resolving functions in class C² under defenite bounding conditions for the first basic and mixed boundary-value problems of theory of elasticity that is connected with the procedure it self with the method of expansion on characteristic vector-functions.

L.V. Stepanova, M.E. Fedina

Asymptotic stress and damage fields for stationary crack under creep conditions for damage-creep coupled statment of the problem is given. Self-similar variable introduced by Riedel is employed for the analysis and self-similar solution of the problem is obtained. It is shown that the fully-damaged zone near the crack tip where all stresses and scalar integrity parameter are equalled to zero exists. The geometry of the fully-damaged zone for different values of material constants is studied and presented.