Keywords: masonry-like materials, temperature-dependent Young's modulus, equilibrium problem, thermal loads.

This paper deals with the thermoelasticity of masonry-like (or no-tension) materials, a special class of nonlinear elastic materials described in [1,2,3], whose constitutive equation is adopted to model the mechanical behavior of solids not withstanding tensile stresses. There are many engineering problems in which the presence of thermal dilatation must be taken into account. Consider, for example the thermomechanical behaviour of masonry under elevated temperatures [4], as well as that of the refractory linings of vessels and ladles used in the iron and steel industry [1,3,5,6,7]. In many such cases, the thermal variation during the thermomechanical process under examination is so high that the dependence of material constants on temperature cannot be ignored. The ultrasonic techniques used in [8] to measure the Young's modulus of MgO/C refractories at high temperatures revealed that the variations of the Young's modulus can reach levels as high as 40%.

In this paper, by limiting ourselves the thermomechanical uncoupling [1,2,3], we study the behaviour of refractory materials and analyse the influence of the temperature dependence of the Young's modulus on the stress field and crack distribution in a masonry-like spherical container subjected to thermal loads. We solve the equilibrium problem of two spherical containers, one made of a linear elastic material and the other made of a masonry-like material with the same elastic constants, subjected to internal and external uniform radial pressures and steady temperature distributions. In both cases, if the Young's modulus does not depend on the temperature, the solution to the equilibrium problem can be calculated explicitly. Instead, when the Young's modulus depends on the temperature, the solution is calculated numerically using the NOSA code [1]. The solutions corresponding to constant and temperature-dependent Young's moduli are compared. It is shown that for masonry-like materials, both the crack distribution and the stress field depend heavily on the Young's modulus. On the contrary, the dependence of the specific heat on the Young's modulus is very weak.

1

M. Lucchesi, C. Padovani, G. Pasquinelli, N. Zani, "Masonry constructions: mechanical models and numerical Applications", Lecture Notes in Applied and Computational Mechanics, 39, Springer-Verlag Berlin Heidelberg, 2008.

2

M. Lucchesi, C. Padovani, G. Pasquinelli, "Thermodynamics of no-tension materials", International Journal of Solids and Structures 37, 6581-6004, 2000. doi:10.1016/S0020-7683(99)00204-8

3

C. Padovani, G. Pasquinelli, N. Zani, "A numerical method for solving equilibrium problems of no-tension solids in the presence of thermal expansion", Comput. Methods Appl. Mech. Engrg., 90, 55-73, 2000.

4

A. Nadjai1, M. O'Garra, F.A. Ali, D. Laverty, "A numerical model for the behaviour of masonry under elevated temperatures", Fire Mater., 27, 163-182, 2003. doi:10.1002/fam.824

5

P. Boisse, A. Gasser, J. Rousseau, "Computations of refractory lining structures under thermal loading", Advances in Engineering Software, 33, 487-496, 2002. doi:10.1016/S0965-9978(02)00064-9

6

D. Gruber, K. Andreev, H. Harmuth, "FEM simulation of the thermomechanical behaviour of the refractory lining of a blast furnace", Journal of Material Processing Technology, 155-156, 1539-1543, 2004. doi:10.1016/j.jmatprotec.2004.04.249

7

V.V. Kolomeitsev, O V. Lolomeitseva, E.F. Kolomeitseva, "Dynamic problems of thermoelasticity and thermoplasticity applied to high-temperature and ceramic materials", Refractories and Industrial Ceramics, 49, 290-292, 2008. doi:10.1007/s11148-008-9079-2

8

H. Baudson, F. Debucquoy, M. Huger, C. Gault, M. Rigaud, "Ultrasonic measurement of Young's modulus MgO/C refractories at high temperature", Journal of the European Ceramic Society, 19, 1895-1901, 1999. doi:10.1016/S0955-2219(98)00268-4

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