Mathematical model of the modified tissue deformation under stretching

One of the effective methods for modifying natural and synthetic materials is a use of the flocking process. To analyze a quality of the modified fabrics, it is useful to have mathematical models describing a stress-strain state of the fabrics when exposed to various loads. A method has been developed for determining the stiffness characteristics of a flocked fabric based on the results of testing samples cut at different angles to the base at different tensile forces. This technique makes it possible to analyze the effect of flocking on the mechanical characteristics of the fabric. It was revealed that the theory of mixtures, when averaging the properties of the fabrics and glue with respect to thickness, does not allow determining the stiffness characteristics with acceptable accuracy. The limits of applicability of the theory of mixtures were determined when carrying out averaging of the mechanical characteristics with respect to the area of the flocked fabrics.

A simple theory of mixtures for the study of the temperature dependence of thermo-structural properties of Al-Ga liquid alloy

A simple theory of mixtures for symmetric alloys was used to study the thermodynamic and structural properties of the Al-Ga alloy in the liquid state at 1023 K. The computed thermodynamic properties are in a very good agreement with the observed values and show that the alloy is weakly interacting. The computed structural properties show that the Al-Ga alloy is segregating in nature which is in agreement with the observed values. The excess free energy of mixing, activity of monomers and concentration fluctuation in the long wavelength limit was extrapolated to higher temperatures by optimising the temperature dependent parameters. As the temperature increases, the behaviour of the alloy shifts towards the ideality.

Load Ratios Carried by Each Constituent for Some Problems of a Particulate Composite Modeled as a Mixture of Two Linear Elastic Solids

ABSTRACTThe basic constitutive equations of theory of mixtures obtained for a mixture of two linear elastic solids can be used as an alternative way to describe the mechanical behavior of binary composite materials. Determining the load ratios carried by each constituent solid of a binary composite is one of challenges of this theory. In this study, the results of directly calculating the ratios of external load carried by each constituent solid for the case of perfectly bonded interface between binary mixture constituents are discussed. Thus, the effects of loading type and volume fraction of the constituent solids to the load ratios carried by each constituent solid are investigated by using three different loading cases and three different volume fractions. Finally, displacement, stress and diffusive force results of two constituent solids using the calculated load ratios are given.

Adiabatic Thermodyhamics

This is a review of efforts to discover action principles for Hydrodynamics and Thermodynamics. The work began with a determined attempt to create sources for Einstein's equations that describe continuous matter - as opposed to point particles. This requires a relativistic action principle. This report is mainly about (non relativistic) Adiabatic Thermodynamics, non equilibrium thermodynamics based on the method of Gibbs. The main relations of classical thermodynamics can be derived from an action principle, in the classical global form and in the local form advocated by Callen. The entropy is defined as the negative derivative of the free energy (free energy density) with respect to the volume (density). This is integrated with an action principle for hydrodynamics that was known to Lagrange in 1760. It is strongly limited to irrotational velocity fields, nevertheless it provides the needed Lagrangian for a large part of thermodynamics. This is the subject of the first 3 sections. It includes a brief review of a new theory of mixtures. The most difficult part of the program has been the discovery of Conservative Hydrodynamics with the required four independent degrees of freedom, with general flows. We give an account of the genesis and the structure of this theory, then a tour of recent applications.

Fundamental approaches in mathematical modeling of drying processes of capillary-porous and dispersed materials

A review of main approaches to the mathematical modeling of heat and mass transfer in the process of drying of capillary-porous and disperse materials is presented. The peculiarities of the models construction from the point of view of the mechanics of a continuous medium, the theory of mixtures, statistical approaches and with taking into account the fractal structure are considered, which allows one to expand the many implementations of models, to take into account the anisotropy of thermo-mechanical characteristics, elastic and visco-elastic properties, etc.