Papers by Arkadi Berezovski
Internal variables representation of generalized heat equations
Continuum Mechanics and Thermodynamics
Internal Variables in Thermoelasticity
Solid Mechanics and Its Applications
Smart Structures and Systems, 2008
Damping capacity of SMA damping devices is simulated numerically under distinct geometry and load... more Damping capacity of SMA damping devices is simulated numerically under distinct geometry and loading conditions. Two-dimensional numerical simulations are performed on the basis of a phenomenological model of dynamics of martensite-austenite phase boundaries. Results of the simulations predict the time delay and the value of the stress transferred to other parts of a construction by a damper device.
Effect of leading edge on free-convection heat transfer
Journal of Engineering Physics, 1977
ABSTRACT
Journal of Engineering Physics, 1977
The effect of the boundary layer at the leading edge on heat transfer near a vertical semiinfinit... more The effect of the boundary layer at the leading edge on heat transfer near a vertical semiinfinite heated plate is determined by means of matched asymptotic expansions. The criterial relation for air is in good agreement with existing experimentaldata.
Mechanics Research Communications, 2016
Mindlin's microelasticity theory is reduced to the one-dimensional setting to examine its predict... more Mindlin's microelasticity theory is reduced to the one-dimensional setting to examine its prediction of the response of microstructured materials on a pulse loading. The one-dimensional setting requires a minimal number of additional material parameters. Since analytical solutions may be found only in highly simplified asymptotic cases, numerical simulations are performed by means of a finite-volume numerical scheme modifying the wave-propagation algorithm. The calculated response of a material described by the Mindlin microelasticity is compared then with the corresponding response of an "equivalent" periodic laminate.
A common problem in crack tip or phase-transition front propagation is the determination of the v... more A common problem in crack tip or phase-transition front propagation is the determination of the velocity of the irreversible motion of the singularity set. A supplementary constitutive assumption is needed for this determination. A typical solution is the introduction of a kinetic relation between the velocity and the driving force acting on the singularity set. Any kind of such kinetic relation determines entropy production at the singularity set. This means that a direct assumption about the entropy production can be equivalently employed. The entropy production supposes a non-equilibrium description of the process. The corresponding non-equilibrium description is developed in the case of phase-transition front propagation. The nonequilibrium jump relations at the phase boundary followed by a simple hypothesis about entropy production at the front provide a good agreement with experimental observations and theoretical predictions. The same approach can be applied to the problem of crack propagation.
Results of thermomechanical modelling of moving discontinuities in heterogeneous solids are discu... more Results of thermomechanical modelling of moving discontinuities in heterogeneous solids are discussed. Attention is focused on the velocity of the discontinuity which cannot be calculated by means of standard thermomechanical conservation laws. The corresponding kinetic relations for phase transition fronts and straight through crack propagation are derived on the basis of the material description of continuum mechanics and the thermodynamics of discrete systems.
We present a comparison of Finite Element Method, Isogeometric Analysis, and Finite Volume Method... more We present a comparison of Finite Element Method, Isogeometric Analysis, and Finite Volume Method in numerical simulation of one-dimensional elastic wave propagation problems with stress discontinuities. The special attention is paid to accuracy of tested numerical methods and the appearance of spurious oscillations and dissipation effects occurring close to theoretical sharp wavefronts. FEM and FVM are widely accepted as numerical methods used for numerical solution of hyperbolic (wave-like) problems. IGA, the spline variant of FEM, is a modern strategy for numerical solution of partial differential equations. This method is based on splines as shape functions in FEM content. In IGA and FEM, the Newmark method, the central difference method, the generalized-α method and the Park method are employed as time integrators. All the tested numerical strategies are applied for elastic wave propagation in a bar. At the end, main advantages and disadvantages of the numerical methods in wave propagation are summed up.
A non-equilibrium contact between two discrete systems by an inert partition is considered. One o... more A non-equilibrium contact between two discrete systems by an inert partition is considered. One of these two systems, the equilibrium environment reservoir, is controlling the other non-equilibrium system which is described by two levels of different accuracy: firstly as an undecomposed system and secondly as an endoreversible composite system of noninteracting subsystems. The intensive variables of the system in its undecomposed description are non-equilibrium contact quantities which are defined by inequalities induced by the second law. The intensive variables of the system in its description as a composite system are given by the equilibrium variables of the reversible subsystems. The different accuracy of the two descriptions leads to the introduction of the concept of compound deficiency. In particular, the sub-additivity of the entropy rates belonging to the different descriptions is caused by compound deficiency. Finally, the relations between different forms of the Clausius inequality of closed systems are derived by using the concept of compound deficiency.
Configurational forces are thermodynamic conjugates to irreversible material body evolutions such... more Configurational forces are thermodynamic conjugates to irreversible material body evolutions such as extension of cracks, progress of phase-transition fronts, movement of shock waves, etc. They do correspond to a change of material configuration. Accordingly, their realm is the material manifold of a body. Furthermore, they acquire a physical meaning only in so far as they contribute to the global dissipation. Therefore, the present contribution of a pedagogical nature proposes a primer introduction to the thermodynamics of configurational forces. To that purpose, we first introduce a consistent thermomechanics of general deformable continua on the material manifold (and not in physical space). This is achieved in a canonical manner by full projection of the balance equation of momentum onto the material manifold and constructing in parallel a formally consistent expression of the energy conservation. Then various configurational forces such as those appearing in inhomogeneous bodies, at the tip of a propagating crack, at the surface of a propagating phase-transition front, or of a shock wave, and those due to local structural rearrangements (plasticity, damage, growth), are examined from the point of view of their dissipated power.
Wave Motion, 2015
A series of numerical simulations is carried on in order to understand the accuracy of dispersive... more 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 finite-volume numerical scheme, which belongs to the class of wave-propagation 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.
Methode der singulären Störungen im Problem der freien Konvektion mit konstantem Wärmezustrom an einer vertikalen Fläche
Izvestiya Akademii Nauk. Mekhanika Zhidkosti I Gaza
Iutam Bookseries, 2009
Internal variables are introduced in the framework of canonical thermomechanics on the material m... more Internal variables are introduced in the framework of canonical thermomechanics on the material manifold. The canonical equations for energy and pseudomomentum cannot be separated by means of the scale separation because these equations should concern all fields together and, therefore, all scales together. However, the intrinsic interaction force requires a kinetic relation for internal variables. This kinetic relation depends on representation of the internal variable as "internal variable of state" or "internal degree of freedom".
Numerical Simulation of Thermoelastic Wave and Phase-Transition Front Propagation
Mathematical and Numerical Aspects of Wave Propagation WAVES 2003, 2003
Solid Mechanics and Its Applications, 2003
Mathematics and Mechanics of Complex Systems, 2015
This paper describes the mathematical models derived for wave propagation in solids with internal... more This paper describes the mathematical models derived for wave propagation in solids with internal structure(s). The focus of the overview is on one-dimensional models which enlarge the classical wave equation by higher-order terms. The crucial parameter in models is the ratio of characteristic lengths of the excitation and the internal structure. The novel approaches based on the concept of internal variables permit to take directly the thermodynamical conditions into account. Examples of its generalisations include frequency-dependent multiscale models, nonlinear models and thermoelasticity. The substructural complexity within the framework of elasticity gives rise to dispersion of waves. Dispersion analysis shows that acoustic and optical branches of dispersion curves together describe properly wave phenomena in microstructured solids. In case of nonlinear models the governing equations are of the Boussinesq type. It is argued that such models of waves in solids with the microstructure display properties that can be analysed as phenomena of complexity.
Weakly nonlocal thermoelasticity for microstructured solids: microdeformation and microtemperature
Archive of Applied Mechanics, 2014
ABSTRACT Prediction of the thermoelastic behavior of microstructured materials suggests a more ge... more ABSTRACT Prediction of the thermoelastic behavior of microstructured materials suggests a more general description of thermal processes in addition to the generalized continuum description extending the conventional continuum mechanics for incorporating intrinsic microstructural effects. Double dual internal variables are introduced in order to couple inertial microstructural effects like microdeformation and diffusive microstructural effects like microtemperature. The full coupled system of governing equations provides a complete extension of the classical thermoelasticity theory onto the case of microstructured solids.
Buoyancy effects on vortex rings diffusion
Proceedings of the Estonian Academy of Sciences
Simulation of vortex rings interaction by the method of liquid particles
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Papers by Arkadi Berezovski