Derivation of Linearized Polycrystals from a Two-Dimensional System of Edge Dislocations
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Publication:5236901
DOI10.1137/18M118726XzbMath1425.74071arXiv1805.04484WikidataQ127020153 ScholiaQ127020153MaRDI QIDQ5236901
Marcello Ponsiglione, Mariapia Palombaro, Silvio Fanzon
Publication date: 16 October 2019
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1805.04484
Methods involving semicontinuity and convergence; relaxation (49J45) Analysis of microstructure in solids (74N15) Crystals in solids (74N05) Equations linearized about a deformed state (small deformations superposed on large) (74B15)
Related Items (9)
Long range order in atomistic models for solids ⋮ Line-tension limits for line singularities and application to the mixed-growth case ⋮ A generalized conditional gradient method for dynamic inverse problems with optimal transport regularization ⋮ Plasticity as the \(\Gamma\)-limit of a two-dimensional dislocation energy: the critical regime without the assumption of well-separateness ⋮ Uniform distribution of dislocations in Peierls-Nabarro models for semi-coherent interfaces ⋮ Coarse-graining of a discrete model for edge dislocations in the regular triangular lattice ⋮ Emergence of rigid polycrystals from atomistic systems with Heitmann-Radin sticky disk energy ⋮ On the Motion of Curved Dislocations in Three Dimensions: Simplified Linearized Elasticity ⋮ Derivation of a Line-Tension Model for Dislocations from a Nonlinear Three-Dimensional Energy: The Case of Quadratic Growth
Cites Work
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- \(\Gamma\)-convergence analysis of systems of edge dislocations: the self energy regime
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- Plasticity as the \(\Gamma\)-limit of a two-dimensional dislocation energy: the critical regime without the assumption of well-separateness
- Geometric rigidity for incompatible fields and an application to strain-gradient plasticity
- Line-Tension Model for Plasticity as the $\Gamma$-Limit of a Nonlinear Dislocation Energy
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- Dislocation Models of Crystal Grain Boundaries
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