Nous étudions lʼhomogénéisation de problèmes du type :
(1) |
We study the homogenization of elasticity problems like (1) when f, g are strictly convex functions satisfying a growth condition of order , g is positively homogeneous of degree p, , and consists of an ε-periodic distribution of parallel fibers of cross sections of size . The problem (1) corresponds to a simplified model of small deformation nonlinear elasticity describing, for instance, the small deformations of an Ogdenʼs material (Ogden, 1972 [8]). When , it may also characterize the viscoplastic creep experienced, at high temperatures, by a metallic composite governed by the Norton–Hoff model (Friaâ, 1979 [7]). In this case, represents the velocity vector field. We show that if , a concentration of strain energy appears in a small region of space surrounding the fibers. This extra contribution is characterized by a local density of the sections of the fibers with respect to some appropriate capacity depending, if , on the angles of rotation of the fibers with respect to their principal axis. This rotating behavior generates, in parallel, the emergence of torsional strain energy within the fibers.
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@article{CRMATH_2013__351_5-6_241_0, author = {Bellieud, Michel}, title = {Probl\`emes capacitaires en viscoplasticit\'e avec effets de torsion}, journal = {Comptes Rendus. Math\'ematique}, pages = {241--245}, publisher = {Elsevier}, volume = {351}, number = {5-6}, year = {2013}, doi = {10.1016/j.crma.2013.03.005}, language = {fr}, url = {http://www.numdam.org/articles/10.1016/j.crma.2013.03.005/} }
TY - JOUR AU - Bellieud, Michel TI - Problèmes capacitaires en viscoplasticité avec effets de torsion JO - Comptes Rendus. Mathématique PY - 2013 SP - 241 EP - 245 VL - 351 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2013.03.005/ DO - 10.1016/j.crma.2013.03.005 LA - fr ID - CRMATH_2013__351_5-6_241_0 ER -
%0 Journal Article %A Bellieud, Michel %T Problèmes capacitaires en viscoplasticité avec effets de torsion %J Comptes Rendus. Mathématique %D 2013 %P 241-245 %V 351 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2013.03.005/ %R 10.1016/j.crma.2013.03.005 %G fr %F CRMATH_2013__351_5-6_241_0
Bellieud, Michel. Problèmes capacitaires en viscoplasticité avec effets de torsion. Comptes Rendus. Mathématique, Tome 351 (2013) no. 5-6, pp. 241-245. doi : 10.1016/j.crma.2013.03.005. http://www.numdam.org/articles/10.1016/j.crma.2013.03.005/
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