Parametric Experimentation on Pantographic Unit Cells Reveals Local Extremum Configuration

Abstract

Pantographic metamaterials are known for their ability to have large deformation while remaining in the elastic regime. We have performed a set of experiments on 3D printed pantographic unit cells to parametrically investigate their response when undergoing tensile, compression, and shear loading with the aim of i) studying the role of each parameter in the resultant mechanical behavior of the sample, and ii) providing a benchmark for the mathematical models developed to describe pantographic structures. Results show the existence of local extrema in the space of the geometrical parameters, suggesting the use of optimization techniques to find optimal geometrical parameters resulting in desired functionalities. We have also performed tensile relaxation tests on the samples, with the results indicating the complexity of the dynamic behavior and the existence of multiple relaxation characteristic times. Such results can be used to for calibrating mathematical models describing pantographic structures under dynamic loadings.

Three-point bending test of pantographic blocks: numerical and experimental investigation

“…De Angelo et al [28] investigated the behavior of metallic pantographic sheets. In a number of papers, researchers have worked on the identification of constitutive parameters for second gradient materials (see Giorgio [29], Placidi et al [30], Yang et al [31], De Angelo et al [32], Nejadsadeghi et al [33], Solyaev et al [34], and Turco [35]). In a few studies, the 3D deformation of pantographic structures has been investigated in the context of second gradient modeling, for example in the studies presented by Steigmann and dell’Isola [36], Giorgio et al [37, 38], and Scerrato et al [39].…”

A discrete formulation of Kirchhoff rods in large-motion dynamics

“…together with the initial conditions for the variable r and its derivativeṙ. Equations (45) are numerically solved by the technical computing system Wolfram Mathematica with a differential-algebraic system of equations (DAEs) solver implemented with the NDSolve routine.…”

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

“…This arrangement of the fibers has been specially conceived with the purpose of employing the superior capability of curved fibers to bear loads (fibers tend to behave like arches) and to have reinforcement in long boundaries (see Figure 1). Therefore, the sample has a notably anisotropic behavior with an extremely soft core (due to the pantographic effect [16,17,[48][49][50][51]) and a stiffer part at the borders.…”