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

Abstract

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.

Green’s functions and integral representation of generalized continua: the case of orthogonal pantographic lattices

“…This understanding can be applied to the description of real pantographic sheets, that are constituted by a finite number of beams. In fact, it has to be remarked, in this context, that the range of applicability of homogenized models seems to be larger than expected [31]. In this paper, also by exploiting the mentioned mechanical interpretation of macro-constitutive parameters, it is shown how the method of representation by means of Green's functions is applicable to find the linearized equilibrium configurations of pantographic continua.…”

Characterization of the symmetry class of an elasticity tensor using polynomial covariants

“…It could be applied to strain gradient elasticity (for which a justification can be found in [63]), or to related continuum models such as micromorphic continuum [64]. The synthesis problem of such continua, obtained using lattice structure [65][66][67], would also benefit of such explicit symmetry classes characterization. For these, even large deformation [68] or singular constitutive laws [69] could be considered.…”

Electrical analogs of curved beams and application to piezoelectric network damping

“…It is believed that such a result represents a further step towards the design of more complex piezo-electromechanical structures, eventually aiming to the conception of multi-physics metamaterials [36][37][38][39][40]. To this aim, future works may consider assembling different simple piezo-electro-mechanical microsubstructures in order to synthesize [41][42][43][44][45] novel metamaterials showing an optimized dynamic behavior.…”