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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.
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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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