Volume 14, Number 1, January-March 2008
|Page(s)||148 - 159|
|Published online||21 September 2007|
Curl bounds Grad on SO(3)
Department of Mathematics, Technische Universität Darmstadt, Schlossgartenstrasse 7, 64289 Darmstadt, Germany; firstname.lastname@example.org
2 Institut für Baustatik, Universität Karlsruhe (TH), Kaiserstrasse 12, 76131 Karlsruhe, Germany; email@example.com
Revised: 5 September 2006
Let be the plastic deformation from the multiplicative decomposition in elasto-plasticity. We show that the geometric dislocation density tensor of Gurtin in the form applied to rotations controls the gradient in the sense that pointwise . This result complements rigidity results [Friesecke, James and Müller, Comme Pure Appl. Math. 55 (2002) 1461–1506; John, Comme Pure Appl. Math. 14 (1961) 391–413; Reshetnyak, Siberian Math. J. 8 (1967) 631–653)] as well as an associated linearized theorem saying that .
Mathematics Subject Classification: 74A35 / 74E15 / 74G65 / 74N15 / 53AXX / 53B05
Key words: Rotations / polar-materials / microstructure / dislocation density / rigidity / differential geometry / structured continua
© EDP Sciences, SMAI, 2007
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