Multiscale DIC Applied to Pantographic Structures
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RESEARCH PAPER
Multiscale DIC Applied to Pantographic Structures F. Hild1
· A. Misra2
· F. dell’Isola3
Received: 20 January 2020 / Accepted: 9 July 2020 © Society for Experimental Mechanics 2020
Abstract Background: Since the mechanical behavior of pantographic metamaterials depends upon the properties of their microstructure, accurate descriptions of unit cells are needed. Objective: The present effort is motivated by this requirement to characterize the detailed deformation of unit cells formed of two orthogonal sets of 3 beams. Methods: Their deformations in a bias extension test were measured via digital image correlation performed at different scales. Results: Thanks to the gray level residuals, the microscale results were found in better agreement with the experiment than mesoscale and macroscale analyses. Fine analyses around the hinges showed that relative displacements occurred between the two beam layers. Conclusions: Such experimental analyses supply full-field data to validate models (e.g., as a starting point in homogenization procedures) for describing the mechanical behavior of pantographic metamaterials. Keywords Digital image correlation (DIC) · Finite element · Gray level residuals · Metamaterial · Multiscale analyses
Introduction At least three different characteristic scales can be distinguished when studying pantographic structures [1]. The description at the microscale considers the metamaterial as constituted by a standard Cauchy continuum whose shape is detailed as the union of rectangular and circular cylinders (see Fig. 1(b)). At this scale, the detailed deformation of the considered body is fully described. The material is geometrically complex but its constitutive equations are those of a simple first gradient isotropic continuum. At the mesoscale, the metamaterial may be considered as made of elastic, extensional and flexible beams interconnected by possibly elastic constraints. At the macrolevel, it is possible to introduce, as a predictive model, a second gradient continuum whose geometry is particularly simple. However, F. Hild
[email protected] 1
Universit´e Paris-Saclay, ENS Paris-Saclay, CNRS, LMT–Laboratoire de M´ecanique et Technologie, Gif-sur-Yvette, France
2
Civil, Environmental and Architectural Engineering Department, University of Kansas, 1530 W. 15th Street, Learned Hall, Lawrence, KS 66045-7609, USA
3
MEMOCS and DICEEA Universit`a dell’Aquila, DISG Universit`a di Roma La Sapienza, Rome, Italy
it is governed by more complex deformation energy functionals. The pantographic structure that is considered herein is characterized, at the mesoscale, by two families of equally spaced beams interconnected at their intersection points by means of deformable cylinders. The question addressed herein concerns the description of the deformation phenomenology involving these cylinders, namely, can they be modeled as hinges (i.e., constraints prescribing equality of displacements and allowing for relative rotations) possibly with a deformation energy relate
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