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Quasiconvex relaxation of isotropic functions in incompressible planar hyperelasticity
Published online by Cambridge University Press: 11 June 2019
Abstract
In this note, we provide an explicit formula for computing the quasiconvex envelope of any real-valued function W; SL(2) → ℝ with W(RF) = W(FR) = W(F) for all F ∈ SL(2) and all R ∈ SO(2), where SL(2) and SO(2) denote the special linear group and the special orthogonal group, respectively. In order to obtain our result, we combine earlier work by Dacorogna and Koshigoe on the relaxation of certain conformal planar energy functions with a recent result on the equivalence between polyconvexity and rank-one convexity for objective and isotropic energies in planar incompressible nonlinear elasticity.
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- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 5 , October 2020 , pp. 2620 - 2631
- Creative Commons
- This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
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- Copyright © Royal Society of Edinburgh 2019
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