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Journal Articles Journal of Engineering Mathematics Year : 2016

Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies

Abstract

We consider a bi-dimensional sheet consisting of two orthogonal families of inextensible fibres. Using the representation due to Rivlin and Pipkin for admissible placements, i.e. placements preserving the lengths of the inextensible fibres, we numerically simulate a standard bias extension test on the sheet, solving a non-linear constrained optimization problem. Several first and second gradient deformation energy models are considered, depending on the shear angle between the fibres and on its gradient, and the results obtained are compared. The proposed numerical simulations will be helpful in designing a systematic experimental campaign aimed at characterizing the internal energy for physical realizations of the ideal pantographic structure presented in this paper.
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Dates and versions

hal-01354960 , version 1 (21-08-2016)

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Francesco Dell'Isola, Massimo Cuomo, Leopoldo Greco, Alessandro Della Corte. Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies. Journal of Engineering Mathematics, 2016, pp.1-31. ⟨10.1007/s10665-016-9865-7⟩. ⟨hal-01354960⟩

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