scholarly journals Homogenization of periodic graph-based elastic structures

2018 ◽  
Vol 5 ◽  
pp. 259-288 ◽  
Author(s):  
Houssam Abdoul-Anziz ◽  
Pierre Seppecher
Keyword(s):  
Elastic Structures ◽  
Periodic Graph

scholarly journals Homogenization of an elastic material reinforced by very strong fibres arranged along a periodic lattice

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200620
Author(s):  
Houssam Abdoul-Anziz ◽  
Lukáš Jakabčin ◽  
Pierre Seppecher
Keyword(s):  
Strain Gradient ◽  
Periodic Lattice ◽  
Minimizing Sequences ◽  
Elastic Structures ◽  
Generalized Continua ◽  
Minimization Problems ◽  
Weak Part ◽  
Periodic Graph ◽  
The Matrix ◽  
Gradient Models

We provide in this paper homogenization results for the L 2 -topology leading to complete strain-gradient models and generalized continua. Actually, we extend to the L 2 -topology the results obtained in (Abdoul-Anziz & Seppecher, 2018 Homogenization of periodic graph-based elastic structures. Journal de l’Ecole polytechnique–Mathématiques 5 , 259–288) using a topology adapted to minimization problems set in varying domains. Contrary to (Abdoul-Anziz & Seppecher, 2018 Homogenization of periodic graph-based elastic structures. Journal de l’Ecole polytechnique–Mathématiques 5 , 259–288) we consider elastic lattices embedded in a soft elastic matrix. Thus our study is placed in the usual framework of homogenization. The contrast between the elastic stiffnesses of the matrix and the reinforcement zone is assumed to be very large. We prove that a suitable choice of the stiffness on the weak part ensures the compactness of minimizing sequences while the energy contained in the matrix disappears at the limit: the Γ-limit energies we obtain are identical to those obtained in (Abdoul-Anziz & Seppecher, 2018 Homogenization of periodic graph-based elastic structures. Journal de l’Ecole polytechnique–Mathématiques 5 , 259–288).

scholarly journals Homogenization of Interfaces Between Rapidly Oscillating Fine Elastic Structures and Fluids

2005 ◽  
Vol 65 (3) ◽  
pp. 983-1005 ◽  
Author(s):  
K. H. Hoffmann. ◽  
N. D. Botkin ◽  
V. N. Starovoitov
Keyword(s):  
Elastic Structures

scholarly journals Statistical distributions in the folding of elastic structures

2010 ◽  
Vol 2010 (11) ◽  
pp. P11027 ◽  
Author(s):  
Mokhtar Adda-Bedia ◽  
Arezki Boudaoud ◽  
Laurent Boué ◽  
Stéphanie Debœuf
Keyword(s):  
Statistical Distributions ◽  
Elastic Structures
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