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Optimal Control of Large Deformation Elasticity by Fiber Tension
Author(s) -
Günnel Andreas,
Herzog Roland
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410420
Subject(s) - hyperelastic material , tension (geology) , elasticity (physics) , fiber bundle , deformation (meteorology) , fiber , mechanics , materials science , computer science , structural engineering , composite material , physics , engineering , finite element method , ultimate tensile strength
Object of our interest is an elastic body Ω ⊂ ℝ 3 which we can deform by applying a tension along certain given short fibers inside the body. The deformation of the body is desribed by a hyperelastic model with polyconvex energy density and a special energy functional for the tension along the fibers. We seek to apply (possibly large) deformations to the body so that a desired shape is obtained. To this end, we formulate an optimal control problem for the fiber tension field. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)