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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

DOBBS, NEIL, and MIKKO STENLUND. "Quasistatic dynamical systems." Ergodic Theory and Dynamical Systems 37, no. 8 (May 12, 2016): 2556–96. http://dx.doi.org/10.1017/etds.2016.9.

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Анотація:

We introduce the notion of a quasistatic dynamical system, which generalizes that of an ordinary dynamical system. Quasistatic dynamical systems are inspired by the namesake processes in thermodynamics, which are idealized processes where the observed system transforms (infinitesimally) slowly due to external influence, tracing out a continuous path of thermodynamic equilibria over an (infinitely) long time span. Time evolution of states under a quasistatic dynamical system is entirely deterministic, but choosing the initial state randomly renders the process a stochastic one. In the prototypical setting where the time evolution is specified by strongly chaotic maps on the circle, we obtain a description of the statistical behavior as a stochastic diffusion process, under surprisingly mild conditions on the initial distribution, by solving a well-posed martingale problem. We also consider various admissible ways of centering the process, with the curious conclusion that the ‘obvious’ centering suggested by the initial distribution sometimes fails to yield the expected diffusion.

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2

Davoli, Elisa. "Quasistatic evolution models for thin plates arising as low energy Γ-limits of finite plasticity". Mathematical Models and Methods in Applied Sciences 24, № 10 (27 травня 2014): 2085–153. http://dx.doi.org/10.1142/s021820251450016x.

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Анотація:

In this paper we deduce by Γ-convergence some partially and fully linearized quasistatic evolution models for thin plates, in the framework of finite plasticity. Denoting by ε the thickness of the plate, we study the case where the scaling factor of the elasto-plastic energy is of order ε2α-2, with α ≥ 3. These scalings of the energy lead, in the absence of plastic dissipation, to the Von Kármán and linearized Von Kármán functionals for thin plates. We show that solutions to the three-dimensional quasistatic evolution problems converge, as the thickness of the plate tends to zero, to a quasistatic evolution associated to a suitable reduced model depending on α.

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3

Kružík, Martin, David Melching, and Ulisse Stefanelli. "Quasistatic evolution for dislocation-free finite plasticity." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 123. http://dx.doi.org/10.1051/cocv/2020031.

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We investigate quasistatic evolution in finite plasticity under the assumption that the plastic strain is compatible. This assumption is well-suited to describe the special case of dislocation-free plasticity and entails that the plastic strain is the gradient of a plastic deformation map. The total deformation can be then seen as the composition of a plastic and an elastic deformation. This opens the way to an existence theory for the quasistatic evolution problem featuring both Lagrangian and Eulerian variables. A remarkable trait of the result is that it does not require second-order gradients.

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4

Mora-Corral, Carlos. "Quasistatic Evolution of Cavities in Nonlinear Elasticity." SIAM Journal on Mathematical Analysis 46, no. 1 (January 2014): 532–71. http://dx.doi.org/10.1137/120872498.

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5

FRIGERI, SERGIO, PAVEL KREJČÍ, and ULISSE STEFANELLI. "QUASISTATIC ISOTHERMAL EVOLUTION OF SHAPE MEMORY ALLOYS." Mathematical Models and Methods in Applied Sciences 21, no. 12 (December 2011): 2409–32. http://dx.doi.org/10.1142/s0218202511005787.

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This paper focuses on a three-dimensional phenomenological model for the isothermal evolution of a polycrystalline shape memory alloy. The model, originally proposed by Auricchio, Taylor, and Lubliner in 1997, is thermodynamically consistent and reproduces the crucial martensitic reorientation effect as well as the tension-compression asymmetric behavior of the material. We prove the existence of a weak solution of the corresponding quasistatic evolution problem by passing to the limit within a time-discretization procedure.

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6

Babadjian, Jean-François. "Quasistatic evolution of a brittle thin film." Calculus of Variations and Partial Differential Equations 26, no. 1 (January 30, 2006): 69–118. http://dx.doi.org/10.1007/s00526-005-0369-y.

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7

Kružík, Martin, Ulisse Stefanelli, and Chiara Zanini. "Quasistatic evolution of magnetoelastic plates via dimension reduction." Discrete and Continuous Dynamical Systems 35, no. 12 (May 2015): 5999–6013. http://dx.doi.org/10.3934/dcds.2015.35.5999.

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8

Thomas, Marita. "Quasistatic damage evolution with spatial $\mathrm{BV}$-regularization." Discrete & Continuous Dynamical Systems - S 6, no. 1 (2013): 235–55. http://dx.doi.org/10.3934/dcdss.2013.6.235.

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9

Dal Maso, G., Antonio DeSimone, M. G. Mora, and M. Morini. "Globally stable quasistatic evolution in plasticity with softening." Networks & Heterogeneous Media 3, no. 3 (2008): 567–614. http://dx.doi.org/10.3934/nhm.2008.3.567.

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10

Kuttler, K. L., and M. Shillor. "Quasistatic evolution of damage in an elastic body." Nonlinear Analysis: Real World Applications 7, no. 4 (September 2006): 674–99. http://dx.doi.org/10.1016/j.nonrwa.2005.03.026.

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11

Bucur, Dorin, Giuseppe Buttazzo, and Anne Lux. "Quasistatic Evolution in Debonding Problems via Capacitary Methods." Archive for Rational Mechanics and Analysis 190, no. 2 (September 2, 2008): 281–306. http://dx.doi.org/10.1007/s00205-008-0166-9.

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12

Maso, Gianni Dal, Alexey Demyanov, and Antonio DeSimone. "Quasistatic Evolution Problems for Pressure-sensitive Plastic Materials." Milan Journal of Mathematics 75, no. 1 (September 27, 2007): 117–34. http://dx.doi.org/10.1007/s00032-007-0071-y.

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13

Lipton, Robert, Michael Stuebner, and Yuanjie Lua. "Multi-scale quasistatic damage evolution for polycrystalline materials." International Journal of Engineering Science 58 (September 2012): 85–94. http://dx.doi.org/10.1016/j.ijengsci.2012.03.027.

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14

Shustov, B. M., and A. V. Tutukov. "On Early Evolution of Accreting Stars." Symposium - International Astronomical Union 115 (1987): 440–41. http://dx.doi.org/10.1017/s0074180900096169.

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Анотація:

Accretion is a dominant factor in the early evolution of stars. The first time an accretion regime settles in is when a dusty opaque core forms. The mass of adiabatically contracting core inside the isothermally collapsing envelope depends only on the optical properties of dust. Spherically symmetric models of dusty cores were constructed using the Henyey technique with accretion boundary conditions (Menshchikov 1986). It appears that all protostars with normal chemical composition should pass through the stage of a quasistatic dusty core. The evolution of dusty cores is similar to that of “normal” young stars with accretion. One could distinguish convective, radiative and central core contraction phases. The life-time tc of the core depends on the core mass Mc and the accretion rate Ṁ (for Mc = 0.01 M⊙ and Ṁ = 1.6x10−6, 1.6x10−5 M⊙/year tc = 1.2x104, 3x103 yrs consequently). After dust exhaustion in the core it collapses and a central ionized quasistatic region grows in several tens of years. A flash of infrared radiation at the moment is not excluded.

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15

Teniou, Boudjemaa, and Sabrina Benferdi. "Quasistatic Elastic Contact with Adhesion." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–13. http://dx.doi.org/10.1155/2011/686139.

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Анотація:

The aim of this paper is the variational study of the contact with adhesion between an elastic material and a rigid foundation in the quasistatic process where the deformations are supposed to be small. The behavior of this material is modelled by a nonlinear elastic law and the contact is modelled with Signorini's conditions and adhesion. The evolution of bonding field is described by a nonlinear differential equation. We derive a variational formulation of the mechanical problem, and we prove the existence and uniqueness of the weak solution using a theorem on variational inequalities, the theorem of Cauchy-Lipschitz, a lemma of Gronwall, as well as the fixed point of Banach.

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16

Alduncin, Gonzalo. "Composition duality methods for quasistatic evolution elastoviscoplastic variational problems." Nonlinear Analysis: Hybrid Systems 5, no. 1 (February 2011): 113–22. http://dx.doi.org/10.1016/j.nahs.2010.10.003.

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17

Maso, Gianni Dal, Antonio DeSimone, and Maria Giovanna Mora. "Quasistatic Evolution Problems for Linearly Elastic–Perfectly Plastic Materials." Archive for Rational Mechanics and Analysis 180, no. 2 (February 6, 2006): 237–91. http://dx.doi.org/10.1007/s00205-005-0407-0.

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18

Alberti, Giovanni, and Antonio DeSimone. "Quasistatic Evolution of Sessile Drops and Contact Angle Hysteresis." Archive for Rational Mechanics and Analysis 202, no. 1 (June 28, 2011): 295–348. http://dx.doi.org/10.1007/s00205-011-0427-x.

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19

Solombrino, Francesco. "Quasistatic Evolution in Perfect Plasticity for General Heterogeneous Materials." Archive for Rational Mechanics and Analysis 212, no. 1 (December 14, 2013): 283–330. http://dx.doi.org/10.1007/s00205-013-0703-z.

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20

Caillerie, D., and C. Dascalu. "One-dimensional Localization Solutions for Time-dependent Damage." International Journal of Damage Mechanics 20, no. 8 (November 2011): 1178–97. http://dx.doi.org/10.1177/1056789510395553.

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Анотація:

This article presents analytical solutions for a class of one-dimensional time-dependent elasto-damage problems. The considered damage evolution law may be seen as a one-dimensional version of the Kachanov–Rabotnov creep damage model with classical loading–unloading conditions. We construct analytical solutions for the quasistatic one-dimensional problem. The evolution consists of a first regime, in which damage and strain grow uniformly, followed by a regime in which localization occurs. In the second regime, the uniqueness of the solution is lost and the deformation of the body is represented by a sequence of arbitrary alternate loading/unloading regions. Complex evolutions with progressive enlargement of the unloading regions in a finite number of steps are also constructed. We study analytically and numerically the features of the obtained bifurcated solutions. It is shown that, at every instant of time, a lower limit exists for the size of the localization zone. This lower limit is actually realized by the solution with successive unloadings constructed in this article. These features help us to understand the behavior of numerical solutions for time-dependent damage in the quasistatic approximation.

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21

Nifagin, V. A., and M. A. Gundina. "QUASISTATIC STATIONARY GROWTH OF ELASTOPLASTICAL CRACK." Vestnik of Samara University. Natural Science Series 20, no. 7 (May 30, 2017): 85–95. http://dx.doi.org/10.18287/2541-7525-2014-20-7-85-95.

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Анотація:

The boundary value problem with relations to the theory of ﬂow with non- linear hardening in derivatives stress and strain tensors in the parameter loading is formulated to estimate local mechanical properties in the vicinity of crack tip of mode of loading for plane strain of elastic-plastic material at the stage of quasi-static growth. Complete solutions are obtained by the method of asymp- totic decompositions. The redistribution of stress and strain ﬁelds in the plastic region at quasi-static growing crack for the intermediate structure is investigat- ed. The form of plastic zones was found in the evolution of fracture process of material. We also obtained direct estimates of errors and diameters of con- vergence when dropping residues of series.

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22

DAL MASO, GIANNI, and ANTONIO DESIMONE. "QUASISTATIC EVOLUTION FOR CAM-CLAY PLASTICITY: EXAMPLES OF SPATIALLY HOMOGENEOUS SOLUTIONS." Mathematical Models and Methods in Applied Sciences 19, no. 09 (September 2009): 1643–711. http://dx.doi.org/10.1142/s0218202509003942.

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We study a quasistatic evolution problem for Cam-Clay plasticity under a special loading program which leads to spatially homogeneous solutions. Under some initial conditions, the solutions exhibit a softening behavior and time discontinuities. The behavior of the solutions at the jump times is studied by a viscous approximation.

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23

Solombrino, Francesco. "Quasistatic evolution for plasticity with softening: The spatially homogeneous case." Discrete & Continuous Dynamical Systems - A 27, no. 3 (2010): 1189–217. http://dx.doi.org/10.3934/dcds.2010.27.1189.

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24

Agostiniani, Virginia. "Second order approximations of quasistatic evolution problems in finite dimension." Discrete & Continuous Dynamical Systems - A 32, no. 4 (2012): 1125–67. http://dx.doi.org/10.3934/dcds.2012.32.1125.

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25

Dal Maso, Gianni, and Francesco Solombrino. "Quasistatic evolution for Cam-Clay plasticity: The spatially homogeneous case." Networks & Heterogeneous Media 5, no. 1 (2010): 97–132. http://dx.doi.org/10.3934/nhm.2010.5.97.

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26

Crismale, Vito. "Globally stable quasistatic evolution for a coupled elastoplastic–damage model." ESAIM: Control, Optimisation and Calculus of Variations 22, no. 3 (June 23, 2016): 883–912. http://dx.doi.org/10.1051/cocv/2015037.

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27

Maso, Gianni Dal, and Riccardo Scala. "Quasistatic Evolution in Perfect Plasticity as Limit of Dynamic Processes." Journal of Dynamics and Differential Equations 26, no. 4 (November 12, 2014): 915–54. http://dx.doi.org/10.1007/s10884-014-9409-7.

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28

Adly, S., and T. Haddad. "An Implicit Sweeping Process Approach to Quasistatic Evolution Variational Inequalities." SIAM Journal on Mathematical Analysis 50, no. 1 (January 2018): 761–78. http://dx.doi.org/10.1137/17m1120658.

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29

Leppänen, Juho. "Intermittent quasistatic dynamical systems: weak convergence of fluctuations." Nonautonomous Dynamical Systems 5, no. 1 (April 3, 2018): 8–34. http://dx.doi.org/10.1515/msds-2018-0002.

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Анотація:

Abstract This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influences. We focus on the case where the time-evolution is described by intermittent interval maps (Pomeau-Manneville maps) with time-dependent parameters. In a suitable range of parameters, we obtain a description of the statistical properties as a stochastic diffusion, by solving a well-posed martingale problem. The results extend those of a related recent study due to Dobbs and Stenlund, which concerned the case of quasistatic (uniformly) expanding systems.

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30

Andrews, K. T., K. L. Kuttler, and M. Shillor. "Quasistatic evolution of damage in an elastic body with random inputs." Applicable Analysis 97, no. 8 (October 7, 2017): 1416–31. http://dx.doi.org/10.1080/00036811.2017.1385063.

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31

Maso, Gianni Dal, Antonio DeSimone, Maria Giovanna Mora, and Massimiliano Morini. "A Vanishing Viscosity Approach to Quasistatic Evolution in Plasticity with Softening." Archive for Rational Mechanics and Analysis 189, no. 3 (May 6, 2008): 469–544. http://dx.doi.org/10.1007/s00205-008-0117-5.

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32

Barreto, W. "An evolution of adiabatic matter: a case for the quasistatic regime." General Relativity and Gravitation 45, no. 11 (August 11, 2013): 2223–38. http://dx.doi.org/10.1007/s10714-013-1580-3.

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33

Dal Maso, Gianni, Antonio DeSimone, and Francesco Solombrino. "Quasistatic evolution for Cam-Clay plasticity: properties of the viscosity solution." Calculus of Variations and Partial Differential Equations 44, no. 3-4 (August 10, 2011): 495–541. http://dx.doi.org/10.1007/s00526-011-0443-6.

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34

Fiaschi, Alice. "Quasistatic evolution for a phase-transition model: a Young measure approach." GAMM-Mitteilungen 34, no. 1 (April 2011): 124–29. http://dx.doi.org/10.1002/gamm.201110020.

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35

Babadjian, Jean-François. "A Quasistatic Evolution Model for the Interaction Between Fracture and Damage." Archive for Rational Mechanics and Analysis 200, no. 3 (October 5, 2010): 945–1002. http://dx.doi.org/10.1007/s00205-010-0379-6.

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36

Crismale, Vito. "Globally stable quasistatic evolution for strain gradient plasticity coupled with damage." Annali di Matematica Pura ed Applicata (1923 -) 196, no. 2 (July 21, 2016): 641–85. http://dx.doi.org/10.1007/s10231-016-0590-7.

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37

Maggiani, G. B., and M. G. Mora. "Quasistatic evolution of perfectly plastic shallow shells: a rigorous variational derivation." Annali di Matematica Pura ed Applicata (1923 -) 197, no. 3 (October 13, 2017): 775–815. http://dx.doi.org/10.1007/s10231-017-0704-x.

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38

Plekhov, Oleg, and Oleg Naimark. "Experimental Study of Defect Induced Temperature Evolution in Polycrystalline Metals." Key Engineering Materials 592-593 (November 2013): 509–12. http://dx.doi.org/10.4028/www.scientific.net/kem.592-593.509.

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This work is devoted to theoretical and experimental study of energy dissipation and storage processes in titanium alloys under quasistatic loading. The specimen surface temperature was measured by infrared camera FLIR SC 5000 (a spectral range of 3-5 micron). Extending previous results of the research group in Perm, we coupled the experimental investigation of temperature evolution with a statistical description of the mesodefect ensemble. It allowed us to propose a thermodynamic internal variable model of heat dissipation in metals.

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39

Li, Ye, and Claus O. Wilke. "Digital Evolution in Time-Dependent Fitness Landscapes." Artificial Life 10, no. 2 (March 2004): 123–34. http://dx.doi.org/10.1162/106454604773563559.

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Анотація:

We study the response of populations of digital organisms that adapt to a time-varying (periodic) fitness landscape of two oscillating peaks. We corroborate in general predictions from quasi-species theory in dynamic landscapes, such as adaptation to the average fitness landscape at small periods (high frequency) and quasistatic adaptation at large periods (low frequency). We also observe adaptive phase shifts (time lags between a change in the fitness landscape and an adaptive change in the population) that indicate a low-pass filter effect, in agreement with existing theory. Finally, we witness long-term adaptation to fluctuating environments not anticipated in previous theoretical work.

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40

Orlik, Julia. "Existence and Stability Estimate for the Solution of the Ageing Hereditary Linear Viscoelasticity Problem." Abstract and Applied Analysis 2009 (2009): 1–19. http://dx.doi.org/10.1155/2009/828315.

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The paper is concerned with the existence and stability of weak (variational) solutions for the problem of the quasistatic evolution of a viscoelastic material under mixed inhomogenous Dirichlet-Neumann boundary conditions. The main novelty of the paper relies in dealing with continuous-in-time weak solutions and allowing nonconvolution and weak-singular Volterra's relaxation kernels.

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41

Crismale, Vito, Giuliano Lazzaroni, and Gianluca Orlando. "Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue." Mathematical Models and Methods in Applied Sciences 28, no. 07 (June 19, 2018): 1371–412. http://dx.doi.org/10.1142/s0218202518500379.

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Анотація:

In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.

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42

LO SURDO, C. "Quasistatic evolution of a dissipative plasma column in vacuum: errata and addenda." Journal of Plasma Physics 63, no. 1 (January 2000): 21–41. http://dx.doi.org/10.1017/s0022377899008119.

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Анотація:

We provide a revised, and substantially enriched, version of an old study of ours, dealing with the theory of the slow evolution of a strictly dissipative, cylindrical plasma column in vacuum [J. Plasma Phys.43, 217–237 (1990)]. After correcting a technical mistake made in our previous formulation of the model of the physical system under consideration, we develop a fully amended version of the associated theory, paying special attention to the problem's well-posedness. A number of comments, generalizations and further details have also been added.

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43

Davoli, Elisa, та Maria Giovanna Mora. "A quasistatic evolution model for perfectly plastic plates derived by Γ -convergence". Annales de l'Institut Henri Poincare (C) Non Linear Analysis 30, № 4 (липень 2013): 615–60. http://dx.doi.org/10.1016/j.anihpc.2012.11.001.

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44

Davoli, Elisa, and Maria Giovanna Mora. "Stress regularity for a new quasistatic evolution model of perfectly plastic plates." Calculus of Variations and Partial Differential Equations 54, no. 3 (May 28, 2015): 2581–614. http://dx.doi.org/10.1007/s00526-015-0876-4.

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45

Fiaschi, Alice. "A vanishing viscosity approach to a quasistatic evolution problem with nonconvex energy." Annales de l'Institut Henri Poincare (C) Non Linear Analysis 26, no. 4 (July 2009): 1055–80. http://dx.doi.org/10.1016/j.anihpc.2008.02.003.

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46

Kostina, Anastasia, Yuriy Bayandin, Oleg Naimark, and Oleg Plekhov. "Numerical Simulation of Damage to Fracture Transition in Metals Based on the Statistical Model of Mesodefect Evolution." Key Engineering Materials 592-593 (November 2013): 205–8. http://dx.doi.org/10.4028/www.scientific.net/kem.592-593.205.

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Анотація:

A comprehensive approach, including statistical physics and thermodynamics is required in the modelling of phenomena underlying the processes of deformation and fracture of solids. This work is devoted to the description of the damage to fracture transition, using statistically based thermodynamic model of mesocracks and mesoshifts evolution. Numerical simulation of quasistatic tensile experiment of vanadium plate specimen illustrated the influence of bulk and shear defects on stress-strain state.

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47

DEMYANOV, ALEXEY. "QUASISTATIC EVOLUTION IN THE THEORY OF PERFECTLY ELASTO-PLASTIC PLATES PART I: EXISTENCE OF A WEAK SOLUTION." Mathematical Models and Methods in Applied Sciences 19, no. 02 (February 2009): 229–56. http://dx.doi.org/10.1142/s0218202509003413.

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Анотація:

The existence of weak solutions to the quasistatic problems in the theory of perfectly elasto-plastic plates is studied in the framework of the variational theory for rate-independent processes. Approximate solutions are constructed by means of incremental variational problems in spaces of functions with bounded hessian. The constructed weak solution is shown to be absolutely continuous in time. A strong formulation of the flow rule is obtained.

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48

Campo, M., J. R. Fernández, K. L. Kuttler, and M. Shillor. "Quasistatic evolution of damage in an elastic body: numerical analysis and computational experiments." Applied Numerical Mathematics 57, no. 9 (September 2007): 975–88. http://dx.doi.org/10.1016/j.apnum.2006.09.005.

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49

Nazarov, S. A. "A quasistatic model of the evolution of an interface inside a deformed solid." Journal of Applied Mathematics and Mechanics 70, no. 3 (September 2006): 416–29. http://dx.doi.org/10.1016/j.jappmathmech.2006.07.002.

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50

Fedelich, B., and G. Zanzotto. "One-dimensional quasistatic nonisothermal evolution of shape-memory material inside the hysteresis loop." Continuum Mechanics and Thermodynamics 3, no. 4 (1991): 251–76. http://dx.doi.org/10.1007/bf01126410.

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