Journal of Convex Analysis 29 (2022), No. 3, 649--668
Copyright Heldermann Verlag 2022
Dual Formulations of the Elasticity Problem for a Homogeneous Elastic Body with Fractures
Riuji Sato
Dept. of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, U.S.A.
risato@wpi.edu
Bogdan Vernescu
Dept. of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, U.S.A.
vernescu@wpi.edu
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.
Keywords: Duality, fractures, elasticity, minimization.
MSC: 74B05, 74G35, 74R99, 35Q74, 47N50.
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