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Relevant bibliographies by topics / Quasistatic evolution

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Academic literature on the topic 'Quasistatic evolution'

Author: Grafiati

Published: 14 March 2023

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Journal articles on the topic "Quasistatic evolution"

1

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

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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 (2014): 2085–153. http://dx.doi.org/10.1142/s021820251450016x.

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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 (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 (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 (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 (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 (2006): 674–99. http://dx.doi.org/10.1016/j.nonrwa.2005.03.026.

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