Mechanics of granular and cellular materials
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Instytut Fizyki, UMCS, pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland
Publication date: 2020-04-30
Acta Agroph. 1999, (24), 57–65
Elements of new approach to the unified description of granular and cellular agrophysical materials is proposed. The idea is based on a quantum mechanical type formalism allowing to introduce the state vector for the individual cell. It allows to construct the total state vector in the form of the simple product of the single cell state vectors by minimization of the total energy of the cellular (granular) medium. In principle the energy should be determined from microscopical interactions among cells. In practice one can postulate the more simple phenomenological interactions describing the most important features of the agrobiological media under considerations. As first step widely analysed the geometrical limit of the granular materials (the model of hard spheres) is considered. It is usefull for simple analysis of some porous materials and flow of the water through it. This limit can be also obtained from the more general approach mentioned above. Depending on the form of the single cell state vector, describing the probability amplitude of finding a given mass distribution in the cell, and the interactions within cells one can simulate and calculate different mechanical properties of the media. The real granular or cellular media are arranged by a stochastic or nearly stochastic mechanism. To construct the models of the media one need to use the computer simulation with the appropriate random number generator. In this way one can obtain the appropriate geometry of the medium and its mechanical properties like stress-strength relations. This powerful tool seems to be flexible enough to reproduce, for example, the distributions either grains in the container or cells in a biological material.
Mechanika ośrodków komórkowych i granularnych
mechanika, ośrodki granularne, ośrodki komórkowe
W pracy przedstawiono zarysy metody jednolitego opisu ośrodków granularnych i komórkowych. Formalizm wykorzystuje elementy mechaniki kwantowej chociaż można go zakwalifikować do metod mikroskopowo-makroskopowych. Pozwala on modelować własności ośrodka bazując na znajomości fenomenologicznych oddziaływań pomiędzy jego granulami lub komórkami.