The research relates to studying a mixture of grained oilseeds saturated with oil and deformed with plunger molding. Mathematical simulations aim was determination of oil extraction velocity under the set loading conditions. Current statement treats processed material as biphasic mixture. Oilseed cake presented the first phase, which also was material’s porous skeleton. Vegetable oil filling the porous skeleton was the second phase of the mixture. Multiphase dynamics approach was applied in current research for material behavior description. Balance equations were set up for each mixture components. Interfacial volumetric force introduction modelled filtration of liquid. According to former researches, viscous liquid model described properties of porous skeleton as well as properties of vegetable oil. Porous skeleton viscosity assumed to be pressure dependent. Numerical solution of problem was carried out in two-dimensional statement for expression chamber middlesection using finite element approach. The primary variables were constituent’s velocity and pressure fields. Current study used cake pressure dependent porosity model that is common in porous media mechanics. Computational domain discretization was carried out using nine-node rectangular finite elements with linear and quadratic approximation for pressure and velocity fields respectively. Oil saturation distribution along expression chamber height obtained in numerical experiments demonstrates nonlinearity under high external loads. Moreover, the study investigated porosity changes influence on vegetable oil flow during expression.

This paper considers the developed mathematical model of inelastic deformation in structural steels, describing thermoviscoplastic deformation taking into account mutual influence of plasticity and creep effects. An integration algorithm for constitutive relations of thermoviscoplasticity has been developed. It consists in the formulation of constitutive relations in increments, depending on the selected time step. In difficult areas of deformation paths, time step can be adjusted throughout the whole estimation time in case of stability calculations. Stresses, plastic deformations and creep deformations are determined by integrating the defining relations of thermal creep by Runge-Kutta method with the correction of stress deviator and subsequent determination of stress according to thermal plasticity equations with regard to the average creep strain at the next sampling time. Experimental studies of influence between creep processes and plasticity under high temperature using 12H18N9 steel have been conducted. By numerical computer simulation of stress-strain state (SSS) kinetics in laboratory samples and by comparing the obtained results with field experiments, the authors carried out certification of the developed thermoviscoplastic model and integration algorithm of constitutive relations. All of these led to the conclusion about the reliability of model concepts and methods for determining material parameters under joint actions of fatigue and creep mechanisms. The authors have compared computer and physical tensile experiments of laboratory 12H18N9 steel samples with different histories of changes in temperature and mechanical deformation. It is shown that the developed thermoviscoplastic model qualitatively and quantitatively describes main effects of inelastic deformation in structural steels with different histories of mechanical deformation and changes in temperature. It is concluded that the defining relations of thermoviscoplasticity are reliable, and the above methods of integration are accurate.

Currently biology and medicine become one of the most attractive areas of applied mathematics. To fix certain pathologies of children, growth modelling for living tissue and growth management are the issues of major importance. In the process of growth a growing body itself experiences deformation that proves a fundamental difference of mechanics of growing bodies from the classical mechanics of bodies of constant composition. This paper presents an analysis of publications related to various models of the mechanism of living tissues growth and a brief analysis of biological growth concept. The authors considered basic principles of growth modelling and specified major areas for developing certain models of body-growing tissue. The following classification of growth models for living tissue has been given: models based on the hypothesis about the influence of intracellular pressure on tissue growth as a stimulating factor; models of multiphase media, the so-called “mixture theory”; model based on the hypothesis about the influence of residual stresses on tissue growth as a stimulating factor; models connecting the rate of growth from the deformations known from observations and experiments. The analysis resulted in specifying factors influencing the growth of living tissue. These are the chemical composition, concentration, transport and stresses in the material body. Stress is a significant factor affecting growth. The practical importance of growth model for mechanical deformation is based on its wide application for describing normal and pathological growth of hard tissues in the human body. In this case, from mechanical point of view, it becomes possible to model and control growth.

The plane-stress state in the vicinity of singular point, in a plate composed of two identical elements with interlayer such as glue is studied. The purpose of this study is determining characteristics of this solid mechanics problem and influence of material properties and interlayer thickness on stress concentration near the edge of the combining the elements (at the singular point ). Analytical estimation of the restrictions count on the state parameters at the line edge of junction plate element and interlayer is conducted. It is shown that the count of independent restrictions depends on the material properties of the plate elements and is usually redundant (non-standard). Standard restrictions count is only an exceptional case, when certain combinations of plate elements material parameters take place. In this particular case the solution is named as a “ basic-solution ”. For considered case of stress-strained plate basic-solution has uniform stress and piecewise-homogeneous strain state solution. With material parameters near the basic-solution the nonstandard problem is considered by iterative numerical-analytical method based on minimizing the residual divergence of all the boundary conditions at the singular point vicinity. A set of stress state problems is calculated. It is shown that the solution is practically independent of the interlayer thickness, but it depends drastically on the material properties of the elements. The more rigid material has the highest value concentration ratio.