The Line-Tension Approximation as the Dilute Limit of Linear-Elastic Dislocations
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| 024 | 7 | 0 | |a 10.1007/s00205-015-0869-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0869-7 | ||
| 245 | 0 | 4 | |a The Line-Tension Approximation as the Dilute Limit of Linear-Elastic Dislocations |h [Elektronische Daten] |c [Sergio Conti, Adriana Garroni, Michael Ortiz] |
| 520 | 3 | |a We prove that the classical line-tension approximation for dislocations in crystals, that is, the approximation that neglects interactions at a distance between dislocation segments and accords dislocations energy in proportion to their length, follows as the Γ-limit of regularized linear-elasticity as the lattice parameter becomes increasingly small or, equivalently, as the dislocation measure becomes increasingly dilute. We consider two regularizations of the theory of linear-elastic dislocations: a core-cutoff and a mollification of the dislocation measure. We show that both regularizations give the same energy in the limit, namely, an energy defined on matrix-valued divergence-free measures concentrated on lines. The corresponding self-energy per unit length $${\psi(b, t)}$$ ψ ( b , t ) , which depends on the local Burgers vector and orientation of the dislocation, does not, however, necessarily coincide with the self-energy per unit length $${\psi_0(b, t)}$$ ψ 0 ( b , t ) obtained from the classical theory of the prelogarithmic factor of linear-elastic straight dislocations. Indeed, microstructure can occur at small scales resulting in a further relaxation of the classical energy down to its $${\mathcal H^1}$$ H 1 -elliptic envelope. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 700 | 1 | |a Conti |D Sergio |u Institut für Angewandte Mathematik, Universität Bonn, 53115, Bonn, Germany |4 aut | |
| 700 | 1 | |a Garroni |D Adriana |u Dipartimento di Matematica, Università di Roma, Sapienza, 00185, Rome, Italy |4 aut | |
| 700 | 1 | |a Ortiz |D Michael |u Division of Engineering and Applied Science, California Institute of Technology, 91125, Pasadena, CA, USA |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 699-755 |x 0003-9527 |q 218:2<699 |1 2015 |2 218 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0869-7 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0869-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Conti |D Sergio |u Institut für Angewandte Mathematik, Universität Bonn, 53115, Bonn, Germany |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Garroni |D Adriana |u Dipartimento di Matematica, Università di Roma, Sapienza, 00185, Rome, Italy |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Ortiz |D Michael |u Division of Engineering and Applied Science, California Institute of Technology, 91125, Pasadena, CA, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/2(2015-11-01), 699-755 |x 0003-9527 |q 218:2<699 |1 2015 |2 218 |o 205 | ||