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Strain gradient and
generalized continua obtained by homogenizing frame
lattices
Houssam Abdoul-Anziz and Pierre Seppecher
Vol. 6 (2018), No. 3, 213–250
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Abstract |
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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 extensional one, we bypass classical homogenization formulas and obtain totally different types of effective energies. We work in the framework of linear elasticity. We give different examples of 2D or 3D microstructures which lead to generalized 1D, 2D, or 3D continua like the Timoshenko beam, Mindlin–Reissner plate, strain gradient, or Cosserat or micromorphic continua. |
Keywords
strain gradient, generalized continua, homogenization,
lattices, $\Gamma$-convergence
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Mathematical Subject Classification 2010
Primary: 35B27, 74Q05, 78M40
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Milestones
Received: 22 December 2017
Revised: 27 March 2018
Accepted: 28 April 2018
Published: 26 July 2018
Communicated by Pierre Suquet
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Authors |
| Houssam Abdoul-Anziz | |
| Institut de Mathématiques de
Toulon Université de Toulon Toulon France |
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| Pierre Seppecher | |
| Institut de Mathématiques de
Toulon Université de Toulon Toulon France |
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