Strain gradient and generalized continua obtained by homogenizing frame lattices

Abstract

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.