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

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

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

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

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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