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Search results for: MICROPOLAR CONTINUUM
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CONTINUUM MECHANICS AND THERMODYNAMICS
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Jacek Tejchman prof. dr hab. inż.
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On some constitutive equations for micropolar plates
PublicationW pracy porównano równania konstytutywne dla płyt podane przez Altenbacha i Eremeyeva. Na podstawie ich wyprowadzeń określono zakres zmienności współczynnika momentów owinięcia i jego możliwy wpływ na wyniki otrzymane w rozwiązaniach MES w zakresie liniowym
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Optics Continuum
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On Dynamic Extension of a Local Material Symmetry Group for Micropolar Media
PublicationFor micropolar media we present a new definition of the local material symmetry group considering invariant properties of the both kinetic energy and strain energy density under changes of a reference placement. Unlike simple (Cauchy) materials, micropolar media can be characterized through two kinematically independent fields, that are translation vector and orthogonal microrotation tensor. In other words, in micropolar continua...
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Computational Continuum Mechanics
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Linear Micropolar Elasticity Analysis of Stresses in Bones Under Static Loads
PublicationWe discuss the finite element modeling of porous materials such as bones using the linear micropolar elasticity. In order to solve static boundary-value problems, we developed new finite elements, which capture the micropolar behavior of the material. Developed elements were implemented in the commercial software ABAQUS. The modeling of a femur bone with and without implant under various stages of healing is discussed in details
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Surface and interfacial anti-plane waves in micropolar solids with surface energy
PublicationIn this work, the propagation behaviour of a surface wave in a micropolar elastic half-space with surface strain and kinetic energies localized at the surface and the propagation behaviour of an interfacial anti-plane wave between two micropolar elastic half-spaces with interfacial strain and kinetic energies localized at the interface have been studied. The Gurtin–Murdoch model has been adopted for surface and interfacial elasticity....
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Extended micropolar approach within the framework of 3M theories and variations thereof
PublicationAs part of his groundbreaking work on generalized continuum mechanics, Eringen proposed what he called 3M theories, namely the concept of micromorphic, microstretch, and micropolar materials modeling. The micromorphic approach provides the most general framework for a continuum with translational and (internal) rotational degrees of freedom (DOF), whilst the rotational DOFs of micromorphic and micropolar continua are subjected...
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On Solvability of Boundary Value Problems for Elastic Micropolar Shells with Rigid Inclusions
PublicationIn the framework of the linear theory of micropolar shells, existence and uniqueness theorems for weak solutions of boundary value problems describing small deformations of elastic micropolar shells connected to a system of absolutely rigid bodies are proved. The definition of a weak solution is based on the principle of virial movements. A feature of this problem is non-standard boundary conditions at the interface between the...
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On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions
PublicationThe problem of dynamics of a linear micropolar shell with a finite set of rigid inclusions is considered. The equations of motion consist of the system of partial differential equations (PDEs) describing small deformations of an elastic shell and ordinary differential equations (ODEs) describing the motions of inclusions. Few types of the contact of the shell with inclusions are considered. The weak setup of the problem is formulated...
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NEW TRENDS IN DEVELOPMENT OF ORC'S FOR MICROPOWER GENERATION
PublicationIn the paper, new trends in development of micropower generation of heat and electricity are presented. New type of CHP for domestic usage is developed in the Institute of Fluid-Flow Machinery PAS and methods of its design are presented. The most promising trends in equipment of ORC cycle for this purpose were discussed. Main attention was focused on micro-heat exchangers design based on micro-channels and micro-jets. In our opinion...
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CONTINUUM Lifelong Learning in Neurology
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Theoretical calculation of pKas of phosphoric (V) acidin the polarisable continuum and cluster-continuum models
PublicationW pracy oceniono dokładność modelu polaryzowalnego kontinuum (PCM) i mieszanego modelu klaster-kontinuum do przewidywania wartości trzech kolejnych stałych dysocjacji kwasu fosforowego (V). Obliczenia PCM na poziomie MP2/6-31+G(d,p) odtwarzają wartość pierwszego pKa z rozsądną niepewnością, jednak wartości kolejnych pKa obarczone są bardzo dużym błędem, nawet po podniesieniu poziomu teorii do metody zespolonej G3B3. Dopiero obliczenia...
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Two- and three-dimensional elastic networks with rigid junctions: modeling within the theory of micropolar shells and solids
PublicationFor two- and three-dimensional elastic structures made of families of flexible elastic fibers undergoing finite deformations, we propose homogenized models within the micropolar elasticity. Here we restrict ourselves to networks with rigid connections between fibers. In other words, we assume that the fibers keep their orthogonality during deformation. Starting from a fiber as the basic structured element modeled by the Cosserat...
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Acceleration waves in the nonlinear micromorphic continuum
PublicationWithin the framework of the nonlinear elastic theory of micromorphic continua we derive the conditions for propagation of acceleration waves. An acceleration wave, also called a wave of weak discontinuity of order two, can be treated as a propagating nonmaterial surface across which the second derivatives of the placement vector and micro-distortion tensor may undergo jump discontinuities. Here we obtain the acoustic tensor for...
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Applications of Tensor Analysis in Continuum Mechanics
PublicationA tensor field is a tensor-valued function of position in space. The use of tensor fields allows us to present physical laws in a clear, compact form. A byproduct is a set of simple and clear rules for the representation of vector differential operators such as gradient, divergence, and Laplacian in curvilinear coordinate systems. The tensorial nature of a quantity permits us to formulate transformation rules for its components...
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Continuum-Journal of Media & Cultural Studies
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A Nonlinear Model of a Mesh Shell
PublicationFor a certain class of elastic lattice shells experiencing finite deformations, a continual model using the equations of the so-called six-parameter shell theory has been proposed. Within this model, the kinematics of the shell is described using six kinematically independent scalar degrees of freedom — the field of displacements and turns, as in the case of the Cosserat continuum, which gives reason to call the model under consideration...
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DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
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Implementation of continuum damage in elasto-viscoplastic constitutive equations
PublicationW pracy opisano podstawowy wariant modelu Chaboche, oraz założenia i implementacje kontynualnego modelu zniszczenia do komercyjnego programu MES. W pracy zaprazentowano dwa podejścia zobrazowane na przykładach obliczeń numerycznych.
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Survey of modern trends in analysis of continuum damage mechanics
PublicationW artykule dokonano szerokiego przegladu literatury z zakresu mechaniki zniszczenia izotropowego. Przedstawiono równania stosowane w opisie zniszczenia materiału.
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Practical Applications for Single Pill Combinations in the Cardiovascular Continuum
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Continuous Optimisation Algorithms
PublicationKsiążka poświęcona jest zagadnieniom optymalizacji ciągłej. Oprócz klasycznych algorytmów gradientowych omawiane są w współczesne algorytmy bezgradientowe, które stosowane są z powodzeniem w optymalizacji globalnej. Większość prezentowanych algorytmów określona może być mianem metaheurystycznych. Zaliczyć do nich można metody optymalizacji inspirowane procesami zachodzącymi w przyrodzie, które dalej można dzielić na inspirowane...
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On Non-holonomic Boundary Conditions within the Nonlinear Cosserat Continuum
PublicationWithin the framework of the nonlinear micropolar elastic continuum we discuss non-holonomic kinematic boundary conditions. By non-holonomic boundary conditions we mean linear relations between virtual displacements and virtual rotations given on the boundary. Such boundary conditions can be used for modelling of complex material interactions in the vicinity of the boundaries and interfaces.
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Numerical simulation of asphalt mixtures fracture using continuum models
PublicationThe paper considers numerical models of fracture processes of semi-circular asphalt mixture specimens subjected to three-point bending. Parameter calibration of the asphalt mixture constitutive models requires advanced, complex experimental test procedures. The highly non-homogeneous material is numerically modelled by a quasicontinuum model. The computational parameters are averaged data of the components, i.e. asphalt, aggregate...
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FE analysis of reinforced concrete corbels with enhanced continuum models
PublicationW artykule pokazano wyniki MES symulacji wsporników żelbetowych. Zachowanie wsporników modelowano przy zastosowaniu 3 różnych modeli betonu: sprężysto-plastycznego, degradacji sprężystej i rozmytych rys. Modele rozszerzono o długość mikrostruktury przy zastosowaniu teorii nielokalnej. Wyniki numeryczne porównano z doświadczeniami z literatury.
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Modelling of concrete behaviour with a non-local continuum damage approach
PublicationW artykule przedstawiono wyniki numerycznej dla różnych problemów brzegowych związanych z powstawaniem rys w betonie. Obliczenia wykonano przy zastosowaniu modelu zniszczeniowego (z uwzględnieniem degradacji sztywności). Do opisu rys, model rozszerzono o nielokalność.
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Numerical investigations of micropolar effects in granular materials undercyclic shearing. Numeryczne badania efektów mikropolarnych w materiałach granulowanych podczas cyklicznego ścinania.
PublicationOmówiono wpływ cyklicznego ścinania na lokalizację odkształceń stycznych w materiałach granulowanych. Obliczenia wykonano metodą elementów skończonych na bazie mikropolarnego prawa hipoplastycznego dla wąskiej warstwy piasku. Obliczenia wykonano dla dużej amplitudy ścinania i różnych początkowych zagęszczeń piasku.
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Advances in Continuous and Discrete Models
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Acrodermatitis continua Hallopeau
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OSA Continuum
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Zero-range potentials for Direc particles: scattering and related continuum problems
PublicationW pracy przedstawiono rozszerzenie metody potencjałów zerowego promienia, szeroko wykorzystywanej w nierelatywistycznej mechanice , na przypadek cząstek Diraca. Nacisk położono na zagadnienie rozproszeniowe, do analizy którego zastosowano metodę kanałów własnych.
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Continuum models for pantographic blocks with second gradient energies which are incomplete
PublicationWe postulate a deformation energy for describing the mechanical behavior of so called pantographic blocks, that is bodies constituted by stacking of layers of pantographic sheets. We remark that the pantographic effect is limited in the plane of pantographic sheets and therefore only the second derivatives of transverse displacements along the pantographic fibers appear in the chosen deformation energy. We use this novel energy...
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J. FE modelling of cracks in concrete elements within continuum mechanics.
PublicationW artykule przedstawiono wyniki symulacji rys zakrzywionych w elementach betonowych w warunkach mieszanego sposobu obciążenia. Symulacje wykonano przy zastosowaniu 3 różnych modeli: modelu sprężysto-plastycznego, modelu w ramach mechaniki zniszczeniowej i modelu z rysami obracającymi się.
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Patterns of shear zones in granular bodies within a polar hypoplastic continuum
PublicationPrzedstawiono wyniki numerycznej analizy tworzenia się stref ścinania w materiałach granulowanych podczas ściskania dwuosiowego. Obliczenia wykonano stosując metodę elementów skończonych na bazie mikropolarnego hypoplsastycznego prawa materiałowego. Obliczenia wykonywano dla różnych warunków brzegowych wstępnego zagęszczenia piasku, poziomu naprężenia i rozkładu stochastycznego imperfekcji.
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Modelling of localization of deformation in quasi-brittle materials with a continuum and discrete model
PublicationW artykule przedstawiono wyniki obliczeń lokalizacji odkształceń w materiałach kruchych przy zastosowaniu 2 modeli w ramach mechaniki ośrodka ciągłego i jednego modelu w ramach ośrodka dyskretnego. W przypadku pierwszy zastosowano model sprężysto-plastyczny i model zniszczeniowy rozszerzony o długość charakterystyczną mikrostruktury. W przypadku drugim przyjęto model rusztowy złożony z beleczek.
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Parallelization Method for a Continuous Property
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Modelling of continuum damage for application in elasto-viscoplastic Bodner-Partom constitutive equations
PublicationW artykule zaproponowano zastosowanie modelu zniszczenia Lemaitre w sprężysto-lepkoplastycznym modelu Bodnera-Partoma. Opisane podejście jest wprowadzone do programu MSC.Marc z wykorzystaniem podprocedury UVSCPL. Przedstawiono wyniki analiz numerycznych potwierdzających przyjęte założenia.
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SIMULATIONS OF FRACTURE IN CONCRETE BEAMS UNDER BENDING USING A CONTINUUM AND DISCRETE APPROACH
PublicationThe paper describes two-dimensional meso-scale results of fracture in notched concrete beams under bending. Concrete was modelled as a random heterogeneous 4-phase material composed of aggregate particles, cement matrix, interfacial transitional zones and air voids. Within continuum mechanics, the simulations were carried out with the finite element method based on a isotropic damage constitutive model enhanced by a characteristic...
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Modelling of strain localization in quasi-brittle materials with non-local continuum models
PublicationW artykule przedstawiono wyniki numerycznej lokalizacji odkształceń w elementach betonowych przy zastosowaniu modelu sprężysto-plastycznego i modelu z degradacja sztywności. Do opisu rys, model rozszerzono o składniki nielokalne. Obliczenia wykonano dla prostych problemów brzegowych
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Comparative modelling of shear localization in granular bodies using a discrete and continuum approach
PublicationW artykule przedstawiono pierwsze wyniki symulacji rys w betonie przy zastosowaniu metody elementów dyskretnych. W obliczeniach wykorzystano program YADE. W symulacjach wykorzystano kulki o różnych średnicach. Przyjęto dodatkowo działanie momentu symulującego szorstkość ziaren.
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Equivalence scales for continuous distributions of expenditure
PublicationResearch background: In the actual sizable populations of households, the standard microeconomic concept of equivalence scales is intractable since its necessary condition of equality of household welfare levels is unlikely to be fulfilled. Purpose of the article: This paper aims to develop a concept of an equivalence scale, which can be suitable for continuous distributions of expenditures in the population. Methods: Using household...
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Shadowing is generic---a continuous map case
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The modelling method of discrete-continuous systems
PublicationThe paper introduces a method of discrete-continuous systems modelling. In the proposed method a three-dimensional system is divided into finite elements in only two directions, with the third direction remaining continuous. The thus obtained discrete-continuous model is described by a set of partial differential equations. General difference equations of discrete system are obtained using the rigid finite element method. The limit...
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Hybrid Reduced Model of Continuous System
PublicationThe paper introduces an alternative method of modelling and modal reduction of continuous systems. Presented method is a hybrid one. It combines the advantages of modal decomposition method and the rigid finite element method. In the proposed method continuous structure is divided into one-dimensional continuous elements. For each 1D element modal decomposition and reduction is applied. Interactions between substructures are...
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RESHAPING THE GDANSK HARBOR –THE CONTINUOUS PROCESS
PublicationGdańsk is the harbour city with a history of more than 1000 years. For many centuries the harbour structures were evolving within the central part of the historic city centre, and – in result – a specific urban structures associated with these functions were created. But the evolution of the maritime technology as well as new needs regarding servicing the ships and cargo-handling activities effected in creation of the more modern...
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Anti-plane surface waves in media with surface structure: Discrete vs. continuum model
PublicationWe present a comparison of the dispersion relations derived for anti-plane surface waves using the two distinct approaches of the surface elasticity vis-a-vis the lattice dynamics. We consider an elastic half-space with surface stresses described within the Gurtin–Murdoch model, and present a formulation of its discrete counterpart that is a square lattice half-plane with surface row of particles having mass and elastic bonds different...
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Hybrid model of moving or rotating continua
PublicationThe paper introduces the method of the model reduction of systems that experience a Coriolis acceleration or gyroscopic effect component. In such causes that corresponding system equations are non-self-adjoined. Modal reduced model is built up for the system without Coriolis or gyroscopic effect terms. These phenomena are next included by application of any lumping technique. Hence, the final reduced model is a hybrid one, obtained...
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Hybrid Model of Axially Moving Continua
PublicationThe paper introduces the method of the model reduction of systems that experience a Coriolis acceleration component. It causes that system equations are non-self-adjoined. To avoid such problem modal, reduced model is built up for the system without Coriolis acceleration terms which are next included by application of any lumping technique. Hence, the final reduced model is a hybrid one, obtained by both lumping and modal methods...