DYNAMIC PROBLEMS OF THERMOELASTICITY
AND THERMOELASTOPLASTICITY APPLIED
TO HIGH-TEMPERATURE AND CERAMIC MATERIALS
V. V. Kolomeitsev, O. V. Kolomeitseva, and E. F. Kolomeitseva
Translated from Novye Ogneupory, No. 6, pp. 51 – 54, June 2008.
Original article submitted February 7, 2008.
Methods are considered for resolving dynamic problems of thermoelasticity and thermoelastoplasticity.
It is shown that as a result of incorrect physical hypotheses, lying at the basis of thermal conductivity and
wave formation mechanisms in a solid with thermal shock in the region of acoustic waves of stresses, well
known methods for resolving dynamic problems cannot lead to universal strength and heat resistance criteria.
This complicates development of principles for designing high-temperature, and especially refractory and
ceramic materials, resistant to thermal shock.
The solution of dynamic (transient) problems of thermo-
elasticity and thermoelastoplasticity has important practical
applications for designing and preparing high-temperature
materials and objects resistant to thermal shock in the range
of acoustic or shock-wave stresses.
A widespread group in the class of materials are silicate
and refractory non-metallic materials, including refractories,
i.e. refractory materials and objects, engineering and structural
ceramics. By exhibiting unique properties these materials are
extremely sensitive to thermal shock in the range of acoustic
stress waves as a result of brittleness, high elasticity modulus
and reduced thermal conductivity, that limit the range of their
application and reduce life under conditions of the operation
of transient thermal fluxes.
Since 1950 the dynamic problem of thermoelasticity and
thermoelastoplasticity and problems of preparing high-
temperature thermally stable materials has been the subject
of 17000 publications
, that points to the importance, and in
a number of cases, the irresolution of these problems. It is
surprising for more than 50 years of the history of the
development of contemporary solid mechanics and physics
unified model representations have not been developed in
strength and thermoelasticity theories
Dynamic problems of thermoelasticity are resolved
within the framework of the mathematical body of solid
mechanics using the generalized Hooke’s law, differential
equations for movement, a differential equation for Fourier
transient thermal conductivity, geometric relationships,
initial and boundary conditions, and also a series of assump-
tions whose basis is either not clear or it is not generally
considered incorrect. In particular, the last affirmation
concerns the mechanism of wave formation with thermal
shock and the mechanism of heat propagation that are
definitive in constructing an adequate practical physical
model of thermal shock, for example in the range of acoustic
waves and stresses.
In order to resolve a set of dynamic of thermoelasticity
equations the Fourier transient thermal conductivity equation
is written taking account of the interconnection of tempe
rature and stress fields. There is also consideration of the
problem of dynamic thermoelasticity that separates the
problem of thermal conductivity and the problem of deter
mining thermal stresses according to temperature field
found. The problem is resolved by both mathematical and
analytical methods. Pointing to the importance of analytical
solution of unidimensional problems makes it possible to
obtain precise constitutive relationships . An adequate
unidimensional model of the unconnected problem of
thermoelasticity is reduced to calculating only temperature
T(x, t) and stress tensor components s
(x, t). The remaining
nonzero stress tensor components are linear combinations of
these two functions.
Thus, known methods for resolving dynamic problems
of thermoelasticity and thermoelastoplasticity are reduced to
calculating thermal stresses in relation to the thermophysical
properties of a body, its shape and dimensions, and also
Refractories and Industrial Ceramics Vol. 49, No. 4, 2008
1083-4877/08/4904-0290 © 2008 Springer Science+Business Media, Inc.
This is a rough number of publications.
Unified representation models in strength and thermoelasticity
theory applied to high-temperature non-metallic materials have been
developed by the authors of the present article in 1989 – 2001.