Analysis of the Incompatibility Operator and Application in Intrinsic Elasticity with Dislocations

DOI10.1137/15M1020113zbMath1398.35044OpenAlexW2266218136MaRDI QIDQ5743839

Samuel Amstutz, Nicolas Van Goethem

Publication date: 8 February 2016

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/15m1020113

zbMATH Keywords

Sobolev spacesliftingdislocationsincompatibilitytransmission conditionsintrinsic elasticity

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Variational methods for elliptic systems (35J50) Theories of fracture and damage (74A45) Surfaces in Euclidean and related spaces (53A05) Boundary value problems for second-order elliptic systems (35J57)

Related Items (15)

L^p-trace-free generalized Korn inequalities for incompatible tensor fields in three space dimensions ⋮ Incompatibility-governed singularities in linear elasticity with dislocations ⋮ A finite element elasticity complex in three dimensions ⋮ Analysis of curvature approximations via covariant curl and incompatibility for Regge metrics ⋮ DIRECT EXPRESSION OF INCOMPATIBILITY IN CURVILINEAR SYSTEMS ⋮ Existence and asymptotic results for an intrinsic model of small-strain incompatible elasticity ⋮ A fourth-order gauge-invariant gradient plasticity model for polycrystals based on Kröner’s incompatibility tensor ⋮ The Incompatibility Operator: from Riemann’s Intrinsic View of Geometry to a New Model of Elasto-Plasticity ⋮ Topological defects and metric anomalies as sources of incompatibility for piecewise smooth strain fields ⋮ Incompatibility-governed elasto-plasticity for continua with dislocations ⋮ The Frank tensor as a boundary condition in intrinsic linearized elasticity ⋮ Poincaré path integrals for elasticity ⋮ Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy ⋮ Complexes from complexes ⋮ Matrix representation of a cross product and related curl-based differential operators in all space dimensions

Cites Work

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• Topological asymptotic analysis of the Kirchhoff plate bending problem
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• The lifting of polynomial traces revisited
• Estimating ∇u by divu and curlu
• Intrinsic formulation of the displacement-traction problem in linearized elasticity
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
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