Mechano-matematické modelovanie väzkopružného kontinua - konštitutívne rovnice

Phenomenological models of continuum mechanics applied on the rigid body are more or less idealized. Experimental measuring showed there is a plastic flow, respectively relaxation in real rigid bodies, i.e. stress is the function of strain, strain velocity and the higher time derivatives. The paper deals with the rheological models based on the Hook elastic and Newton viscous masses. The corresponding constitutive equations are described.Fenomenologické modely mechaniky kontinua aplikované v tuhých telesách sú viac či menej idealizované. Experimentálne merania ukázali, že v tuhých telesách dochádza k dotvarovaniu, resp. relaxácii, t. j. že napätie je funkciou nielen deformácie, ale aj jej časových derivácií. Článok pojednáva o reologických modeloch, ktorých základom je Hookova pružná a Newtonova viskózna látka. Sú popísané aj príslušné konštitutívne rovnice

Application of more complex rheological models in continuum mechanics

The paper deals with mathematical modeling of the structural materials representing their rheological properties. The materials are modeled by more complex models (enhancement of Voigt and Maxwell models). The constitutive equations are derived; the relationships within the creep and relaxation process are developed. The rheological behavior of the materials is introduced

Fractal Analysis for Cancer Research: Case Study and Simulation of Fractals

2010 Mathematics Subject Classification: 65D18.This paper discusses the possibilities of application of fractal geometry for cancer research. Fractal geometry is a new tool that can be extremely useful for many problems in almost every scientific field. The studies recently done in medicine show fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Cancer diagnosis can be done via determination of fractal dimension. A likelihood ratio test for the Hausdorff dimension is employed in [7] We empirically checked the obtained tests on Sierpinski Carpet and on cancer data. However, several issues arisen, especially those related to simulation of fractals which may mimic tissues. These are discussed in the present paper

Simulation of Indoor Humidity

summary:The paper deals with the moisture in the internal air of a modeling room. The problems connected with the undesired relative humidity of the indoor air are introduced, the reviewing of the hygric situation in the modeling room is described, the less or more precise models for relative humidity estimation depending on the influencing parameters are performed and the reasoning—when, why and how the particular models should be used, is added. As in particular hygric conditions some of the influencing parameters can be neglected, the models differ each from other by the parameters being involved or neglected

Odozva medzistavcovej platničky v rámci pohybového segmentu l3-l4 ľudskej chrbtice na rôzne typy fyziologického zaťaženia

The paper deals with the biomechanical investigation on the motion segment – basic part of the human lumbar spine focused on the intervertebral disc response to the various types of load. It contains the description and the reason of the simplification of the model, the biomechanical laws; the mathematical treatment with the computational implementation added. The results are presented and discussed especially for the intervertebral disc.Článok sa zoberá skúmaním reakcie pohybového segmentu ľudskej chrbtice na rôzne druhy zaťaženia. Zameriava sa prioritne na odozvu medzistavcovej platničky na tieto zaťaženia. Popisuje geometriu zjednodušeného modelu pohybového segmentu spolu s odôvodnením tohto zjednodušenia, biomechanické zákony, matematický model popisujúci fyzikálny dej. Načrtáva konečno prvkovú analýzu, podáva a analyzuje výsledky počítačovej implementácie

Isothermal viscoelasticity and energy

Within the scope of the linear viscoelasticity theory, the change in the inner energy of a viscoelastic body is induced either by heat exchange or by a work performance. The first law of thermodynamics, balance equation of a closed system is mostly referred when the thermodynamic consistency of some rheological model is required. Accordingly, within the frame of the isothermal viscoelastic investigation we just distinguish between the stored and dissipated energy. And this is the issue that the paper is focused on. Subjected to a load, the one degree of freedom viscoelastic models’ behaviour is traced, together with the observation of the energy – total, stored and dissipated. Nevertheless, the only stored energy in viscoelastic model is potential energy. General considerations are applied on Maxwell model subjected to the standard both creep and relaxation tests

Simulation of Indoor Humidity

summary:The paper deals with the moisture in the internal air of a modeling room. The problems connected with the undesired relative humidity of the indoor air are introduced, the reviewing of the hygric situation in the modeling room is described, the less or more precise models for relative humidity estimation depending on the influencing parameters are performed and the reasoning—when, why and how the particular models should be used, is added. As in particular hygric conditions some of the influencing parameters can be neglected, the models differ each from other by the parameters being involved or neglected

Stress - Strain Response of the Human Spine Intervertebral Disc As an Anisotropic Body. Mathematical Modeling and Computation

The paper deals with the biomechanical investigation on the human lumbar intervertebral disc under the static load. The disc is regarded as a two - phased ambient consisting of a fibrous outer part called annulus fibrosis and a liquid inner part nucleus pulposus. Due to the fibrous structure, the annulus fibrosis can be treated by using a special case of anisotropy - transversal isotropy

Application Of More Complex Rheological Models In Continuum Mechanics

The paper deals with mathematical modeling of the structural materials representing their rheological properties. The materials are modeled by more complex models (enhancement of Voigt and Maxwell models). The constitutive equations are derived; the relationships within the creep and relaxation process are developed. The rheological behavior of the materials is introduced