Equivalence between Rank-One Convexity and Polyconvexity for Some Classes of Elastic Materials |
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| Authors: | Márcio José Horta Dantas |
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| Institution: | (1) Faculdade de Matemática, Universidade Federal de Uberlândia, 38400-902 Uberlândia, MG, Brazil |
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| 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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| Keywords: | convexity polyconvexity rank-one convexity finite elasticity |
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