Drying, as a process of changing the moisture content and temperature of capillary-porous materials, is a necessary step in many technologies. When predicting moisture changes, it is necessary to find a balance between the complexity of a model and the accuracy of the simulation results. The purpose of this work was the development of a mathematical model for drying a capillary-porous material with direct consideration of its initial moisture content and drying temperature. Methods of mathematical modeling were used in the work. Using the developed model, an analysis of the features of the drying process of materials with high and low initial moisture content has been carried out. The analytical relationship for determining the time at which the extremum of the drying rate is reached has been substantiated. A model has been developed to directly take into account the influence of the initial material moisture content and drying temperature. The simulation results are consistent with the experiments on drying ceramic blocks for construction which are described in the literature. The obtained results can be taken into account in studies of the effect of drying modes on the energy consumption of a drying process.

An experimental study and modeling of the behavior of wood during compression along the fibers was carried out. The nonlinear analytical dependence of the load on the strain was considered. Attention was focused on the post-peak stage of deformation in order to determine the load and displacement at which the transition to the stage of plastic deformation occurs. The work was aimed at substantiating the application of the energy criterion of brittle fracture as a criterion for the transition to the stage of plastic deformation. To achieve this goal, methods of mathematical modeling and analysis of test results were used. As an upshot, a simple and practical procedure was developed to predict the transition point to the above stage of plastic deformation. The simulation results were consistent with laboratory tests of samples and fragments of structures. The practical significance of this criterion lies in its possible use as an additional tool for analyzing the condition of some wooden structures. Energy criteria, including the one mentioned above, belong to fairly universal criteria. Accordingly, the research methodology can be adapted to analyze the behavior of, for example, composites under other types of loads in further studies.

Low-temperature cracking is one of the main reasons for the deterioration of the upper layer of roads in regions with cold winters. A large number of works focused on deterioration prevention are known, however the interdisciplinary problem of low-temperature cracking remains relevant. The important, but insufficiently studied factor is the distribution of normal and tangential (shear) forces acting on the upper layer of the road. The objective of the current study was to clarify insight about the distribution of tangential forces in the contact area of the upper layer of the road with the base. There are works in which it is assumed that these forces are distributed by a piecewise linear law. We propose a mechanical and mathematical model and an analytical solution to the problem of the distribution of shear forces in the contact area of the upper layer with the base. The main result of the study: it is found that the distribution of shear forces in the segment of the asphalt concrete layer is described by a second-order polynomial. However, the shear stresses are distributed linearly over the entire length of the segment and reach the highest modulo values in the area of the end sections of the segment. The results of the presented study clarify the understanding of functioning of the upper road layer at low temperatures. By that, the contribution to the solution of the problem of increasing the crack resistance of roads in regions with cold winters is made.

This article considers the effect of constant and variable Poisson’s ratio on cracking in concrete and rock specimens under uniaxial compression using mechanical systems modeling methods. The article presents an analysis of the data confirming the increase in Poisson’s ratio under specimen loading. A system of equations for modeling the effect of Poisson’s ratio on cracking under uniaxial compression is proposed. The comparison showed that the model with a constant Poisson’s ratio predicts a thickness of the surface layer with cracks that is underestimated by approximately 10%. In practice, this means that the model with a constant Poisson’s ratio underestimates the risk of failure. A technique for analyzing random deviations of Poisson’s ratio from the variable mathematical expectation is proposed. The comparison showed that the model with a variable Poisson’s ratio leads to results that are more cautious, i.e., it does not potentially overestimate the safety factor. The model predicts an increase in uniaxial compression strength when using external reinforcement. An equation is proposed for determining the required wall thickness of a conditional reinforcement shell depending on the axial compressive stress. The study contributes to understanding the potential vulnerability of load-bearing structures and makes a certain contribution to increasing their reliability.

Low-temperature cracking is one of the main reasons for the deterioration of the upper layer of roads in regions with cold climate. The material of the top layer can be, e.g., asphalt concrete or frozen soil. In this paper it is assumed that the temperature of the underlying layer is non- negative, i.e. a model in the form of a two-layer structure is used. A large number of works aimed at preventing wear are known, but the interdisciplinary problem of low-temperature cracking in seasonal freezing of soils remains relevant. In publications, as a rule, consider the destruction of freezing, that is, with a decrease in temperature. Much less attention is paid to the modeling and forecasting of damage to the upper layer of roads, if its temperature rises, but remains negative. In this case, the layer is compressed and the appearance of wave-like irregularities on the day surface (buckling) is possible. The objective of the current study was modeling the conditions of occurrence and prediction of damage to the upper layer of roads when the changes negative temperature. The paper uses methods of mathematical modeling of mechanical systems, as well as adaptation of the known results of other authors. The estimation of the critical wavelength at a bend of the compressed upper layer is given. The results of numerical simulation are consistent with the experimental data known in the literature.