Pantographic metamaterials: an example of mathematically driven design and of its technological challenges

F Dell'Isola, P Seppecher, JJ Alibert… - Continuum Mechanics …, 2019 - Springer
In this paper, we account for the research efforts that have been started, for some among us,
already since 2003, and aimed to the design of a class of exotic architectured, optimized …

Strain gradient and generalized continua obtained by homogenizing frame lattices

H Abdoul-Anziz, P Seppecher - Mathematics and mechanics of complex …, 2018 - msp.org
We determine the effective behavior of periodic structures made of welded elastic bars.
Taking into account the fact that flexural and torsional stiffnesses are much smaller than the …

[HTML][HTML] Research perspective on multiphysics and multiscale materials: a paradigmatic case

A Ciallella - Continuum Mechanics and Thermodynamics, 2020 - Springer
Pantographic fabrics are presented as a paradigmatic example to discuss the research
perspective on multiphysics and multiscale materials. Reduced-order modeling, obtained by …

[HTML][HTML] Linear pantographic sheets: existence and uniqueness of weak solutions

VA Eremeyev, F Dell'Isola, C Boutin, D Steigmann - Journal of Elasticity, 2018 - Springer
The well-posedness of the boundary value problems for second gradient elasticity has been
studied under the assumption of strong ellipticity of the dependence on the second …

[HTML][HTML] Additive manufacturing introduced substructure and computational determination of metamaterials parameters by means of the asymptotic homogenization

BE Abali, E Barchiesi - Continuum Mechanics and Thermodynamics, 2021 - Springer
Metamaterials exhibit materials response deviation from conventional elasticity. This
phenomenon is captured by the generalized elasticity as a result of extending the theory at …

[HTML][HTML] Verification of asymptotic homogenization method developed for periodic architected materials in strain gradient continuum

H Yang, BE Abali, WH Müller, S Barboura… - International Journal of …, 2022 - Elsevier
Strain gradient theory is an accurate model for capturing the size effect and localization
phenomena. However, the challenge in identification of corresponding constitutive …

Determination of metamaterial parameters by means of a homogenization approach based on asymptotic analysis

H Yang, BE Abali, D Timofeev, WH Müller - Continuum mechanics and …, 2020 - Springer
By using modern additive manufacturing techniques, a structure at the millimeter length
scale (macroscale) can be produced showing a lattice substructure of micrometer …

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

M Spagnuolo, ME Yildizdag… - … and Mechanics of …, 2021 - journals.sagepub.com
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 …

Investigation of deformation behavior of PETG-FDM-printed metamaterials with pantographic substructures based on different slicing strategies

A Özen, G Ganzosch, E Barchiesi… - Composites and …, 2021 - journals.sagepub.com
Based on the progress and advances of additive manufacturing technologies, design and
production of complex structures became cheaper and therefore rather possible in the …

A Lagrangian Hencky-type non-linear model suitable for metamaterials design of shearable and extensible slender deformable bodies alternative to Timoshenko …

E Turco, E Barchiesi, I Giorgio, F Dell'Isola - International Journal of Non …, 2020 - Elsevier
Among the most studied models in mathematical physics, Timoshenko beam is outstanding
for its importance in technological applications. Therefore it has been extensively studied …