A refined assumed strain finite element model for statics and dynamics of laminated plates

Cazzani, Antonio; Serra, Mauro; Stochino, Flavio; Turco, Emilio

doi:10.1007/s00161-018-0707-x

Cited by 26 publications

(18 citation statements)

References 67 publications

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“…It should now be clear that such a structure, which can be considered as the corresponding homogenized metamaterial (even when one is very far from having a dense knitting), really exhibits high-performance mechanical properties. In the different fields of applications, it could be useful for considering the coupling with other kind of material (e.g., granular materials [39][40][41][42][43][44][45], laminated plates [46][47][48][49][50], and micropolar materials [51][52][53]).…”

Section: Discussionmentioning

confidence: 99%

Are higher-gradient models also capable of predicting mechanical behavior in the case of wide-knit pantographic structures?

Spagnuolo

Yildizdag

Andreaus

et al. 2020

Mathematics and Mechanics of Solids

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The central theme of this study is to investigate a remarkable capability of a second-gradient continuum model developed for pantographic structures. The model is applied to a particular type of this metamaterial, namely the wide-knit pantograph. As this type of structure has low fiber density, the applicability of such a continuum model may be questionable. To address this uncertainty, numerical simulations are conducted to analyze the behavior of a wide-knit pantographic structure, and the predicted results are compared with those measured experimentally under bias extension testing. The results presented in this study show that the numerical predictions and experimental measurements are in good agreement; therefore, in some useful circumstances, this model is applicable for the analysis of wide-knit pantographic structures.

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Section: Discussionmentioning

confidence: 99%

Are higher-gradient models also capable of predicting mechanical behavior in the case of wide-knit pantographic structures?

Spagnuolo

Yildizdag

Andreaus

et al. 2020

Mathematics and Mechanics of Solids

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“…However, we are well-aware that, to have an efficient numerical implementation for complex systems such as those analyzed, ad hoc codes must be implemented optimized for each particular case investigated. As examples of numerical formulations, reference may be made to the works in [66][67][68][69] related to a Hencky discrete approach, that in [70] for Ritz's method, those in [71][72][73][74][75][76] for shell or plate structures, [77][78][79][80] for rods, and those in [81][82][83][84][85] regarding applications to composites and lattices.…”

Section: Numerical Examples Of Equilibrium Shapesmentioning

confidence: 99%

Equilibrium of Two-Dimensional Cycloidal Pantographic Metamaterials in Three-Dimensional Deformations

Scerrato

Giorgio

2019

Symmetry

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A particular pantographic sheet, modeled as a two-dimensional elastic continuum consisting of an orthogonal lattice of continuously distributed fibers with a cycloidal texture, is introduced and investigated. These fibers conceived as embedded beams on the surface are allowed to be deformed in a three-dimensional space and are endowed with resistance to stretching, shearing, bending, and twisting. A finite element analysis directly derived from a variational formulation was performed for some explanatory tests to illustrate the behavior of the newly introduced material. Specifically, we considered tests on: (1) bias extension; (2) compressive; (3) shear; and (4) torsion. The numerical results are discussed to some extent. Finally, attention is drawn to a comparison with other kinds of orthogonal lattices, namely straight, parabolic, and oscillatory, to show the differences in the behavior of the samples due to the diverse arrangements of the fibers.

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“…To this end we compare the predictions of the present model with numerical simulations based on a refined three-dimensional continuum model, obtained with codes and numerical procedures which are further optimized relative to those used in [Giorgio 2016;De Angelo et al 2019a;Cazzani et al 2018a;2018b].…”

Section: Introductionmentioning

confidence: 99%

A two-dimensional continuum model of pantographic sheets moving in a 3D space and accounting for the offset and relative rotations of the fibers

Giorgio

Rizzi

Andreaus

et al. 2019

Math. Mech. Compl. Sys.

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Recently growing attention has been paid to the particular class of metamaterials which has been called pantographic. Pantographic metamaterials have the following peculiar features: (i) their continuum model, at the macroscale, has to include a term of the deformation energy depending on the second gradient of placement, (ii) they can show an elastic behavior in large deformation regimes, and (iii) they are resilient and tough during rupture phenomena (dell'Isola et al. 2015). In order to predict pantographic metamaterials' mechanical behavior, it is possible to introduce a three-dimensional continuum micromodel, in which their internal geometrical microstructure is described in detail. However, the computational costs of this choice are presently prohibitive. In this paper, we introduce a reduced order model for pantographic sheets-which are an example of an elastic surface-whose kinematics include, for each of the two constituting families of fibers fully independent three-dimensional (i) placement and (ii) rotation fields. In this way it is possible to include, also in the reduced order model, (i) the initial and the actual offset between the fibers and (ii) the deformation energy of the interconnecting pivots. By postulating a simplified expression for the deformation energy we prove that also a reduced order model can describe some experimental observed buckling and postbuckling phenomena. The promising results which we present here motivate the quest of more general expressions for deformation energy capable of capturing the fully nonlinear behavior exhibited by pantographic sheets.

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A refined assumed strain finite element model for statics and dynamics of laminated plates

Cited by 26 publications

References 67 publications

Are higher-gradient models also capable of predicting mechanical behavior in the case of wide-knit pantographic structures?

Are higher-gradient models also capable of predicting mechanical behavior in the case of wide-knit pantographic structures?

Equilibrium of Two-Dimensional Cycloidal Pantographic Metamaterials in Three-Dimensional Deformations

A two-dimensional continuum model of pantographic sheets moving in a 3D space and accounting for the offset and relative rotations of the fibers

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