dorsal/arxiv
View SchemaA distributional approach to the geometry of dislocations at the mesoscale
| Authors | Nicolas Van Goethem, F. Dupret |
|---|---|
| Categories | |
| ArXiv ID | physics/0703227 |
| URL | https://arxiv.org/abs/physics/0703227 |
Abstract
We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new understanding of the continuum theory of defects as developed by Kroener (1980) and other authors. Fundamental 2D identities relating the incompatibility tensor to the Frank and Burgers vectors are proved under global strain assumptions relying on the geometric measure theory, thereby giving rise to rigorous homogenisation from mesoscopic to macroscopic scale.
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"abstract": "We develop a theory to represent dislocated single crystals at the mesoscopic\nscale by considering concentrated effects, governed by the distribution theory\ncombined with multiple-valued kinematic fields. Our approach gives a new\nunderstanding of the continuum theory of defects as developed by Kroener (1980)\nand other authors. Fundamental 2D identities relating the incompatibility\ntensor to the Frank and Burgers vectors are proved under global strain\nassumptions relying on the geometric measure theory, thereby giving rise to\nrigorous homogenisation from mesoscopic to macroscopic scale.",
"arxiv_id": "physics/0703227",
"authors": [
"Nicolas Van Goethem",
"F. Dupret"
],
"categories": [
"physics.class-ph",
"cond-mat.mtrl-sci",
"math.DG"
],
"title": "A distributional approach to the geometry of dislocations at the mesoscale",
"url": "https://arxiv.org/abs/physics/0703227"
},
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