Application of the Inhomogeneous Elasticity Theory to the Description of the Mechanical State of a Single-Rooted Tooth*

2021 ◽  
Author(s):  
A. Ya. Grigorenko ◽  
V. A. Malanchuk ◽  
G. V. Sorochenko ◽  
J. J. Rushchitsky
Keyword(s):  
Elasticity Theory ◽  
Mechanical State

The Absolute Constitution

2018 ◽  
Author(s):  
Benjamin A. Schupmann
Keyword(s):  
State Theory ◽  
Public Order ◽  
Constitutional Theory ◽  
Mechanical State ◽  
Equal Chance ◽  
Basic Purpose ◽  
The Absolute

Chapter 4 analyzes Schmitt’s constitutional theory and how it complements his state theory. It begins with Schmitt’s criticism of the predominant positivist conception of the constitution. Schmitt argued that the positivists’ “relativized” conception of the constitution was committed above all to the equal chance of any belief to be enacted into law. This chapter then analyzes Schmitt’s counterargument that, without a prior and “absolute” commitment to some substantive value, a constitution could not fulfill its basic purpose of providing a clearly defined and stable public order. Schmitt’s typology of Relative and Absolute Constitution maps onto his state theoretical distinction between mechanical state and absolute state. This chapter concludes by discussing Schmitt’s later analysis of the concept nomos and how his analysis builds on and develops his earlier work on the concept of the absolute constitution.

scholarly journals A Damage Model to Trabecular Bone and Similar Materials: Residual Resource, Effective Elasticity Modulus, and Effective Stress under Uniaxial Compression

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1051
Author(s):  
Gennady Kolesnikov ◽  
Rudolf Meltser
Keyword(s):  
Mathematical Modeling ◽  
Trabecular Bone ◽  
Bone Tissue ◽  
Uniaxial Compression ◽  
Effective Stress ◽  
Analytical Solutions ◽  
Energy Criterion ◽  
Empirical Models ◽  
Mechanical State ◽  
Similar Materials

Experimental research of bone strength remains costly and limited for ethical and technical reasons. Therefore, to predict the mechanical state of bone tissue, as well as similar materials, it is desirable to use computer technology and mathematical modeling. Yet, bone tissue as a bio-mechanical object with a hierarchical structure is difficult to analyze for strength and rigidity; therefore, empirical models are often used, the disadvantage of which is their limited application scope. The use of new analytical solutions overcomes the limitations of empirical models and significantly improves the way engineering problems are solved. Aim of the paper: the development of analytical solutions for computer models of the mechanical state of bone and similar materials. Object of research: a model of trabecular bone tissue as a quasi-brittle material under uniaxial compression (or tension). The new ideas of the fracture mechanics, as well as the methods of mathematical modeling and the biomechanics of bone tissues were used in the work. Compression and tension are considered as asymmetric mechanical states of the material. Results: a new nonlinear function that simulates both tension and compression is justified, analytical solutions for determining the effective and apparent elastic modulus are developed, the residual resource function and the damage function are justified, and the dependences of the initial and effective stresses on strain are obtained. Using the energy criterion, it is proven that the effective stress continuously increases both before and after the extremum point on the load-displacement plot. It is noted that the destruction of bone material is more likely at the inflection point of the load-displacement curve. The model adequacy is explained by the use of the energy criterion of material degradation. The results are consistent with the experimental data available in the literature.

scholarly journals Double mode model of size-dependent chaotic vibrations of nanoplates based on the nonlocal elasticity theory

2021 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
Olga Mazur
Keyword(s):  
Elasticity Theory ◽  
Nonlocal Elasticity ◽  
Scale Effects ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Phase Portraits ◽  
Small Scale ◽  
Governing System ◽  
Account Due

AbstractIn this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations of the problem are based on the von Kármán plate theory and Kirchhoff–Love hypothesis. The small-size effect is taken into account due to the nonlocal elasticity theory. The formulation of the problem is mixed and employs the Airy stress function. The two-mode approximation of the deflection and application of the Bubnov–Galerkin method reduces the governing system of equations to the system of ordinary differential equations. Varying the load parameters and the nonlocal parameter, the bifurcation analysis is performed. The bifurcations diagrams, the maximum Lyapunov exponents, phase portraits as well as Poincare maps are constructed based on the numerical simulations. It is shown that for some excitation conditions the chaotic motion may occur in the system. Also, the small-scale effects on the character of vibrating regimes are illustrated and discussed.

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