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Applied Mathematical Sciences, 2015
This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully rate-independent systems, first on an abstract level either with or even without a linear structure, discussing various ...
Mielke, Alexander, Roubíček, Tomáš
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This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully rate-independent systems, first on an abstract level either with or even without a linear structure, discussing various ...
Mielke, Alexander, Roubíček, Tomáš
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Mechanics of rate-independent materials
Zeitschrift für angewandte Mathematik und Physik ZAMP, 1965In this paper we consider the formulation of constitutive equations for rate-independent materials with memory, i.e. materials for which the stress at any instant of time depends on the deformation history, but not on the rate at which the deformation history is executed.
Allen C. Pipkin, Ronald S. Rivlin
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Free rate‐independent elastoplastic equations
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2013AbstractNew rate‐independent finite elastoplastic equations are proposed in unified forms applicable to all loading‐unloading cases. A departure from the classical elastoplastic equations is that these new equations are not subjected to and hence free from the usual extrinsic restrictive conditions, including the yield condition as well as the loading ...
Xiao, Heng +2 more
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2015
Sometimes, dynamical systems host various processes, only some of which are rate-independent. These processes can be manifested depending on loading regimes, and only in some regimes (typically very slow) do the rate-independent processes dominate; cf. also Sect. 5.1.2.2 below.
Alexander Mielke, Tomàš Roubíček
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Sometimes, dynamical systems host various processes, only some of which are rate-independent. These processes can be manifested depending on loading regimes, and only in some regimes (typically very slow) do the rate-independent processes dominate; cf. also Sect. 5.1.2.2 below.
Alexander Mielke, Tomàš Roubíček
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On rate-independent hysteresis models
Nonlinear Differential Equations and Applications, 2004The authors develop a general approach based on energy principles for studying rate-independent processes with hysteresis. The involved energy functionals are the potential energy \(I(t,z)\) and the dissipation \(\Delta(\dot{z})\), where \(z\) is the variable describing the process and \(\dot{z}\) is the time variable, assuming that \(\Delta\) is ...
Mielke, Alexander, Theil, Florian
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Relaxation of rate-independent evolution problems
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2002The relaxation of certain time-evolution problems is investigated. As a conceptually simple example, we study elastically deformable bodies that undergo martensitic phase transformations. The movement of the phase boundaries is hindered by dry friction.
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Energetic rate-independent systems
2015To keep the connection with continuum mechanics, cf. also Section 1.3.2, we consider the basic state space split to two spaces $$\displaystyle\begin{array}{rcl} \mathcal{Q} = \mathcal{Y}\times \mathcal{Z},& &{}\end{array}$$ (2.0.1) where the fast component y and the slow component z of the state q = (y, z) live. Whenever possible, however, we
Alexander Mielke, Tomàš Roubíček
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BV‐extension of rate independent operators
Mathematische Nachrichten, 2008AbstractRate independent operators naturally arise in the mathematical analysis of hysteresis. Among rate independent operators, the locally monotone ones are those better suited for the study of PDE's with hysteresis. We prove that a rate independent operator R:Lip(0,T) →BV(0,T) ∩C(0,T) which is locally monotone and continuous with respect to the ...
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Shear-Rate-Independent Diffusion in Granular Flows
Physical Review Letters, 2015We computationally study the behavior of the diffusion coefficient D in granular flows of monodisperse and bidisperse particles spanning regions of relatively high and low shear rate in open and closed laterally confined heaps. Measurements of D at various flow rates, streamwise positions, and depths collapse onto a single curve when plotted as a ...
Yi, Fan +3 more
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A ‘stack’ model of rate-independent polycrystals
International Journal of Plasticity, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Arul Kumar, M. +2 more
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