Iterative Model of Elastic Deformation of a Particle Conglomerate Taking into Account the Compressibility of the Medium during Pressing

Introduction. Briquetting and pressing of wood and other powdered materials are becoming key processes in the circular economy and recycling of wood processing waste. Accurate calculation of compaction pressure is essential for equipment selection and optimization, making the task of modeling the deformation of conglomerates both practical and economically significant. The literature addresses the mechanics of powder media, porous materials, and the modeling of elastic-plastic deformations of granular conglomerates. However, most models assume fixed mechanical characteristics or approximations that do not account for the dependence of strength and elastic properties on changing density under compression. This leaves a gap in theoretical and applied approaches to adequately calculating pressure for materials with variable density. Therefore, the objective of this work is to develop an approach for calculating the compaction pressure of a particle conglomerate as a function of the degree of elastic compression, taking into account changes in the mechanical characteristics of the medium.

Materials and Methods. In the mathematical description of the research problem, the provisions of the theory of elasticity were used. Based on the principle of superposition, the process of medium deformation was divided into a number of stages, within which the particle conglomerate received a small increment in height, and the mechanical characteristics assumed a constant value. The proposed approach for determining the compaction pressure was based on the solution to a series of inverse elastic problems in which the displacement of the upper boundary of a conglomerate of rectangular particles was specified, and the normal stress that caused this increment was sought. To account for changes in the density of the medium during deformation, the method of sequential loads was used, within each of them, the density was taken to be constant and was determined depending on the magnitude of the total compressive deformation. The Hencky strain, which has the property of additivity, was used as a measure of deformation.

Results. As part of the study, an iterative model was constructed for calculating the compaction pressure of a particle conglomerate when the mechanical characteristics change depending on the degree of elastic compression. Series of test calculations were conducted using a conglomerate of wood particles, whose Young's modulus is described by a power-law density function. At each stage of deformation, the elastic constants of the material were assumed to be constant, depending on the density of the medium. Using the equilibrium equation and the superposition principle, based on the results of solving elastic deformation problems, the compaction pressure was calculated at each loading stage, and the dependence of the compaction pressure on the magnitude of the compressive deformation and the degree of compaction was constructed.

Discussion. The obtained results of deformation of the medium taking into account the change in mechanical characteristics depending on the degree of compression showed a clearly expressed nonlinearity of the curve of dependence of the compaction pressure on the compression deformation — with an increase in pressure, both the degree of compaction of the medium and the compression deformation increase. A comparative analysis of calculations using the example of a conglomerate of wood particles under the condition of a constant density of the medium and taking into account the change in density during the deformation process revealed a significant error in estimating the compaction pressure when averaging the density or when using constant density values corresponding to the initial (undeformed) or final state.

Conclusion. The constructed iterative model allows for calculating the compaction pressure of a particle conglomerate, taking into account changes in mechanical properties under elastic compression. The proposed approach accounts for the nonlinearity of the compaction pressure dependence on the degree of compaction of the medium and can be applied to briquetting processes for wood waste.

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