On rate-independent hysteresis models

By Alexander Mielke, Florian Theil. 2004

338 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Control and Systems Engineering, Electronic, Optical and Magnetic Materials

View Paper: https://www.semanticscholar.org/paper/cd2c4f3549e82d7ad93bd96530e87bfa1fdb8464

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In Atomic and Molecular Physics, and Optics

In Control and Systems Engineering

In Electronic, Optical and Magnetic Materials

Citations in the corpus

Energetic formulation of multiplicative elasto-plasticity using dissipation distances (2003, methodology): “The point is that true solutions of (S) & (E) (which are global minimizers) do in fact satisfy an energy equality and not just an inequality, see Lemma 3.7 in [ MT01 ] and also our lower estimate in Theorem 2.3(ii).”
On Uniqueness in Evolution Quasivariational Inequalities (2004, background): “Another approach to nonsmooth evolution differential inclusions based on energy considerations was recently proposed by Mielke and Theil in [9].”
Chapter 6 – Evolution of Rate-Independent Systems (2005, methodology): “In most parts we will follow [MT04] and use the classical convexity with respect to the linear Banach space structure, since the general theory of geodesic convexity is not developed enough.”
Existence results for energetic models for rate-independent systems (2005, methodology): “However, using the uniform convexity of E(t,·) this result can be considerably improved; the theory in [ MT01 , Sect.7] provides uniqueness and z 2 CLip([0,T ], H10()).”
Existence results for a class of rate-independent material models with nonconvex elastic energies (2006, background): “A priori estimates on uðtÞ, zðtÞ are obtained as in [11], [25], [34], [35], [36].”
A metric approach to a class of doubly nonlinear evolution equations and applications (2008, methodology): “The variational scheme yielding the approximate solutions is indeed the metric analog of the implicit Euler scheme used for doubly nonlinear evolution equations in Banach spaces (see [15,16,42]).”
Γ-limits and relaxations for rate-independent evolutionary problems (2008, background): “[14,25,27, 32,34]), there is still a need to develop a theory for parameter dependence and for numerical approximation properties.”
Modeling solutions with jumps for rate-independent systems on metric spaces (2008, background): “5 in [22], which states that for a Banach space Q, a convex energy functional E, and a translation invariant metric d the subdifferential formulation and the energetic formulation for (Q, d, E) are equivalent.”
On the Rate-Independent Limit of Systems with Dry Friction and Small Viscosity (2006, methodology): “In that case (1.1) is in fact equivalent to the weaker energetic form introduced in [MiTh99, MiTh01 , MiThL02]:”