For α ∈ (-1, n-2], the unique minimizer of I_α is the normalized characteristic function of a spheroid.
An Energy Estimate for Dislocation Configurations and the Emergence of Cosserat-Type Structures in Metal Plasticity
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We investigate low energy structures of a lattice with dislocations in the context of nonlinear elasticity. We show that these low energy configurations exhibit in the limit a Cosserat-like behavior. Moreover, we give bounds from above and below to the energy of such configurations.
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math.AP 2representative citing papers
A physically motivated grain-boundary construction in a general 2D Bravais lattice yields energy that matches the Read-Shockley logarithmic scaling for small misorientation.
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The equilibrium measure for an anisotropic nonlocal energy
For α ∈ (-1, n-2], the unique minimizer of I_α is the normalized characteristic function of a spheroid.
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Read--Shockley formula for a general Bravais lattice in two dimensions
A physically motivated grain-boundary construction in a general 2D Bravais lattice yields energy that matches the Read-Shockley logarithmic scaling for small misorientation.