Geometric rigidity for incompatible fields and an application to strain-gradient plasticity

Stafan Mueller, Lucia Scardia, Caterina Zeppieri

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)
173 Downloads (Pure)

Abstract

In this paper, we show that a strain-gradient plasticity
model arises as the Γ -limit of a nonlinear semi-discrete dislocation
energy. We restrict our analysis to the case of plane elasticity,
so that edge dislocations can be modelled as point singularities of
the strain field.
A key ingredient in the derivation is the extension of the rigidity
estimate [9, Theorem 3.1] to the case of fields β : U ⊂ R2 → R2×2
with nonzero curl. We prove that the L2-distance of β from a
single rotation matrix is bounded (up to a multiplicative constant)
by the L2-distance of β from the group of rotations in the plane,
modulo an error depending on the total mass of Curlβ. This
reduces to the classical rigidity estimate in the case Curlβ = 0.
Original languageEnglish
Pages (from-to)1365-1396
Number of pages32
JournalIndiana University Mathematics Journal
Volume63
Issue number5
DOIs
Publication statusPublished - 2014

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