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 Microstructured solids (7)
 Wave propagation (7)
 Internal Variable (4)
 Dispersion (3)
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 Thermoelastic Wave (2)
 Heterogeneous solids (2)
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Articles 1  20 of 20
FullText Articles in Physical Sciences and Mathematics
Full Field Computing For Elastic Pulse Dispersion In Inhomogeneous Bars, A. Berezovski, R. Kolman, M. Berezovski, D. Gabriel, V. Adamek
Full Field Computing For Elastic Pulse Dispersion In Inhomogeneous Bars, A. Berezovski, R. Kolman, M. Berezovski, D. Gabriel, V. Adamek
Publications
In the paper, the finite element method and the finite volume method are used in parallel for the simulation of a pulse propagation in periodically layered composites beyond the validity of homogenization methods. The direct numerical integration of a pulse propagation demonstrates dispersion effects and dynamic stress redistribution in physical space on example of a onedimensional layered bar. Results of numerical simulations are compared with analytical solution constructed specifically for the considered problem. Analytical solution as well as numerical computations show the strong influence of the composition of constituents on the dispersion of a pulse in a heterogeneous bar and ...
Numerical Simulation Of Energy Localization In Dynamic Materials, Arkadi Berezovski, Mihhail Berezovski
Numerical Simulation Of Energy Localization In Dynamic Materials, Arkadi Berezovski, Mihhail Berezovski
Publications
Dynamic materials are artificially constructed in such a way that they may vary their characteristic properties in space or in time, or both, by an appropriate arrangement or control. These controlled changes in time can be provided by the application of an external (nonmechanical) field, or through a phase transition. In principle, all materials change their properties with time, but very slowly and smoothly. Changes in properties of dynamic materials should be realized in a short or quasinil time lapse and over a sufficiently large material region. Wave propagation is a characteristic feature for dynamic materials because it is also ...
Dynamics Of Discontinuities In Elastic Solids, Arkadi Berezovski, Mihhail Berezovski
Dynamics Of Discontinuities In Elastic Solids, Arkadi Berezovski, Mihhail Berezovski
Publications
The paper is devoted to evolving discontinuities in elastic solids. A discontinuity is represented as a singular set of material points. Evolution of a discontinuity is driven by the configurational force acting at such a set. The main attention is paid to the determination of the velocity of a propagating discontinuity. Martensitic phase transition fronts and brittle cracks are considered as representative examples.
Thermoelastic Waves In Microstructured Solids, Arkadi Berezovski, Mihhail Berezovski
Thermoelastic Waves In Microstructured Solids, Arkadi Berezovski, Mihhail Berezovski
Publications
Thermoelastic wave propagation suggests a coupling between elastic deformation and heat conduction in a body. Microstructure of the body influences the both processes. Since energy is conserved in elastic deformation and heat conduction is always dissipative, the generalization of classical elasticity theory and classical heat conduction is performed differently. It is shown in the paper that a hyperbolic evolution equation for microtemperature can be obtained in the framework of the dual internal variables approach keeping the parabolic equation for the macrotemperature. The microtemperature is considered as a macrotemperature fluctuation. Numerical simulations demonstrate the formation and propagation of thermoelastic waves in ...
Pattern Formation Of Elastic Waves And Energy Localization Due To Elastic Gratings, A. Berezovski, J. Engelbrecht, Mihhail Berezovski
Pattern Formation Of Elastic Waves And Energy Localization Due To Elastic Gratings, A. Berezovski, J. Engelbrecht, Mihhail Berezovski
Publications
Elastic wave propagation through diffraction gratings is studied numerically in the plane strain setting. The interaction of the waves with periodically ordered elastic inclusions leads to a selfimaging Talbot effect for the wavelength equal or close to the grating size. The energy localization is observed at the vicinity of inclusions in the case of elastic gratings. Such a localization is absent in the case of rigid gratings.
Dispersive Waves In Microstructured Solids, A. Berezovski, J. Engelbrecht, A. Salupere, K. Tamm, T. Peets, Mihhail Berezovski
Dispersive Waves In Microstructured Solids, A. Berezovski, J. Engelbrecht, A. Salupere, K. Tamm, T. Peets, Mihhail Berezovski
Publications
The wave motion in micromorphic microstructured solids is studied. The mathematical model is based on ideas of Mindlin and governing equations are derived by making use of the Euler–Lagrange formalism. The same result is obtained by means of the internal variables approach. Actually such a model describes internal fields in microstructured solids under external loading and the interaction of these fields results in various physical effects. The emphasis of the paper is on dispersion analysis and wave profiles generated by initial or boundary conditions in a onedimensional case.
Influence Of Microstructure On Thermoelastic Wave Propagation, Arkadi Berezovski, Mihhail Berezovski
Influence Of Microstructure On Thermoelastic Wave Propagation, Arkadi Berezovski, Mihhail Berezovski
Publications
Numerical simulations of the thermoelastic response of a microstructured material on a thermal loading are performed in the onedimensional setting to examine the influence of temperature gradient effects at the microstructure level predicted by the thermoelastic description of microstructured solids (Berezovski et al. in J. Therm. Stress. 34:413–430, 2011). The system of equations consisting of a hyperbolic equation of motion, a parabolic macroscopic heat conduction equation, and a hyperbolic evolution equation for the microtemperature is solved by a finitevolume numerical scheme. Effects of microtemperature gradients exhibit themselves on the macrolevel due to the coupling of equations of the ...
On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski
On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski
Publications
Abstract
The asymptotic stability of solutions of the Mindlintype microstructure model for solids is analyzed in the paper. It is shown that short waves are asymptotically stable even in the case of a weakly nonconvex free energy dependence on microdeformation.
Research highlights
The Mindlintype microstructure model cannot describe properly short wave propagation in laminates. A modified Mindlintype microstructure model with weakly nonconvex free energy resolves this discrepancy. It is shown that the improved model with weakly nonconvex free energy is asymptotically stable for short waves.
Wave Propagation And Dispersion In Microstructured Solids, Arkadi Berezovski, Juri Engelbrecht, Mihhail Berezovski
Wave Propagation And Dispersion In Microstructured Solids, Arkadi Berezovski, Juri Engelbrecht, Mihhail Berezovski
Publications
A series of numerical simulations is carried on in order to understand the accuracy of dispersive wave models for microstructured solids. The computations are performed by means of the finitevolume numerical scheme, which belongs to the class of wavepropagation algorithms. The dispersion effects are analyzed in materials with different internal structures: microstructure described by micromorphic theory, regular laminates, laminates with substructures, etc., for a large range of material parameters and wavelengths.
TwoScale Microstructure Dynamics, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht
TwoScale Microstructure Dynamics, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht
Publications
Wave propagation in materials with embedded two different microstructures is considered. Each microstructure is characterized by its own length scale. The dual internal variables approach is adopted yielding in a Mindlintype model including both microstructures. Equations of motion for microstructures are coupled with the balance of linear momentum for the macromotion, but not coupled with each other. Corresponding dispersion curves are provided and scale separation is pointed out.
Waves In Microstructured Solids: A Unified Viewpoint Of Modelling, Arkadi Berezovski, Juri Engelbrecht, Mihhail Berezovski
Waves In Microstructured Solids: A Unified Viewpoint Of Modelling, Arkadi Berezovski, Juri Engelbrecht, Mihhail Berezovski
Publications
The basic ideas for describing the dispersive wave motion in microstructured solids are discussed in the onedimensional setting because then the differences between various microstructure models are clearly visible. An overview of models demonstrates a variety of approaches, but the consistent structure of the theory is best considered from the unified viewpoint of internal variables. It is shown that the unification of microstructure models can be achieved using the concept of dual internal variables.
On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski
On The Stability Of A Microstructure Model, Mihhail Berezovski, Arkadi Berezovski
Publications
The asymptotic stability of solutions of the Mindlintype microstructure model for solids is analyzed in the paper. It is shown that short waves are asymptotically stable even in the case of a weakly nonconvex free energy dependence on microdeformation.
Dispersive Wave Equations For Solids With Microstructure, A. Berezovski, Juri Engelbrecht, Mihhail Berezovski
Dispersive Wave Equations For Solids With Microstructure, A. Berezovski, Juri Engelbrecht, Mihhail Berezovski
Publications
The dispersive wave motion in solids with microstructure is considered in the onedimensional setting in order to understand better the mechanism of dispersion. It is shown that the variety of dispersive wave propagation models derived by homogenization, continualisation, and generalization of continuum mechanics can be unified in the framework of dual internal variables theory.
Deformation Waves In Microstructured Materials: Theory And Numerics, Juri Engelbrecht, Arkadi Berezovski, Mihhail Berezovski
Deformation Waves In Microstructured Materials: Theory And Numerics, Juri Engelbrecht, Arkadi Berezovski, Mihhail Berezovski
Publications
A linear model of the microstructured continuum based on Mindlin theory is adopted which can be represented in the framework of the internal variable theory. Fully coupled systems of equations for macromotion and microstructure evolution are represented in the form of conservation laws. A modification of wave propagation algorithm is used for numerical calculations. Results of direct numerical simulations of wave propagation in periodic medium are compared with similar results for the continuous media with the modelled microstructure. It is shown that the proper choice of material constants should be made to match the results obtained by both approaches
Elements Of Study On Dynamic Materials, Marine Rousseau, Gerard A. Maugin, Mihhail Berezovski
Elements Of Study On Dynamic Materials, Marine Rousseau, Gerard A. Maugin, Mihhail Berezovski
Publications
As a preliminary study to more complex situations of interest in smallscale technology, this paper envisages the elementary propagation properties of elastic waves in onespatial dimension when some of the properties (mass density, elasticity) may vary suddenly in space or in time, the second case being of course more original. Combination of the two may be of even greater interest. Toward this goal, a critical examination of what happens to solutions at the crossing of pure spacelike and timelike material discontinuities is given together with simple solutions for smooth transitions and numerical simulations in the discontinuous case. The effects on ...
Waves In Materials With Microstructure: Numerical Simulation, Mihhail Berezovski, Arkadi Berezovski, Juri Engelbrecht
Waves In Materials With Microstructure: Numerical Simulation, Mihhail Berezovski, Arkadi Berezovski, Juri Engelbrecht
Publications
Results of numerical experiments are presented in order to compare direct numerical calculations of wave propagation in a laminate with prescribed properties and corresponding results obtained for an effective medium with the microstructure modelling. These numerical experiments allowed us to analyse the advantages and weaknesses of the microstructure model.
Temporal Scales For Transport Patterns In The Gulf Of Finland, Bert Viikmae, Tarmo Soomere, Mikk Viidebaum, Mihhail Berezovski
Temporal Scales For Transport Patterns In The Gulf Of Finland, Bert Viikmae, Tarmo Soomere, Mikk Viidebaum, Mihhail Berezovski
Publications
The basic time scales for currentinduced net transport of surface water and associated time scales of reaching the nearshore in the Gulf of Finland, the Baltic Sea, are analysed based on Lagrangian trajectories of water particles reconstructed from threedimensional velocity fields by the Rossby Centre circulation model for 1987–1991. The number of particles reaching the nearshore exhibits substantial temporal variability whereas the rate of leaving the gulf is almost steady. It is recommended to use an about 3 grid cells wide nearshore area as a substitute to the coastal zone and about 10–15 day long trajectories for calculations ...
Waves In Inhomogeneous Solids, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht
Waves In Inhomogeneous Solids, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht
Publications
The paper aims at presenting a numerical technique used in simulating the propagation of waves in inhomogeneous elastic solids. The basic governing equations are solved by means of a finitevolume scheme that is faithful, accurate, and conservative. Furthermore, this scheme is compatible with thermodynamics through the identification of the notions of numerical fluxes (a notion from numerics) and of excess quantities (a notion from irreversible thermodynamics). A selection of onedimensional wave propagation problems is presented, the simulation of which exploits the designed numerical scheme. This selection of exemplary problems includes (i) waves in periodic media for weakly nonlinear waves with ...
Numerical Simulation Of Waves And Fronts In Inhomogeneous Solids, A. Berezovski, M. Berezovski, J. Engelbrecht, G. A. Maugin
Numerical Simulation Of Waves And Fronts In Inhomogeneous Solids, A. Berezovski, M. Berezovski, J. Engelbrecht, G. A. Maugin
Publications
Dynamic response of inhomogeneous materials exhibits new effects, which often do not exist in homogeneous media. It is quite natural that most of studies of wave and front propagation in inhomogeneous materials are associated with numerical simulations. To develop a numerical algorithm and to perform the numerical simulations of moving fronts we need to formulate a kinetic law of progress relating the driving force and the velocity of the discontinuity. The velocity of discontinuity is determined by means of the nonequilibrium jump relations at the front. The obtained numerical method generalizes the wavepropagation algorithm to the case of moving discontinuities ...
Numerical Simulation Of Nonlinear Elastic Wave Propagation In Piecewise Homogeneous Media, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht
Numerical Simulation Of Nonlinear Elastic Wave Propagation In Piecewise Homogeneous Media, Arkadi Berezovski, Mihhail Berezovski, Juri Engelbrecht
Publications
Systematic experimental work [S. Zhuang, G. Ravichandran, D. Grady, J. Mech. Phys. Solids 51 (2003) 245–265] on laminated composites subjected to high velocity impact loading exhibits the dispersed wave field and the oscillatory behavior of waves with respect to a mean value. Such a behavior is absent in homogeneous solids. An approximate solution to the plate impact in layered heterogeneous solids has been developed in [X. Chen, N. Chandra, A.M. Rajendran, Int. J. Solids Struct. 41 (2004) 4635–4659]. The influence of the particle velocity on many process characteristics was demonstrated. Based on earlier results [A. Berezovski, J ...