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Three-dimensional instabilities of pantographic sheets with parabolic lattices: numerical investigations

Abstract : In this paper, we determine numerically a large class of equilibrium configurations of an elastic two-dimensional continuous pantographic sheet in three-dimensional deformation consisting of two families of fibers which are parabolic prior to deformation. The fibers are assumed: i) to be continuously distributed over the sample, ii) to be endowed of bending and torsional stiffnesses and iii) tied together at their points of intersection to avoid relative slipping by means of internal (elastic) pivots. This last condition characterizes the system as a pantographic lattice [1, 2, 34, 35]. The model that we employ here, developed by Steigmann and dell'Isola [108] and first investigated in [55], is applicable to fiber lattices in which three dimensional bending, twisting and stretching are significant as well as a resistance to shear distortion, i.e. to the angle change between the fibers. Some relevant numerical examples are exhibited in order to highlight the main features of the model adopted: in particular buckling and post-buckling behavior of pantographic parabolic lattices is investigated. The fabric of the metamaterial presented in this paper has been conceived to resist more effectively in the extensional bias tests by storing more elastic bending energy and less energy in the deformation of elastic pivots: a comparison with a fabric constituted by beams which are straight in the reference configuration shows that the proposed concept is promising.
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Submitted on : Friday, April 22, 2016 - 9:08:40 AM
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Daria Scerrato, Ivan Giorgio, Nicola Rizzi. Three-dimensional instabilities of pantographic sheets with parabolic lattices: numerical investigations. Zeitschrift für Angewandte Mathematik und Physik, Springer Verlag, 2016, 67, ⟨10.1007/s00033-016-0650-2⟩. ⟨hal-01305927⟩

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