2017
DOI: 10.1142/s0218202517500531
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Strain gradient visco-plasticity with dislocation densities contributing to the energy

Abstract: We consider the energetic description of a visco-plastic evolution and derive an existence result. The energies are convex, but not necessarily quadratic. Our model is a strain gradient model in which the curl of the plastic strain contributes to the energy. Our existence results are based on a time-discretization, the limit procedure relies on Helmholtz decompositions and compensated compactness.

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Cited by 15 publications
(21 citation statements)
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“…Let us also mention that the div-curl-lemma is particularly useful to treat homogenization of problems arising in plasticity, see, e.g., a recent preprint on this topic [20], for which the preprint [21] provides the important key div-curl-lemma. Unfortunately, in [21,20] a H 1 (Ω)-detour is used as the core argument for the proofs. The same detour is utilized in the recent contribution [11] where div-curl-type lemmas are presented which also allow for inhomogeneous boundary conditions.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…Let us also mention that the div-curl-lemma is particularly useful to treat homogenization of problems arising in plasticity, see, e.g., a recent preprint on this topic [20], for which the preprint [21] provides the important key div-curl-lemma. Unfortunately, in [21,20] a H 1 (Ω)-detour is used as the core argument for the proofs. The same detour is utilized in the recent contribution [11] where div-curl-type lemmas are presented which also allow for inhomogeneous boundary conditions.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…The same detour is utilized in the recent contribution [11] where div-curl-type lemmas are presented which also allow for inhomogeneous boundary conditions. This unnecessarily high regularity assumption of H 1 (Ω)-fields excludes results like [11,21,20] to be applied to important applications which are stated, e.g., in Lipschitz domains.…”
Section: Introduction and Main Resultsmentioning
confidence: 99%
“…At the macroscopic level, the reader is referred to Mielke & Müller [29] and [36] for existence results for incremental problems under boundedness assumptions on the curl of the plastic strain. In the viscoplastic setting, Röger & Schweizer [34] prove that such bounds on the curl allow to find a suitably weak evolution notion.…”
Section: David Melching and Ulisse Stefanellimentioning
confidence: 99%
“…This notion of solution features stability and energy balance on the time-discrete level as well as semistability relation with respect to elastic deformations and an energy inequality in the time-continuous limit. A similar notion has been considered in [12] in the quasistatic setting and in [54] for viscoplasticity and is weaker than the concept of energetic solutions [47]. Still, it implies the validity of the quasistatic equilibrium system as well as the dissipative character of the evolution.…”
Section: Introductionmentioning
confidence: 96%