scholarly journals A second gradient continuum formulation for bi‐pantographic fabrics

PAMM ◽  
2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Simon R. Eugster ◽  
Emilio Barchiesi
Keyword(s):  
Second Gradient ◽  
Continuum Formulation ◽  
Second Gradient Continuum ◽  
Pantographic Fabrics

scholarly journals Large in-plane elastic deformations of bi-pantographic fabrics: asymptotic homogenization and experimental validation

2019 ◽  
Vol 25 (3) ◽  
pp. 739-767 ◽  
Author(s):  
Emilio Barchiesi ◽  
Simon R Eugster ◽  
Francesco dell’Isola ◽  
François Hild
Keyword(s):  
Deformation Energy ◽  
Rate Of Change ◽  
Image Correlation ◽  
Large Strains ◽  
Asymptotic Homogenization ◽  
Second Gradient ◽  
Manufacturing Techniques ◽  
Bias Extension ◽  
Architectured Materials ◽  
Pantographic Fabrics

Bi-pantographic fabrics are composed of two families of pantographic beams and correspond to a class of architectured materials that are described in plane as second-gradient 2D continua. On a discrete level, a pantographic beam is a periodic arrangement of cells and looks like an expanding barrier. The materialization of a bi-pantographic fabric made from polyamide was achieved by additive manufacturing techniques. Starting from a discrete spring system, the deformation energy of the corresponding continuum is derived for large strains by asymptotic homogenization. The obtained energy depends on the second gradient of the deformation through the rate of change in orientation and stretch of material lines directed along the pantographic beams. Displacement-controlled bias extension tests were performed on rectangular prototypes for total elastic extension up to 25%. Force–displacement measurements complemented by local digital image correlation analyses were used to fit the continuum model achieving excellent agreement.

scholarly journals Bias extension test on an unbalanced woven composite reinforcement: Experiments and modeling via a second-gradient continuum approach

2016 ◽  
Vol 51 (2) ◽  
pp. 153-170 ◽  
Author(s):  
Gabriele Barbagallo ◽  
Angela Madeo ◽  
Ismael Azehaf ◽  
Ivan Giorgio ◽  
Fabrice Morestin ◽  
...  
Keyword(s):  
Constitutive Expression ◽  
Woven Fabrics ◽  
Woven Composite ◽  
Plane Shear ◽  
Second Gradient ◽  
Proposed Model ◽  
Bias Extension Test ◽  
Bias Extension ◽  
Deformation Patterns ◽  
Second Gradient Continuum

The classical continuum models used for the woven fabrics do not fully describe the whole set of phenomena that occur during the testing of those materials. This incompleteness is partially due to the absence of energy terms related to some microstructural properties of the fabric and, in particular, to the bending stiffness of the yarns. To account for the most fundamental microstructure-related deformation mechanisms occurring in unbalanced interlocks, a second-gradient, hyperelastic, initially orthotropic continuum model is proposed. A constitutive expression for the strain energy density is introduced to account for (a) in-plane shear deformations, (b) highly different bending stiffnesses in the warp and weft directions, and (c) fictive elongations in the warp and weft directions which eventually describe the relative sliding of the yarns. Numerical simulations which are able to reproduce the experimental behavior of unbalanced carbon interlocks subjected to a bias extension test are presented. In particular, the proposed model captures the macroscopic asymmetric S-shaped deformation of the specimen, as well as the main features of the associated deformation patterns of the yarns at the mesoscopic scale.

A second gradient continuum model accounting for some effects of micro-structure on reconstructed bone remodelling

2012 ◽  
Vol 340 (8) ◽  
pp. 575-589 ◽  
Author(s):  
Angela Madeo ◽  
D. George ◽  
T. Lekszycki ◽  
Mathieu Nierenberger ◽  
Yves Rémond
Keyword(s):  
Continuum Model ◽  
Bone Remodelling ◽  
Micro Structure ◽  
Second Gradient ◽  
Second Gradient Continuum

Construction of second gradient continuum models for random fibrous networks and analysis of size effects

2017 ◽  
Vol 181 ◽  
pp. 347-357 ◽  
Author(s):  
K. Berkache ◽  
S. Deogekar ◽  
I. Goda ◽  
R.C. Picu ◽  
J.-F. Ganghoffer
Keyword(s):  
Size Effects ◽  
Continuum Models ◽  
Second Gradient ◽  
Second Gradient Continuum

scholarly journals A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling

2018 ◽  
Vol 24 (1) ◽  
pp. 258-280 ◽  
Author(s):  
Mario Spagnuolo ◽  
Ugo Andreaus
Keyword(s):  
Large Deformations ◽  
Variational Principles ◽  
Selection Criterion ◽  
Numerical Comparison ◽  
Elastic Beams ◽  
Second Gradient ◽  
Post Buckling ◽  
Live Loads ◽  
Second Gradient Continuum ◽  
Math Phys

In this paper, we give a targeted review of the state of the art in the study of planar elastic beams in large deformations, also in the presence of geometric nonlinearities. The main scope of this work is to present the different methods of analysis available for describing the possible equilibrium forms and the motions of elastic beams. For the sake of completeness, we start by giving an overview of the nonlinear theories introduced for approaching this argument and then we account for the variational principles and deformation energies introduced for modelling beams undergoing large deformations and displacements. We then consider different kinds of loads treated in the literature and the corresponding induced beam deformations. We conclude by accounting for the available analysis for stability and some considerations about problems where live loads are applied, as well as by describing some relevant numerical methods of use in the applications we have in mind. The selection criterion for the reviewed papers is dictated by the need to study large deformations and the dynamics of pantographic sheets. (Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium. Proc R Soc A 2016; 472(2185): 20150790), dell’Isola et al. (Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence. Z Angew Math Phys 2015; 66(6): 3473–3498), Turco et al. (Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models. Z Angew Math Phys 2016; 67(4): 1–28)].

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