Non-classical Theory Research Articles

Buckling analysis of thick cylindrical shells using micropolar theory

Modeling complex materials with internal structure such as porous solids is challenging as in some cases the classical theory cannot provide precise responses. By considering the scale effects through additional kinematic descriptors and six constants for isotropic materials, the micropolar theory can accurately model complex materials like bone. This paper studies the buckling of a thick cylindrical shell using classical and non-classical theories. The cylinder’s material is considered bone and isotropic, and the critical load value for different geometries and boundary conditions has been obtained. Finally, the size-effect and importance of micropolar theory in micro dimensions are investigated. The micropolar equations are solved by a numerical solution using the 3D finite element method. The results show that decreasing the macroscopic length increases the stiffness of the cylinder more than that predicted by classical theory; In addition, by increasing the thickness of the cylinder and the importance of shear stresses, the micropolar theory predicts a more critical load than the classical one, and the result differences become more significant between micropolar and classical theories. Also, the characteristic length of the micropolar is investigated. The results show that the change of the critical load increased by moving toward the micro dimensions.

The strain gradient elasticity via nonlocal considerations

Strain gradient elasticity and nonlocal elasticity are two enhanced elastic theories intensively used over the last fifty years to explain static and dynamic phenomena that classical elasticity fails to do. The nonlocal elastic theory has a clear differentiation from the classical case by considering stresses at a point of the continuum as an integral of classical stresses defined in the treated elastic body. On the other hand, strain gradient elasticity is characterized as a non-classical theory because considers both potential and kinetic energy densities as not only functions of strains and velocities, respectively but also functions of their gradients. Although the two considerations seem to be completely different from each other, it is a common belief that strain gradient elasticity has a lot in common with nonlocal elasticity. The goal of the present work is to derive all the strain gradient elastic theories appearing so far in the literature via the nonlocal definitions of the potential and kinetic energy densities and Hamilton’s principle. Such a consideration manifests the nonlocal nature of the SGE theories, correlates their internal length scale parameters with the nonlocal horizon of each material point, and proposes nonlocality in both elastic and inertia behavior of the continuum. For the sake of simplicity and brevity, only one-dimensional wave propagation phenomena in infinite domain are considered. However, since the Hamilton’s principle is employed, the definition of the corresponding boundary conditions for finite domains is accomplished simultaneously with the definition of the equation of motion.

On the Advances of Computational Nonclassical Continuum Theories of Elasticity for Bending Analyses of Small-Sized Plate-Based Structures: A Review

On the Advances of Computational Nonclassical Continuum Theories of Elasticity for Bending Analyses of Small-Sized Plate-Based Structures: A Review

Nonlinear Buckling Analysis of Cylindrical Nanoshells Conveying Nano-Fluid in Hygrothermal Environment

The present work addresses the critical buckling of circular cylindrical nano-shells containing static/dynamic nanofluids under the influence of different thermal fields that can also lead to appear the effect of thermal moisture so-called hygrothermal forces fields. To this end, the classical Sanders theory of cylindrical plates and shells is generalized by utilizing the non-classical nonlocal elasticity theory to derive the modified dynamic equations governing the nanofluid-nanostructure interaction (nano-FSI) problem. Then, the dimensionless obtained equations are analytically solved using the energy method. Herein, the applied nonlinear heat and humidity fields are considered as three types of longitudinal, circumferential, and simultaneously longitudinal-circumferential forces fields. The mentioned cases are examined separately for both high- and room-temperatures modes. The results show a significant effect of nanofluid passing through the nanostructure and its velocity on the critical buckling strain of the nano-systems, especially at high temperatures.

The Effect of Chain Length and Conformation on the Nucleation of Glycine Homopeptides during the Crystallization Process.

To explore the effect of chain length and conformation on the nucleation of peptides, the primary nucleation induction time of glycine homopeptides in pure water at different supersaturation levels under various temperatures has been determined. Nucleation data suggest that longer chains will prolong the induction time, especially for chains longer than three, where nucleation will occur over several days. In contrast, the nucleation rate increased with an increase in the supersaturation for all homopeptides. Induction time and nucleation difficulty increase at lower temperatures. However, for triglycine, the dihydrate form was produced with an unfolded peptide conformation (pPII) at low temperature. The interfacial energy and activation Gibbs energy of this dihydrate form are both lower than those at high temperature, while the induction time is longer, indicating the classical nucleation theory is not suitable to explain the nucleation phenomenon of triglycine dihydrate. Moreover, gelation and liquid-liquid separation of longer chain glycine homopeptides were observed, which was normally classified to nonclassical nucleation theory. This work provides insight into how the nucleation process evolves with increasing chain length and variable conformation, thereby offering a fundamental understanding of the critical peptide chain length for the classical nucleation theory and complex nucleation process for peptides.

Finite element modelling of exponentially graded composites with microstructure

Composite material properties are dependent on their microstructure. To adequately model these microstructural effects, a formulation of elasticity that accounts for microstructural effects must be considered. Size-dependent behaviour is an inherent property of such materials, resulting in a need for non-classical continuum theories for adequate characterization. A three-dimensional model for an exponentially graded composite with microstructural effects is developed under the framework of Cosserat elasticity. The mixed boundary value problem is formulated and solved through the finite element method, and implemented in the commercial software Abaqus through two user developed elements. Recovery of the classical limit for the Dirichlet problem is discussed as an initial model validation until complete experimental measurements can be conducted.

Free vibrations of Timoshenko nanoscale beams based on a hybrid integral strain- and stress-driven nonlocal model

Several non-classical elasticity theories are used for considering the size-dependent behavior of structures at small scales. The nonlocal theory is widely used to reflect the softening behavior of material at small scales, and theories like the strain gradient theory are employed to reflect the hardening behavior. In this article, the most general form of integral strain- and stress-driven nonlocal models with two nonlocal parameters is developed which is able to consider both hardening and softening influences simultaneously. To this end, it is considered that the stress field at the entire points of the domain is a function of strain field of the entire points of the domain. The free vibration problem of first-order shear deformable beams is solved herein. The integral form of governing equations and associated boundary conditions are obtained first, and then directly solved in a numerical approach. Through developing an efficient matrix formulation and using differential and integral matrix operators, the discretized governing equations are obtained. The simultaneous effects of strain- and stress-driven nonlocal parameters on the natural frequencies of fully clamped, fully simply-supported, and clamped-free nanobeams are investigated. The results indicate that the paradox related to the behavior of clamped-free nanobeams is resolved using the presented integral nonlocal formulation. Also, it is revealed that it is possible to find some specific values of nonlocal parameters at which the prediction of hybrid nonlocal model coincides with that of classical elasticity theory.

Solid mechanics models in application to ophthalmology

The review presents the models on a change in the stress-strain state of the eye shell after vision correction operations and a change in intraocular pressure with the introduction of drugs into the vitreous body. All mathematical models were developed in collaboration with ophthalmologists. Mathematical models that describe the process of determining the true intraocular pressure (IOP) by applanation methods are discussed. New results in solid mechanics were obtained while studying ocular biomechanics problems. For example, the problem of the stability of a spherical shell subjected to a concentrated force and internal pressure was solved and the stability of the axisymmetric equilibrium state of annular inhomogeneous orthotropic plates under normal pressure was studied. The stress-strain states of transversely isotropic spherical and cylindrical layers subjected to internal and external pressures are discussed and the solutions obtained in the framework of the three-dimensional theory are compared with the solutions obtained by non-classical shell theories. This comparison made it possible to assess the accuracy of approximate theories.

Lung Mechanics: A Review of Solid Mechanical Elasticity in Lung Parenchyma.

The lung is the main organ of the respiratory system. Its purpose is to facilitate gas exchange (breathing). Mechanically, breathing may be described as the cyclic application of stresses acting upon the lung surface. These forces are offset by prominent stress-bearing components of lung tissue. These components result from the mechanical elastic properties of lung parenchyma. Various studies have been dedicated to understanding the macroscopic behaviour of parenchyma. This has been achieved through pressure-volume analysis, numerical methods, the development of constitutive equations or strain-energy functions, finite element methods, image processing and elastography. Constitutive equations can describe the elastic behaviour exhibited by lung parenchyma through the relationship between the macroscopic stress and strain. The research conducted within lung mechanics around the elastic and resistive properties of the lung has allowed scientists to develop new methods and equipment for evaluating and treating pulmonary pathogens. This paper establishes a review of mathematical studies conducted within lung mechanics, centering on the development and implementation of solid mechanics to the understanding of the mechanical properties of the lung. Under the classical theory of elasticity, the lung is said to behave as an isotropic elastic continuum undergoing small deformations. However, the lung has also been known to display heterogeneous anisotropic behaviour associated with large deformations. Therefore, focus is placed on the assumptions and development of the various models, their mechanical influence on lung physiology, and the development of constitutive equations through the classical and non-classical theory of elasticity. Lastly, we also look at lung blast mechanics. No explicit emphasis is placed on lung pathology.

Objectivity of scientific reflection

The article focuses on scientific reflection. The transcendental reflection does not analyse the content of knowledge, but reveals its conditions and is a condition of scientific research. This is not only thinking about thinking, but also the operations of identifying and distinguishing sensory data, and the rules for structuring the universe. The selection of input data depends on objective cognitive operations. Reflection reveals possible ways of transforming nature. Different forms of reflection achieve different goals. Reflection as a metatheory builds a fundament for future science. The analysis of cognitive procedures reveals the privileged status of classical theory and possible ways of creating non-classical theories. The classical theory is the original theory from which the non-classical ones are derived. Correspondently, scientific knowledge is divided into initial and derived forms. Derived forms are established by second-order reflection. Thus, the objective structure of science is conditioned by the structure of the reflexive activity of the mind.

Vibrations of a strip with delamination in the framework of the one-parameter Aifantis model of gradient elasticity theory

The problems on in-plane and anti-planar steady-state vibrations of an isotropic elastic strip with delamination at the lower boundary has been investigated. The goal of the study is to analyze the stress-strain state in the crack tips areas and to construct a crack opening function being the main mechanical characteristics in the crack theory problems. The problems under study have been solved in the framework of the nonclassical gradient elasticity theory (GET) on the basis of the one-parameter model proposed by Aifantis. The boundary integral equations (BIE) are obtained with respect to crack opening functions or their derivatives. The analysis of BIEs is carried out, regular and irregular parts are distinguished, the obtained BIEs with singular (e.g., with hypersingular, with cubic singularity) integrals are solved via collocation methods, approximating Chebyshev polynomials, quadrature formulas for singular integrals. For the in-plane problem solution, the simplified Ru-Aifantis method has been applied. The Ru-Aifantis method allows to divide the initial boundary value problem into two sub-problems - the classical linear elasticity theory (LTE) problem and the simplified boundary value problem for finding the gradient solution which includes the solution found via the classical theory. For each of the problems, semi-analytical expressions for the functions of crack opening have been constructed, and the analysis of the stress-strain state in the area of crack tips has been carried out. The problems have also been solved in the case of a crack with small relative length, the analysis of BIE depending on small parameters ratio has been carried out, and explicit expressions for the crack opening functions have been obtained. Numerical calculations have been performed; the applicability conditions for the asymptotic method are determined, and a comparative analysis of the results obtained on the basis of GET and LTE models, depending on the values of the gradient parameter and the delamination length, is realized.

Нация и цивилизация: классические дистинкции

The theory of nation and the theory of civilization attract considerable attention in the field of political and social sciences as well as in philosophy. However, the categories of nation and civilization are usually regarded separately, due to the fact that these two approaches have developed independently. Key thinkers of the theory of nation, as a rule, either ignore the category of civilization or give it only formal attention. The leading figures of the theory of civilization, on the contrary, could not but consider the distinction between nation and civilization. It should be noted that the concept of civilization could only be constructed proceeding from the category of nation, which had acquired a normative status in the social disciplines as early as in the 19th century. This article dwells on the distinction between nation and civilization in the works of the classical theorists of civilization, namely, O. Spengler, A. Toynbee and S. Huntington. In spite of the fact that all of the above authors make this differentiation, it is only in the works of Toynbee and Huntington that nation and civilization are presented as commensurable. Toynbee distinguishes nation and civilization as a part and as a whole, recognizing the subjectivity of civilization. Huntington proposes a hybrid differentiation that both preserves the qualities of the classical theory of civilization and includes elements of constructivism. The latter forms the basis for non-classical theories of civilization, such as G. Therborn’s concept. The non-classical approach allows us to draw not only a quantitative, but also a qualitative distinction between nations and civilizations: while nation-states arise as a result of a break with the past and develop within the framework of modernity, civilizations continue and restore the tradition.

МЕРЕЖЕВА КОМУНІКАЦІЯ ЯК ФАКТОР ФОРМУВАННЯ АУТОПОЄТИЧНОЇ СИСТЕМИ ІНТЕРНЕТ-ПРОСТОРУ

<p><strong><em>The purpose </em></strong><em>of the study is to reveal the features of network communication as a factor in the formation of the autopoetic system of the Internet space.</em></p><p><strong><em>Research methodology</em></strong><strong><em>.</em></strong><em> </em><em>To achieve this goal, general scientific research methods were used: critical and analytical approaches – to highlight the state of the scientific problem and highlight the main directions of development of network communication; historical retrospective method – to study the logic of formation and development of concepts of social communication; conceptualization method – to clarify the content of the concept of network; formalization method – to determine the specifics and basic principles of typology of communication models. </em><em>Appeal to interdisciplinary research, which allows to involve the conceptual apparatus of mathematical and non-classical information theories and theories of complex systems.</em> <em>In this context, the study of the realities of the Internet reality can be transferred to the received texts of the current achievements of the technogenic world, such as N. Luhmann, E. Pickering, K. Knorr-Cetina, B. Latour, M. Castells, L. Memford, they became fundamental for the analysis of the nature of the technosocial class of objects similar to the Internet. Even more heuristic potential, in our opinion, can be the concept of autopoiesis by N. Luhmann, a kind of rethinking in his own line by U. Maturana and F. Varela.</em><em></em></p><p><strong><em>Results.</em></strong><em> The article analyzes the main models of network communication, substantiates the grounds for the typology of network interaction and describes its architecture in the context of the functioning of cyberspace. </em><em>The Internet is defined as an operationally closed structure that has the accumulative power of completely different systems (social and technological), its own border, as well as an autopoietic device that starts the process of self-reproduction in the form of superstructure of new floors of its own complexity. In this study, autopoiesis is an important concept because it allows us to identify the essential properties of the growing Internet space.</em><em></em></p><p><strong><em>Novelty.</em></strong><em> The scientific novelty is to deepen the understanding of the role of autopoiesis in network communication in the first place and the Internet space system in particular. For example, the functions and mechanisms of autopoiesis operation, the main factors of its activities in the Internet communication system were clarified.</em></p><p><strong><em>The practical significance</em></strong><em> of this lies in the fact that, as a kind of social reality, it builds the moderation of communicative processes in social systems. Like the theory of systems by N. Luhmann, the structures of the system are organized in a similar way, as if inspired for work and operations.</em></p><p><strong><em>Key words:</em></strong><em> merezhe communication, autopoiesis, self-organization of the Internet space.</em></p>

The strain gradient-based torsional vibration analysis of micro-rotors with nonlinear flexural-torsional coupling

The powerful non-classical continuum theory of strain gradient elasticity is capable of effectively capturing small-scale effects in micro-structures. Based on this theory, a formulation is developed to investigate the coupled torsional-flexural vibrations of micro-rotors in the presence of inertia nonlinearities arising from the eccentricity and gyroscopic motion of the rotors. With the aid of a weighted-residual technique, coupled nonlinear partial differential equations of motion are truncated into a discrete model. Then, the resonance of the fundamental mode of the torsional vibration excited by the flexural vibration is investigated by utilizing the perturbation method of multiple scales. Moreover, a numerical simulation approach is conducted to confirm the validity of the analytical solution proposed by the multiple scales perturbation method. Obtained results for the resonant frequency and amplitude of the fundamental torsional mode indicate that the strain gradient theory can predict far more reliable results than the classical continuum mechanics for micro-rotors with very thin shafts.

Nonclassical continuum theories for fluent media incorporating rotation rates and their thermodynamic consistency

AbstractIn this paper, we present three micropolar nonclassical continuum theories (NCCT) for fluent medium in which a material point always has velocities as degrees of freedom, additionally, we consider (i) in the first NCCT, we consider classical or internal rotations rates (known) due to skew‐symmetric part of velocity gradient tensor; (ii) in the second NCCT, we consider rotation rates and Cosserat or microrotation rates (unknown degrees of freedom); (iii) in the third NCCT, we consider Cosserat or microrotation rates only, hence are neglected. Conservation and balance laws (CBL) and the constitutive theories are derived for all three NCCT. We examine consistent choice of kinematic variables, modification of the CBL of classical continuum theories (CCT) due to new physics and determine if the new physics of rotation rates requires additional balance law. All three NCCT derived here are examined for thermodynamic and/or mathematical consistency and are compared with published works. Model problem studies are also presented.

Notes on Models of (Partial) Kripke–Feferman Truth

This article investigates models of axiomatizations related to the semantic conception of truth presented by Kripke (J Philos 72(19):690–716, 1975), the so-called fixed-point semantics. Among the various proof systems devised as a proof-theoretic characterization of the fixed-point semantics, in recent years two alternatives have received particular attention: classical systems (i.e., systems based on classical logic) and nonclassical systems (i.e., systems based on some nonclassical logic). The present article, building on Halbach and Nicolai (J Philos Log 47(2):227–257, 2018), shows that there is a sense in which classical and nonclassical theories (in suitable variants) have the same models.

Evaluating Measurement Properties of the Adapted Interprofessional Collaboration Scale through Rasch Analysis.

This study aimed to evaluate the validity and reliability of the German and Italian versions of the Interprofessional Collaboration Scale (IPC scale) by applying a Rasch analysis. Data were gathered from 1182 nurses participating in a cross-sectional study in northern Italy. The scale demonstrated good reliability (Cronbach’s alpha = 0.92). Item polarity of all 13 items was positive, indicating good construct validity. However, revising one item would further improve the validity of the scale. Item stability was confirmed for work experience, workplace, age range, the language version, and gender. The analysis, applying a non-classical test theory, confirmed that the IPC scale is a valid and reliable instrument to measure interprofessional collaboration between nurses and physicians.

From geology to biology: an interdisciplinary course in crystal growth.

This contribution shares experience of teaching an interdisciplinary university course in crystal growth with examples ranging from geology to biology. This is an attempt to combine teaching the basics of the classical and non-classical theories of crystallization with impressive examples of crystals growing around us and in the human body, as well as demonstration of the common phenomena in the growth of minerals in nature, crystalline materials in industry and the laboratory, and biomimetic and stimulus-responsive crystals. Lectures are supported by laboratory exercises. Students can also perform an individual research project and present an oral contribution at a mini-conference. Examples of the topics considered in the course are given, and an extensive list of references to papers and web resources is provided, which may be useful to those who want to implement anything from the authors' experience.

The Axiomatic Approach to Non-Classical Model Theory

Institution theory represents the fully axiomatic approach to model theory in which all components of logical systems are treated fully abstractly by reliance on category theory. Here, we survey some developments over the last decade or so concerning the institution theoretic approach to non-classical aspects of model theory. Our focus will be on many-valued truth and on models with states, which are addressed by the two extensions of ordinary institution theory known as L-institutions and stratified institutions, respectively. The discussion will include relevant concepts, techniques, and results from these two areas.

Research on Mesoscale Nucleation and Growth Processes in Solution Crystallization: A Review

In recent studies, the existence of mesoscale precursors has been confirmed in crystallization. Different from the classical crystallization theory, which only considers the sequential attachment of basic monomers (atoms, ions, or molecules), the nonclassical crystallization process involving precursors such as prenucleation clusters, nanoparticles, and mesocrystals is more complicated. The mesoscale structure is important for the quantitative description and directional regulation of the solution crystallization process. It is necessary to explore the mechanism by the mesoscale scientific research methods on the base of traditional chemical engineering and process system engineering research methods. Therefore, the paper reviews several representative nonclassical nucleation and growth theories, mainly including two-step nucleation theory, prenucleation clusters theory, particle agglomeration theory, amorphous precursor growth theory, particle attachment growth theory and mesocrystal growth theory. Then, the mesoscale structure and its spatiotemporal dynamic behavior are discussed, and the application of the EMMS model in the nucleation and growth process is analyzed. Finally, we put forward our views on the prospect of the paradigms and theoretical innovations of using mesoscale methods in crystal nucleation and growth.