Emergence of rate-independent dissipation from viscous systems with wiggly energies

DOI10.1007/s00161-011-0216-7zbMath1258.74169OpenAlexW2108122596WikidataQ59901819 ScholiaQ59901819MaRDI QIDQ1939380

Alexander Mielke

Publication date: 4 March 2013

Published in: Continuum Mechanics and Thermodynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00161-011-0216-7

zbMATH Keywords

rate-independent plasticityDe Giorgi formulationgamma convergence for evolutionviscous gradient flowwiggly energy landscape

Mathematics Subject Classification ID

Nonlinear constitutive equations for materials with memory (74D10) Problems involving hysteresis in solids (74N30)

Related Items

Variational Approaches and Methods for Dissipative Material Models with Multiple Scales, Viscosity solutions for doubly nonlinear evolution equations, Exploring families of energy-dissipation landscapes via tilting: three types of EDP convergence, A gradient system with a wiggly energy and relaxed EDP-convergence, Instability of Hysteretic Phase Interfaces in a Mean-Field Model with Inhomogeneities, The effect of forest dislocations on the evolution of a phase-field model for plastic slip, Rate-independent dynamics and Kramers-type phase transitions in nonlocal Fokker-Planck equations with dynamical control, On microscopic origins of generalized gradient structures, Quadratic and rate-independent limits for a large-deviations functional

Cites Work

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• Passing to the limit in a Wasserstein gradient flow: from diffusion to reaction
• Gamma-convergence of gradient flows on Hilbert and metric spaces and applications
• Nonequilibrium thermodynamics of pseudoelasticity
• From discrete visco-elasticity to continuum rate-independent plasticity: rigorous results
• Quasistatic delamination problem
• Thermodynamics of rate-independent plasticity
• Rate-independent hysteresis in a bi-stable chain.
• Thermodynamic aspects of shape memory alloys
• Hysteresis and phase transitions
• Mechanics of a discrete chain with bi-stable elements
• \(\Gamma\)-limits and relaxations for rate-independent evolutionary problems
• BV solutions and viscosity approximations of rate-independent systems
• Contact Mechanics and Friction
• EXISTENCE AND UNIQUENESS RESULTS FOR A CLASS OF RATE-INDEPENDENT HYSTERESIS PROBLEMS
• The Brezis–Ekeland Principle for Doubly Nonlinear Equations
• Gamma-convergence of gradient flows with applications to Ginzburg-Landau
• The Derivation of Constitutive Relations from the Free Energy and the Dissipation Function
• Fluctuations and Irreversible Processes