This article deals with the problem of predicting the brittle fracture of rocks and similar materials, which can also include frozen sandy soils. Such materials, due to the diversity of their conditions of origin, are characterized by natural heterogeneity at the micro-, meso-, and macro-levels, which makes it difficult to develop sufficiently universal criteria for their strength. Despite a number of known models and criteria of strength and fracture, the search for such criteria remains an urgent problem. In this paper, using the energy approach to the mathematical modeling of mechanical systems, the fracture criterion is justified, which differs from the known criteria that do not require integration to calculate the strain energy We and dissipation energy Wd. The well-known relation for the input energy W=We+Wd is used. The object of the study was the ratio of dW=dWe+dWd. The main research question concerned what the ratio of dWe and dWd would be at the point of brittle failure. The search for an answer to the question led to the justification of a differential energy criterion for the failure of brittle materials on the descending branch of the full stress–strain curve. It was found that the point of predicted fracture is determined by the equality σ=0.5 εEtangential (if there is an inflection point on the ascending branch) or σ=0.5 εEsecant_secant. The main result of the work was ascertaining the differential strength and fracture criteria of brittle materials in the form of inequalities and equations, which were oriented for application in engineering calculations. Examples of application of the developed criteria are given; their consistency with the experimental data known from the literature confirmed.

Experimental research of bone strength remains costly and limited for ethical and technical reasons. Therefore, to predict the mechanical state of bone tissue, as well as similar materials, it is desirable to use computer technology and mathematical modeling. Yet, bone tissue as a bio-mechanical object with a hierarchical structure is difficult to analyze for strength and rigidity; therefore, empirical models are often used, the disadvantage of which is their limited application scope. The use of new analytical solutions overcomes the limitations of empirical models and significantly improves the way engineering problems are solved. Aim of the paper: the development of analytical solutions for computer models of the mechanical state of bone and similar materials. Object of research: a model of trabecular bone tissue as a quasi-brittle material under uniaxial compression (or tension). The new ideas of the fracture mechanics, as well as the methods of mathematical modeling and the biomechanics of bone tissues were used in the work. Compression and tension are considered as asymmetric mechanical states of the material. Results: a new nonlinear function that simulates both tension and compression is justified, analytical solutions for determining the effective and apparent elastic modulus are developed, the residual resource function and the damage function are justified, and the dependences of the initial and effective stresses on strain are obtained. Using the energy criterion, it is proven that the effective stress continuously increases both before and after the extremum point on the load-displacement plot. It is noted that the destruction of bone material is more likely at the inflection point of the load-displacement curve. The model adequacy is explained by the use of the energy criterion of material degradation. The results are consistent with the experimental data available in the literature.

Forests produce a huge amount of organic matter, which is a source of renewable raw materials for the production of technical, feed, food and pharmaceutical products. The logging and woodworking industry in Karelia, as in Russia as a whole, is based exclusively on stem wood. Woody greens are formed while felling ripe and over-mature stands, thinning and implementation of measures for the conservation, protection and reproduction of forests including forest stands cutting. The development of technologies for the use of woody greens is necessary for the multi-purpose utilization of the entire phytomass produced by forest plant communities. An additional economic incentive for young stands thinning and limbing, that are used to improve the quality of logs, is the ability to reduce costs or even ensure the profitability of these measures driven by the development of processing plants and the use of wastes generated during transportation: thinners, low-quality and low-value decidous wood, woody greens, that are raw materials for the production of biologically active preparations of various action. The urgent tasks are to increase the use of importsubstituting pharmaceutical substances and to search the alternative methods for producing raw materials for nutrient mixtures and feed stuff. Technologies for modifying the biochemical composition of coniferous greens, resulting in production of plant raw materials enriched with target biologically active substances, are being developed for the exploration of new plant sources. The water-soluble fraction of coniferous greens contains free amino acids, in particular L-arginine, which plays an important role in the life of animals. A promising way is to increase the free amino acids content in coniferous raw materials and change their quantitative ratio by regulation of the mineral nutrition regime of woody plants. An original scheme of additional supply of coniferous plants with nitrogen and boron is proposed in order to obtain coniferous greens enriched with L-arginine. The use of conifers as bioproducers of L-arginine and the study of its metabolism with reference to climatic factors, conditions of mineral nutrition, seasonal and daily dynamics in the natural environment, the search for ways to increase its level in organs and tissues is of current interest both on the theoretical and practical sides. Obtaining coniferous greens enriched with L-arginine will allow organizing the production of coniferous products for nutrient and pharmaceutical use. It is necessary to analyze the potential sources of raw materials taking into account their availability, costs for enriching the needles with L-arginine and product yield per unit area to assess the economic feasibility of organizing such production. A developed sequence of forestry measures will make it possible to obtain needles enriched with L-arginine, both in the process of implementing various types of forest use, and in carrying out activities aimed at increasing the productivity of forests and preserving their useful functions. Herewith, it is possible to turn costly cleaning and fertilizing of young Scots pine stands into profitable ones with additional products. Technologies of intentional changes in the chemical composition and pharmacological properties of plant raw materials obtained from woody plants will allow the development of new raw materials for biologically active substances.

In this paper, load-displacement and stress-strain diagrams are considered for the uniaxial compression of concrete and under three-point bending. It is known that the destruction of such materials occurs on the descending branch of the load-displacement diagram. The attention of the presented research is focused on the explanation of this phenomenon. Fracture mechanics approaches are used as a research tool. The method for determining effective stresses and modulus of elasticity of concrete based on the results of uniaxial compression tests has been substantiated. The ratios necessary for the calculation were obtained without any assumptions about the reinforcement of concrete and the mechanical properties of its components. However, the effect of these properties is considered indirectly, using the stress and strain peaks determined by standard concrete compression tests. It was found that the effective stresses increase both on the ascending branch and on the descending branch of the load-displacement diagram. This explains the destruction of concrete on the descending branch of the load-displacement diagram. The results of determining the stresses and modulus of elasticity under uniaxial compression are comparable with the results obtained in experiments known in the literature.

In northern forests, winter is the preferred time for logging operations, since, when wet soils freeze, their strength increases, which ensures a high load-bearing capacity of winter forest roads and reduces the cost of forestry work by increasing the load on forestry equipment, including when driving through frozen lowlands. The present article analyzes frozen loamy–sandy soil, which, at subzero temperatures, behaves like a brittle material with a sufficiently high, but limited, strength. Well-known models commonly use empirical parameters, correlations, and numerical methods to estimate the strength of such materials. An analytical model of the full load–displacement curve would reduce the number of necessary calculations and increase the ability to predict the bearing capacity of winter forest roads. However, there are few of these models. Such models were developed, as a rule, to study stress–strain in concrete and rocks, meaning that researchers have to recalculate the load into stress and displacement into deformation, which is not always simple. This work aimed at theoretically justifying a new analytical model for quantifying the bearing capacity of winter forest roads and assessing the adequacy of the model by comparing it with experimental data. To achieve this purpose, the concepts of fracture mechanics and methods of mathematical modeling were used. The model was verified using experimental data, and model examples for determining the peak load were provided. Prospects for development of the research topic were also considered, taking into account new developments in forest road monitoring for logging management.