Abstract
Let W(F) = φ(λ 1 s + λ 2 s + λ 3 s) + ψ(λ 1 r λ 2 r + λ 1 r λ 3 r + λ 2 r λ 3 r) + f(λ 1 λ 2 λ 3) be a stored energy function. We prove that, for this function, rank-one convexity is equivalent to polyconvexity.under suitable assumptions on φ, ψ and f.
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Dantas, M.J.H. Equivalence between Rank-One Convexity and Polyconvexity for Some Classes of Elastic Materials. J Elasticity 82, 1–7 (2006). https://doi.org/10.1007/s10659-005-9021-5
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DOI: https://doi.org/10.1007/s10659-005-9021-5