Introduction. Thermomechanical effects arising in heterogeneous composite materials under the influence of temperature significantly affect the strength and durability of structures made of them. These effects have a special influence on the thermal deformation of bridge and road structures under conditions of seasonal and daily changes in ambient temperature. They are caused by non-uniformity of the thermomechanical parameters of its fractions and fittings. Until now, the phenomenon of thermomechanical deformation of reinforced structures has not been sufficiently studied, therefore the tasks of their research are urgent.
Problem Statement. The problem of the performed research is to establish the laws of thermomechanical deformation of composite materials (including cement concrete and asphalt concrete), which are reinforced with reinforcing rods, in the fields of variable temperatures.
Purpose. The purpose of the work is to derive mathematical ratios that determine intrastructural thermal stresses in composites caused by variable temperature fields and heterogeneity of materials.
Materials and methods. In this work, based on the provisions of the theory of thermoelasticity, the task of analytical research of intrastructural thermal stresses in composites with rod reinforcement under the influence of variable temperature fields under conditions of thermomechanical incompatibility of the system components is set. A mathematical model of thermoelastic deformation of a non-homogeneous material has been developed, containing a three-point system of ordinary differential equations with boundary equalities at the edges of the area selected for calculation and on the surface of the contact of the reinforcement with the matrix. The solution of these equations for the case of exponential temperature distribution, which is the general solution of the heat conduction equation, was constructed using the methods of mathematical analysis. Displacement and stress distribution functions are formulated.
Results. On the example of asphalt concrete material reinforced with steel rods, distribution functions of thermal displacements and intrastructural thermal stresses are constructed for various cases of exponential temperature distribution in the system at typical values of the thermomechanical characteristics of the system phases.
Conclusions. As a result of mathematical modeling, it was established that in cases of thermal deformation of composite materials in variable temperature fields, two mechanisms of the occurrence of intrastructural thermal stresses in the system are implemented: the internal mechanism and the gradient mechanism. It is shown that even at relatively low temperature values, intrastructural thermal stresses can reach significant values. They are maximal on the contact surface, have a local character and rapidly decrease with distance from it. At the same time, with a change in the exponents of the function of the temperature change, the field of thermal stresses has a tendency to be significantly rearranged. Examples from practice are considered.
