Curl bounds Grad on SO(3)
Patrizio Neff, Ingo Münch (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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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, (2002) 1461–1506; John, (1961) 391–413; Reshetnyak, (1967) 631–653)] as well as an associated linearized theorem saying...