Geodesic
Dual Formulations of the Elasticity Problem for a Homogeneous Elastic Body with Fractures
Journal of convex analysis, Tome 29 (2022) no. 3, pp. 649-668
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We extend previous results on the dual formulations for an elastic body without fractures to a model of a homogeneous elastic body with fractures. In particular, in the framework of Legendre-Fenchel duality, we were able to provide three equivalent formulations for the problem where the displacement, the stress, and the strain are the unknowns respectively. We also provide a characterization of the image of the convex cone of admissible displacements under the linearized strain tensor.
Classification : 74B05, 74G35, 74R99, 35Q74, 47N50
Mots-clés : Duality, fractures, elasticity, minimization 
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     author = {R. Sato and B. Vernescu},
     title = {Dual {Formulations} of the {Elasticity} {Problem} for a {Homogeneous} {Elastic} {Body} with {Fractures}},
     journal = {Journal of convex analysis},
     pages = {649--668},
     year = {2022},
     volume = {29},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2022_29_3_JCA_2022_29_3_a0/}
}
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R. Sato; B. Vernescu. Dual Formulations of the Elasticity Problem for a Homogeneous Elastic Body with Fractures. Journal of convex analysis, Tome 29 (2022) no. 3, pp. 649-668. http://geodesic.mathdoc.fr/item/JCA_2022_29_3_JCA_2022_29_3_a0/