a b s t r a c tRubber components and soft biological tissues are often subjected to large bending deformations while ''in service". The circumferential line elements on the inner face of a bent block can contract up to a certain critical stretch ratio k cr (say) before bifurcation occurs and axial creases appear. For several models used to describe rubber, it is found that k cr ¼ 0:56, allowing for a 44% contraction. For models used to describe arteries it is found, somewhat surprisingly, that the strain-stiffening effect promotes instability. For example, the models used for the artery of a seventy-year old human predict that k cr ¼ 0:73, allowing only for a 27% contraction. Tensile experiments conducted on pig skin indicate that bending instabilities should occur even earlier there.

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This work revisits an interactive buckling model for sandwich beams proposed relatively recently by Hunt and Wadee (Proc R Soc Lond A 454:1197-1216, 1998). Our asymptotic investigations reveal an interesting resonant behaviour which is shown to lie at the origin of the corresponding localised deformations reported in the literature. The very good agreement between the asymptotic results and various direct numerical simulations reinforces the validity of our theoretical arguments and provides an incentive for further research. (2000). 34E13 · 65L15 · 74G60 · 74K99. Mathematics Subject Classification

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