Mechanical characterization of structured sheet materials

C Schumacher, S Marschner, M Gross… - ACM Transactions on …, 2018 - dl.acm.org
We propose a comprehensive approach to characterizing the mechanical properties of
structured sheet materials, ie, planar rod networks whose mechanics and aesthetics are …

Computing the effective bulk and normal to shear properties of common two-dimensional architectured materials

N Karathanasopoulos, F Dos Reis, H Reda… - Computational Materials …, 2018 - Elsevier
In the current work we analyze the bulk and normal to shear properties of a wide range of
two-dimensional artificial materials under small deformations. To that scope, we employ …

Star-shaped metrics for mechanical metamaterial design

J Martínez, M Skouras, C Schumacher… - ACM Transactions on …, 2019 - dl.acm.org
We present a method for designing mechanical metamaterials based on the novel concept
of Voronoi diagrams induced by star-shaped metrics. As one of its central advantages, our …

Handbook of bi-dimensional tensors: Part I: Harmonic decomposition and symmetry classes

N Auffray, B Kolev, M Olive - Mathematics and Mechanics of …, 2017 - journals.sagepub.com
To investigate complex physical phenomena, bi-dimensional models are often an interesting
option. It allows spatial couplings to be produced while keeping them as simple as possible …

[HTML][HTML] Elasticity and symmetry of triangular lattice materials

MLM François, L Chen, M Coret - International Journal of Solids and …, 2017 - Elsevier
The elastic tensor of any triangular (2D) lattice material is given with respect to the geometry
and the mechanical properties of the links between the nodes. The links can bear central …

Computation of minimal covariants bases for 2D coupled constitutive laws

B Desmorat, M Olive, N Auffray, R Desmorat… - International Journal of …, 2023 - Elsevier
We produce minimal integrity bases for both isotropic and hemitropic invariant algebras (and
more generally covariant algebras) of most common bidimensional constitutive tensors and …

[HTML][HTML] Invariant-based reconstruction of bidimensional elasticity tensors

N Auffray, P Ropars - International Journal of Solids and Structures, 2016 - Elsevier
In the present paper a method to reconstruct the 2D elasticity tensor from observations is
proposed. The novelty of the method, compared to other ones, is that this approach is based …

A unified approach to invariants of plane elasticity tensors

S Forte, M Vianello - Meccanica, 2014 - Springer
The action of the orthogonal group O (2) O (2) on the space of plane elasticity tensors has
been the subject of some recent investigations. It is shown here that the approach based on …

Tensorial Polar Decomposition of 2D fourth-order tensors

B Desmorat, R Desmorat - Comptes …, 2015 - comptes-rendus.academie-sciences …
On étudie la structure des tenseurs 2D symétriques d'ordre 4, c'est-à-dire: ayant aussi bien
la symétrie indicielle mineure que la symétrie majeure. La décomposition polaire de …

An alternative to the Kelvin decomposition for plane anisotropic elasticity

B Desmorat, P Vannucci - Mathematical Methods in the …, 2015 - Wiley Online Library
In this paper, we propose an alternative tensorial decomposition to the Kelvin's one
(introduced by Kelvin in 1856) for plane anisotropic elasticity using the polar formalism …