Concentrated loading of a fibre-reinforced composite plate: Experimental and computational modeling of boundary fixity

International audienceWe 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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“…and, using Eqs. (1) and 3, we obtain by integration the relative displacement between two points P, Q of the specimen:…”

Section: Rivlin-pipkin Decomposition Theoremmentioning

confidence: 99%

“…Hence, simulations dealing with the formation of woven fabrics (impregnated with polymer or dry) are very useful for pattern designing in the aforementioned context (e.g. [1][2][3][4][5]).…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2016

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“…The observed experimental evidence will motivate the further development of mathematical and numerical models for considered fabric to include damage onset and development. The reader will find interesting, and relevant, experimental investigation involving fiber reinforcements for composites in the papers, [46,47,[73][74][75][76] where also once set and progress of damaged is considered. In future investigations, the methods there used will be adapted to the present contest.…”

Section: Experimental Evidence: Macroscopic Toughness In Extensionmentioning

confidence: 99%

Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence

Dell’Isola

Lekszycki

Pawlikowski

et al. 2015

Z. Angew. Math. Phys.

162

117

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“…A possible way for assembling fibers could be to weave them: In this case, the constraint is obtained by means of friction forces whose effectiveness may depend on the state of stress at the contact interface between different fibers. In this case, a particular attention must be paid to frictional slip (as done, for instance, in [75]) while other peculiar properties of several kinds of composite materials [66,77,78,103] have also been taken into account.…”

Section: Range Of Applicability For Generalized Continuum Modelsmentioning

confidence: 99%

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

Scerrato

Giorgio

Rizzi

2016

Z. Angew. Math. Phys.

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Abstract. In this paper, we determine numerically a large class of equilibrium configurations of an elastic two-dimensional\ud continuous pantographic sheet in three-dimensional deformation consisting of two families of fibers which are parabolic\ud prior to deformation. The fibers are assumed (1) to be continuously distributed over the sample, (2) to be endowed of\ud bending and torsional stiffnesses, and (3) tied together at their points of intersection to avoid relative slipping by means of\ud internal (elastic) pivots. This last condition characterizes the system as a pantographic lattice (Alibert and Della Corte in\ud Zeitschrift f¨ur angewandte Mathematik und Physik 66(5):2855–2870, 2015; Alibert et al. in Math Mech Solids 8(1):51–73,\ud 2003; dell’Isola et al. in Int J Non-Linear Mech 80:200–208, 2016; Int J Solids Struct 81:1–12, 2016). The model that we\ud employ here, developed by Steigmann and dell’Isola (Acta Mech Sin 31(3):373–382, 2015) and first investigated in Giorgio\ud et al. (Comptes rendus Mecanique 2016, doi:10.1016/j.crme.2016.02.009), is applicable to fiber lattices in which threedimensional\ud bending, twisting, and stretching are significant as well as a resistance to shear distortion, i.e., to the angle\ud change between the fibers. Some relevant numerical examples are exhibited in order to highlight the main features of the\ud model adopted: In particular, buckling and post-buckling behaviors of pantographic parabolic lattices are investigated. The\ud fabric of the metamaterial presented in this paper has been conceived to resist more effectively in the extensional bias tests\ud by storing more elastic bending energy and less energy in the deformation of elastic pivots: A comparison with a fabric\ud constituted by beams which are straight in the reference configuration shows that the proposed concept is promising

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Concentrated loading of a fibre-reinforced composite plate: Experimental and computational modeling of boundary fixity

Cited by 24 publications

References 21 publications

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

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

Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence

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

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