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 .
Classification : 74A35, 74E15, 74G65, 74N15, 53AXX, 53B05
Mots clés : rotations, polar-materials, microstructure, dislocation density, rigidity, differential geometry, structured continua
@article{COCV_2008__14_1_148_0, author = {M\"unch, Ingo and Neff, Patrizio}, title = {Curl bounds grad on {SO(3)}}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {148--159}, publisher = {EDP-Sciences}, volume = {14}, number = {1}, year = {2008}, doi = {10.1051/cocv:2007050}, zbl = {1139.74008}, mrnumber = {2375754}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2007050/} }
TY - JOUR AU - Münch, Ingo AU - Neff, Patrizio TI - Curl bounds grad on SO(3) JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 DA - 2008/// SP - 148 EP - 159 VL - 14 IS - 1 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007050/ UR - https://zbmath.org/?q=an%3A1139.74008 UR - https://www.ams.org/mathscinet-getitem?mr=2375754 UR - https://doi.org/10.1051/cocv:2007050 DO - 10.1051/cocv:2007050 LA - en ID - COCV_2008__14_1_148_0 ER -
Münch, Ingo; Neff, Patrizio. Curl bounds grad on SO(3). ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 1, pp. 148-159. doi : 10.1051/cocv:2007050. http://www.numdam.org/articles/10.1051/cocv:2007050/
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