Young measure flow as a model for damage

Marc Oliver Rieger, J Zimmer

Research output: Contribution to journalArticle

3 Citations (Scopus)
81 Downloads (Pure)

Abstract

Models for hysteresis in continuum mechanics are studied that rely on a time-discretised quasi-static evolution of Young measures akin to a gradient flow. The main feature of this approach is that it allows for local, rather than global minimisation. In particular, the case of a non-coercive elastic energy density of Lennard-Jones type is investigated. The approach is used to describe the formation of damage in a material; existence results are proved, as well as several results highlighting the qualitative behaviour of solutions. Connections are made to recent variational models for fracture.
Original languageEnglish
Pages (from-to)1-32
Number of pages32
JournalZeitschrift für Angewandte Mathematik und Physik
Volume60
Issue number1
Early online date5 Jul 2008
DOIs
Publication statusPublished - Jan 2009

Fingerprint

Quasistatic Evolution
Global Minimization
Variational Model
Young Measures
Gradient Flow
Lennard-Jones
Qualitative Behavior
Continuum Mechanics
Behavior of Solutions
Hysteresis
Energy Density
Existence Results
Damage
damage
continuum mechanics
Continuum mechanics
flux density
hysteresis
gradients
optimization

Keywords

  • Fracture
  • Elasticity
  • Continuum mechanics

Cite this

Young measure flow as a model for damage. / Rieger, Marc Oliver; Zimmer, J.

In: Zeitschrift für Angewandte Mathematik und Physik, Vol. 60, No. 1, 01.2009, p. 1-32.

Research output: Contribution to journalArticle

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