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.
Nous étudions lʼhomogénéisation de problèmes du type :
(1) |
Accepted:
Published online:
@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://archive.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://archive.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://archive.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, Volume 351 (2013) no. 5-6, pp. 241-245. doi : 10.1016/j.crma.2013.03.005. http://archive.numdam.org/articles/10.1016/j.crma.2013.03.005/
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