On the asymptotic behavior of solutions of anisotropic viscoelastic body

The quasistatic problem of a viscoelastic body in a three-dimensional thin domain with Tresca’s friction law is considered. The viscoelasticity coefficients and data for this system are assumed to vary with respect to the thickness ε. The asymptotic behavior of weak solution, when ε tends to zero, is proved, and the limit solution is identified in a new data system. We show that when the thin layer disappears, its traces form a new contact law between the rigid plane and the viscoelastic body. In which case, a generalized weak form equation is formulated, the uniqueness result for the limit problem is also proved.

Investigation on CT characterization of pore structure in nylon-uncured rubber composite from a microscopic view

In order to construct the geometric models characterizing the real micro pore-fracture structures of nylon-uncured rubber composite, and further compare the distribution law in the pore-fracture of solid (nylon)-gas (pore) two-phases with that of solid (nylon)-viscoelastic body (rubber)-gas (pore) three-phases composite, in this paper, the X-ray three-dimensional (3D) microscope is applied for the nylon material and nylon-rubber composite respectively. By employing the 3D visualization software (Avizo), three-dimensional reconstruction and pore-fracture network model is realized, where the quantitative statistics and comparative analysis are carried out. The results demonstrate that the pore/throat number of nylon material accounting for 20.8%/33.9% are the largest when the pore/throat radius is in the range of 3–4 μm/1–2 μm, respectively, however, the pore/throat number of nylon-rubber composite with the radius 3–4 μm/1–2 μm occupies merely 5.49%/11.3%. Furthermore, the average pore radius of nylon material is believed as larger than that of nylon-rubber composite based on the pore network model, where the pore/throat surface area and pore/throat volume have perfect consistent patterns with that of pore radius. This work will offer a theoretical basis for the investigation of gas seepage capability discrepancy between the solid (nylon) one-phase and solid (nylon)-viscoelastic body (rubber) two-phases.

Theoretical study of the grate-saw-type large-litter cleaner of the mounted type

This paper reports a theoretical study into the saw-type-grate section of a large litter cleaner in mounted cleaners that operate on a cotton harvester, as well as the theoretical and experimental justifications for its parameters. The effect exerted by a mounted cleaner on the process of cleaning raw cotton when processing in a cotton gin has been studied. A theoretical model of the impact of grates on weeds in cleaning processes has been developed. A condition for repelling the litter by grates and removing it from a cotton technological flow has been studied. The use of grates with a flat-shaped front edge allows for a steady reduction in the amount of damage in the raw cotton fiber, which improves the fiber quality and leads to a decrease in the number of defects and debris. The experimental and theoretical studies have produced evidence that enables the efficient operation of mounted-type cleaning machines in the cotton-cleaning industry. The movements of raw cotton as a viscoelastic body at the free impact of litter with the teeth of the saw against a stationary surface of the grate were investigated; the force schemes between the grates and saws were considered. The effect of a saw-type drum on the technological properties of raw cotton was investigated, namely on seed damage and the formation of the free fiber. A model of interaction between weed particles and grates was considered; the trajectories of the litter flight were shown in the function of the slope of the grate and the recovery factor. The issues of the relationship between the physical-mechanical properties of raw cotton, the elastic characteristics of raw cotton, and the impact force of cotton flies against the grate with a flat working face. Solving these issues could make it possible to determine the optimal structure of the raw cotton cleaning mechanisms, which would improve the effectiveness of cleaning raw cotton from weeds. Based on the identified functional links, it has become possible to construct new or improve existing structures of the saw-type grate section of mounted cleaners. Practical experience shows that the use of the designed structure in large litter cleaners of the mounted type produces a significant increase in the cleaning effect of the machine

A note on viscoelastic bodies whose material properties depend on the density

In this note, we study the response of a viscoelastic body whose stress relaxation modulus and creep compliance depend on the density of the body in such a manner that the stress and strain appear linearly in the constitutive equation. Such models would be useful to study the response of porous viscoelastic bodies undergoing small deformations, as the moduli depend on the porosity, and hence the density. We study the problem of tension–torsion of cylinders of arbitrary cross-section within the context of this constitutive relation.

DIDACTIC POSSIBILITIES OF COMPUTER MODELING OF BODY MOVEMENT ON LESSONS AT PEDAGOGICAL UNIVERSITY

The didactic possibilities of the body movement modeling by replacing it with the material points system, which connected among themselves by weightless viscous elastic rods, are discussed. It is shown that the modeling of the body by a system of particles bound by viscoelastic weightless rods, obeying the basic law of dynamics, really allows: 1) to obtain the computer animation, i.e. the visual image of moving body at successive moments of time; 2) to plot the change of coordinates, velocities and accelerations of any of its points over time; 3) to model the translational, rotational, flat and spherical motion of the body, the interaction of the body with the surface or other body, to study the swimming of bodies, precession of the gyroscope and other phenomena; 4) to activate the mental activity of students, increase their motivation to learn. The tasks are considered: about collision of viscoelastic body with solid surface; about destruction of beam with defect; about the rotating wheel falling on surface; about flight of the rubber ring; about collision of two bodies; about the swimming of body with attached load; about the flexible ruler falling on cylinder; about the chain falling on cylinder; about the disk rotating on the horizontal surface; about the tumbling disk; about the gyroscope precession. The paper contains 8 figures obtained as a result of computer modeling of the above phenomena. As result of the analysis of the solved problems, it is shown that the modeling of a viscoelastic body by the method of bound particles has great didactic possibilities. It allows: 1) to study translational, rotational motion, deformation of bodies, gyroscope precession, etc., to update the knowledge of the relevant concepts and laws of mechanics; 2) to intensify the educational and cognitive activity of students, to increase their motivation for learning and its effectiveness; 3) to master the method of computer modeling, get acquainted with the solution of various professional tasks, explain the algorithms used and the simulation results at the school or pedagogical university level; 4) to develop the physical and algorithmic thinking, the ability to use the coordinate method and to perform information processing; 5) to organize an interactive dialogue between the student and the computer program; 6) to visualize information about the state of the object, build the trajectory of its points, the dependency graphs of coordinates and speeds on time; 7) to create various animations of body movement, to form a visual image of the corresponding phenomena; 8) to create problematic situations that require editing a computer program, changing system parameters, initial conditions and external influences; 9) to deepen the inter-subject connections between mathematics, physics and computer science.

Approximation of density of potentials for the flat viscoelastic bodies with inclusions, bounded by a piecewise smooth contours

An approach for approximating unknown densities of potentials in the study of the stressed state of a flat viscoelastic piecewise homogeneous body with inclusions, bounded by piecewise smooth contours, is proposed. The method is based on the construction of a system of boundary-time integral equations to determine the unknown densities of potentials along the contours of the inclusions. The approximation of the unknown densities of potentials was performed taking into account the singularity of the stressed state of a flat viscoelastic body near the angular point of the dividing line of the regions.