TY - JOUR
T1 - Limits of elastic models of converging Riemannian manifolds
AU - Kupferman, Raz
AU - Maor, Cy
N1 - Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.
PY - 2016/4/1
Y1 - 2016/4/1
N2 - In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, (Formula presented.). We prove the (Formula presented.) -convergence of elastic energies for configurations of a converging sequence, (Formula presented.) , of body manifolds. This convergence result has several implications: (i) it can be viewed as a general structural stability property of the elastic model. (ii) It applies to certain classes of bodies with defects, and in particular, to the limit of bodies with increasingly dense edge-dislocations. (iii) It applies to approximation of elastic bodies by piecewise-affine manifolds. In the context of continuously-distributed dislocations, it reveals that the torsion field, which has been used traditionally to quantify the density of dislocations, is immaterial in the limiting elastic model.
AB - In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, (Formula presented.). We prove the (Formula presented.) -convergence of elastic energies for configurations of a converging sequence, (Formula presented.) , of body manifolds. This convergence result has several implications: (i) it can be viewed as a general structural stability property of the elastic model. (ii) It applies to certain classes of bodies with defects, and in particular, to the limit of bodies with increasingly dense edge-dislocations. (iii) It applies to approximation of elastic bodies by piecewise-affine manifolds. In the context of continuously-distributed dislocations, it reveals that the torsion field, which has been used traditionally to quantify the density of dislocations, is immaterial in the limiting elastic model.
KW - 53Z05
KW - 74B20
KW - 74Q15
UR - http://www.scopus.com/inward/record.url?scp=84962439084&partnerID=8YFLogxK
U2 - 10.1007/s00526-016-0979-6
DO - 10.1007/s00526-016-0979-6
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AN - SCOPUS:84962439084
SN - 0944-2669
VL - 55
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 2
M1 - 40
ER -