A second-gradient elasticity model and isogeometric analysis for the pantographic ortho-block

Stilz, Maximilian; Eugster, Simon R.; Harsch, Jonas; Gutmann, Florian; Ganzenmüller, Georg; Hiermaier, Stefan

doi:10.1016/j.ijsolstr.2023.112358

Cited by 8 publications

(3 citation statements)

References 31 publications

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“…If perfect pivot joints are introduced, deformation modes that do not change the internal elastic energy, so-called floppy or zero energy modes, appear [23][24][25]. Pantographic ortho-blocks show a strong semi-auxetic behavior [12,13]. Unusual deformed shapes were also found for simulations of cylindrical pantographic shells where pantographic sheets described as second-gradient continua have been initially bent to the shape of a cylinder [26,27].…”

Section: Introductionmentioning

confidence: 90%

“…By adding additional parallel pantographic sheets, which are all interconnected by pivots, pantographic blocks are formed, and a periodicity is added to the third dimension [9][10][11]. For pantographic ortho-blocks, the additional parallel sheets are interconnected by orthogonal pantographics sheets instead of pivots [12,13]. Besides a high compliance compared to their base materials, they typically need to be described with higher-order continuum theories [14][15][16][17][18][19] when viewed as continua to properly predict their deformed shapes [5,[20][21][22].…”

Section: Introductionmentioning

confidence: 99%

“…As an example, for a granular beam, a one-dimensional continuum model including chirality effects has successfully been formulated by Angelo et al [34]. Numerical approaches for second-gradient continuum models needed extensions of common finite element modeling by mixed FEM [35,36], hermite polynomial interpolation [7], or with isogeometric analysis [13,[37][38][39].…”

Section: Introductionmentioning

confidence: 99%

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Chirality effects in panto-cylindrical structures

Stilz,

Breuling,

Eugster

et al. 2024

Mathematics and Mechanics of Solids

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In this paper, we apply a numerical integration strategy recently developed for determining the deformation shapes of structures constituted by Cosserat rods, to predict the behavior of panto-cylinders. Panto-cylinders have, as microstructure, a set of two families of helicoidal beams interconnected by perfect or elastic joints. The pivot’s free rotation axis is, in the reference configuration, orthogonal to the cylindrical surfaces spanned by the beams. We perform a series of numerical simulations looking for the mechanical parameters which exalt the chirality effects in the structure. For the performed compression, extensions, shear, and torsion tests, we find chiral deformation patterns with a dependence on the type of joint and its length.

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Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Chirality effects in panto-cylindrical structures

Stilz,

Breuling,

Eugster

et al. 2024

Mathematics and Mechanics of Solids

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A review of inverse problems for generalized elastic media: formulations, experiments, synthesis

Fedele,

Placidi,

Fabbrocino

2024

Continuum Mech. Thermodyn.

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Starting from the seminal works of Toupin, Mindlin and Germain, a wide class of generalized elastic models have been proposed via the principle of virtual work, by postulating expressions of the elastic energy enriched by additional kinematic descriptors or by higher gradients of the placement. More recently, such models have been adopted to describe phenomena which are not consistent with the Cauchy-Born continuum, namely the size dependence of apparent elastic moduli observed for micro and nano-objects, wave dispersion, optical modes and band gaps in the dynamics of heterogeneous media. For those structures the mechanical response is affected by surface effects which are predominant with respect to the bulk, and the scale of the external actions interferes with the characteristic size of the heterogeneities. Generalized continua are very often referred to as media with microstructure although a rigorous deduction is lacking between the specific microstructural features and the constitutive equations. While in the forward modelling predictions of the observations are provided, the actual observations at multiple scales can be used inversely to integrate some lack of information about the model. In this review paper, generalized continua are investigated from the standpoint of inverse problems, focusing onto three topics, tightly connected and located at the border between multiscale modelling and the experimental assessment, namely: (i) parameter identification of generalized elastic models, including asymptotic methods and homogenization strategies; (ii) design of non-conventional tests, possibly integrated with full field measurements and advanced modelling; (iii) the synthesis of meta-materials, namely the identification of the microstructures which fit a target behaviour at the macroscale. The scientific literature on generalized elastic media, with the focus on the higher gradient models, is fathomed in search of questions and methods which are typical of inverse problems theory and issues related to parameter estimation, providing hints and perspectives for future research.

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