Existence results for energetic models for rate-independent systems

Mainik, Andreas; Mielke, Alexander

doi:10.1007/s00526-004-0267-8

Cited by 173 publications

(200 citation statements)

References 26 publications

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“…This theory is developed in [MaM05,FrM06,Mai07], see also the survey [Mie05] and the further developments in [MRS08]. We use a slightly adapted version as we are in a concrete Banach space setting.…”

Section: Abstract Existence Resultsmentioning

confidence: 99%

“…The first result is implicitly contained in [MaM05] but for the readers we provide a direct short proof. See [MRS08] for a discussion of more general joint recovery sequence conditions.…”

Section: For the Dissipation Distance D : Z×z → [0 ∞] We Impose The mentioning

confidence: 99%

“…This theory was developed in [MiT99,MTL02,MaM05,FrM06], and in Section 4 we provide the suitable version with all the abstract assumptions.…”

Section: Introductionmentioning

confidence: 99%

“…The latter property is essential to provide natural a priori bounds while the former allows to apply a generalized Helly selection principle, cf. [MaM05,FrM06].…”

Section: Introductionmentioning

confidence: 99%

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Global Existence for Rate-Independent Gradient Plasticity at Finite Strain

2008

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Section: Abstract Existence Resultsmentioning

confidence: 99%

“…The first result is implicitly contained in [MaM05] but for the readers we provide a direct short proof. See [MRS08] for a discussion of more general joint recovery sequence conditions.…”

Section: For the Dissipation Distance D : Z×z → [0 ∞] We Impose The mentioning

confidence: 99%

“…This theory was developed in [MiT99,MTL02,MaM05,FrM06], and in Section 4 we provide the suitable version with all the abstract assumptions.…”

Section: Introductionmentioning

confidence: 99%

“…The latter property is essential to provide natural a priori bounds while the former allows to apply a generalized Helly selection principle, cf. [MaM05,FrM06].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global Existence for Rate-Independent Gradient Plasticity at Finite Strain

2008

Self Cite

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“…We then apply Helly's selection principle (see [11,Theorem 3.2]) which ensures, thanks to (3.10), the existence of a further subsequence (independent of time and still not relabeled) such that…”

Section: 2mentioning

confidence: 99%

A note on the derivation of rigid-plastic models

Babadjian

Francfort

2016

Nonlinear Differ. Equ. Appl.

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Small‐strain heterogeneous elastoplasticity revisited

Francfort

Giacomini

2012

Comm Pure Appl Math

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The elastoplastic quasi‐static evolution of a multiphase material—a material with a pointwise varying yield surface and elasticity tensor, together with interfaces between the phases—is revisited in the context of conservative globally minimizing movements. Existence is shown, and classical evolutions are recovered under natural constraints on the plastic dissipation potential. Special attention is paid to the interfaces where the correct dissipation has to be enforced on the interfaces. Further, the evolution is shown to be a limit of that obtained for a model with linear isotropic hardening as the hardening becomes vanishingly small. The duality between plastic strains and admissible stresses is also revisited for Lipschitz boundaries, and its role in deriving a classical evolution is circumscribed. © 2012 Wiley Periodicals, Inc.

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Existence results for energetic models for rate-independent systems

Cited by 173 publications

References 26 publications

Global Existence for Rate-Independent Gradient Plasticity at Finite Strain

Global Existence for Rate-Independent Gradient Plasticity at Finite Strain

A note on the derivation of rigid-plastic models

Small‐strain heterogeneous elastoplasticity revisited

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