On the Rate-Independent Limit of Systems with Dry Friction and Small Viscosity

By Messoud A. Efendiev, Alexander Mielke. 2006

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View Paper: https://www.semanticscholar.org/paper/615755ae45d90b795dfe33d37695288fe3a6994e

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Citations in the corpus

Balanced Viscosity (BV) solutions to infinite-dimensional rate-independent systems (2013, methodology): “nder the working assumptions of §2.1 (in particular, (D.0)–(D.2) and (E.0)–(E.3)), in this section we will present a diﬀerent approach to the vanishing-viscosity analysis of (1.1), which goes back to [EfM06] and was further developed in [MRS09, MRS12a]. The main idea is to rescale time in (1.1) and ”
Modeling solutions with jumps for rate-independent systems on metric spaces (2008, methodology): “Following the approach of [10], for every ε > 0 we now consider the (arclength) rescalings (t̂ε, q̂ε) associated with qε, which in turn fulfill a rescaled version of (5), cf.”
A metric approach to a class of doubly nonlinear evolution equations and applications (2008, background): “Let us point out that this asymptotic analysis has been recently addressed in the paper [22], for general rate-independent problems in a finite-dimensional framework, as well as in [20], in the more specific case of quasistatic evolutions in plasticity with softening.”
Chapter 6 – Evolution of Rate-Independent Systems (2005, background): “4 we explain how rate-independent limits of viscous problems have been obtained in [EM04b].”
Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling (2011, methodology): “This idea has already been used in [8, 17, 18] for rate independent dissipative problems in finite”
BV SOLUTIONS AND VISCOSITY APPROXIMATIONS OF RATE-INDEPENDENT SYSTEMS ∗ (2009, methodology): “The reader may compare this result to [11,18,23,42,48], where similar double-limit passages were performed for specific applied problems, and conditions analogous to (4.”
A Vanishing Viscosity Approach to Quasistatic Evolution in Plasticity with Softening (2006, methodology): “A similar approach in finite dimension was used in [9].”