Strain gradient and generalized continua obtained by homogenizing frame lattices

Houssam Abdoul-Anziz (1, 2) , Pierre Seppecher (2, 1)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]
2 IMATH - Institut de Mathématiques de Toulon - EA 2134

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 overpass classical homogenization formula and obtain totally different types of effective energies. We work in the framework of linear elasticity. We give different examples of two dimensional or three dimensional micro-structures which lead to generalized 1D, 2D or 3D continua like Timoshenko beam, Mindlin-Reissner plate, strain gradient, Cosserat, or micromorphic continua.

Domaines: Mécanique des matériaux [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]; Equations aux dérivées partielles [math.AP]

Houssam Abdoul-Anziz, Pierre Seppecher. Strain gradient and generalized continua obtained by homogenizing frame lattices. 2017. ⟨hal-01672898v1⟩