# Spatial heterogeneity in 3D-2D dimensional reduction

Jean-François Babadjian; Gilles A. Francfort

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 11, Issue: 1, page 139-160
- ISSN: 1292-8119

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topBabadjian, Jean-François, and Francfort, Gilles A.. "Spatial heterogeneity in 3D-2D dimensional reduction." ESAIM: Control, Optimisation and Calculus of Variations 11.1 (2010): 139-160. <http://eudml.org/doc/90754>.

@article{Babadjian2010,

abstract = {
A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret (1995). Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté et al. (2002), the case where external loads induce a density of bending moment that produces a Cosserat vector field is also investigated. Throughout, the 3D-2D dimensional reduction is viewed as a problem of Γ-convergence of the elastic energy, as the thickness tends to zero.
},

author = {Babadjian, Jean-François, Francfort, Gilles A.},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Dimension reduction; Γ-convergence; equi-integrability; quasiconvexity; relaxation.; dimension reduction; -convergence; relaxation},

language = {eng},

month = {3},

number = {1},

pages = {139-160},

publisher = {EDP Sciences},

title = {Spatial heterogeneity in 3D-2D dimensional reduction},

url = {http://eudml.org/doc/90754},

volume = {11},

year = {2010},

}

TY - JOUR

AU - Babadjian, Jean-François

AU - Francfort, Gilles A.

TI - Spatial heterogeneity in 3D-2D dimensional reduction

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 11

IS - 1

SP - 139

EP - 160

AB -
A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret (1995). Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté et al. (2002), the case where external loads induce a density of bending moment that produces a Cosserat vector field is also investigated. Throughout, the 3D-2D dimensional reduction is viewed as a problem of Γ-convergence of the elastic energy, as the thickness tends to zero.

LA - eng

KW - Dimension reduction; Γ-convergence; equi-integrability; quasiconvexity; relaxation.; dimension reduction; -convergence; relaxation

UR - http://eudml.org/doc/90754

ER -

## References

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