TY - JOUR

T1 - Asymptotic Expansion of the Elastic Far-Field of a Crystalline Defect

AU - Braun, Julian

AU - Hudson, Thomas

AU - Ortner, Christoph

N1 - Funding Information:
The authors Julian Braun and Christoph Ortner were supported by EPSRC Grant EP/R043612/1.
Publisher Copyright:
© 2022, The Author(s).

PY - 2022/9

Y1 - 2022/9

N2 - Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work rigorously derives a novel far-field expansion of these fields. The expansion is computable and is expressed as a sum of continuum correctors and discrete multipole terms which decay with increasing algebraic rate as the order of the expansion increases. Truncating the expansion leaves a remainder describing the defect core structure, which is localised in the sense that it decays with an algebraic rate corresponding to the order at which the truncation occurred.

AB - Lattice defects in crystalline materials create long-range elastic fields which can be modelled on the atomistic scale using an infinite system of discrete nonlinear force balance equations. Starting with these equations, this work rigorously derives a novel far-field expansion of these fields. The expansion is computable and is expressed as a sum of continuum correctors and discrete multipole terms which decay with increasing algebraic rate as the order of the expansion increases. Truncating the expansion leaves a remainder describing the defect core structure, which is localised in the sense that it decays with an algebraic rate corresponding to the order at which the truncation occurred.

UR - http://www.scopus.com/inward/record.url?scp=85134565193&partnerID=8YFLogxK

U2 - 10.1007/s00205-022-01810-3

DO - 10.1007/s00205-022-01810-3

M3 - Article

AN - SCOPUS:85134565193

VL - 245

SP - 1437

EP - 1490

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 3

ER -