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

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

Derivation of dual horizon state-based peridynamics formulation based on euler-lagrange equation

The numerical solution of peridynamics equations is usually done by using uniform spatial discretisation. Although implementation of uniform discretisation is straightforward, it can increase computational time significantly for certain problems. Instead, non-uniform discretisation can be utilised and different discretisation sizes can be used at different parts of the solution domain. Moreover, the peridynamic length scale parameter, horizon, can also vary throughout the solution domain. Such a scenario requires extra attention since conservation laws must be satisfied. To deal with these issues, dual-horizon peridynamics was introduced so that both non-uniform discretisation and variable horizon sizes can be utilised. In this study, dual-horizon peridynamics formulation is derived by using Euler–Lagrange equation for state-based peridynamics. Moreover, application of boundary conditions and determination of surface correction factors are also explained. Finally, the current formulation is verified by considering two benchmark problems including plate under tension and vibration of a plate

Out-of-plane deformation reduction via inelastic hinges in fibrous metamaterials and simplified damage approach

The mechanical behavior of fibrous metamaterials is mainly determined by the interactions between the fibers composing the architecture. These interactions are usually of two different kinds: those directly depending on the positions of the fibers and those that need mediators, usually consisting of hinges, either inelastic or perfect, inducing restrictions on the kinematics of the fiber joints. In cases of interest, it has been observed that hinges can either have a certain torsional stiffness or behave as perfect joints, simply ensuring that the fibers remain interconnected, but not applying any constraint on the relative rotations between them. Here the effect of torsional stiffness of inelastic hinges is studied in two shear tests for a selected fibrous metamaterial. It is shown that the stiffness of hinges can be tailored to avoid, or at least reduce, out-of-plane deformations. Moreover, it is shown that, after reaching a threshold, permanent deformations are observed. This phenomenon is treated in a simplified way, by introducing damage in the continuum model

A multi-disciplinary approach for mechanical metamaterial synthesis: a hierarchical modular multiscale cellular structure paradigm

Recent advanced manufacturing techniques such as 3D printing have prompted the need for designing new multiscale architectured materials for various industrial applications. These multiscale architectures are designed to obtain the desired macroscale behavior by activating interactions between different length scales and coupling different physical mechanisms. Although promising results have been recently obtained, the design of such systems still represents a challenge in terms of mathematical modeling, experimentation, and manufacturing. In this paper, some research perspectives are discussed aiming to determine the most efficient methodology needed to design novel metamaterials. A multidisciplinary approach based on Digital Image Correlation (DIC) techniques may be very effective. The main feature of the described DIC-based approach consists of the integration of different methodologies to create a synergistic relationship among the different steps from design to fabrication and validation. Experimental techniques and modeling approaches are envisioned to be combined in feedback loops whose objective is to determine the required multiscale architectures of newly designed metamaterials. Moreover, it is necessary to develop appropriate mathematical models to estimate the behavior of such metamaterials. Within this new design approach, the manufacturing process can be effectively guided by a precise theoretical and experimental framework. In order to show the applicability of the proposed approach, some preliminary results are provided for a particular type of mechanical metamaterial, namely, pantographic metamaterials. Lastly, the most relevant challenges are highlighted among those that must be addressed for future applications