Variational asymptotic homogenization of beam-like square lattice structures

Research output: Contribution to journalArticleScientificpeer-review


  • Emilio Barchiesi
  • Sergei Khakalo

Research units

  • University of Rome Tor Vergata
  • VTT Technical Research Centre of Finland


By means of variational asymptotic homogenization, using Piola's meso-macro ansatz, we derive the linear Timoshenko beam as the macro-scale limit of a meso-scale beam-like periodic planar square lattice structure. By considering benchmarks in statics and dynamics, meso-to-macro convergence is numerically analyzed. At the finest micro-scale, a 2D assembly of elastic, geometrically linear, isotropic and homogeneous Cauchy continua in plane strain with different material parameters is considered. Using this description, we calibrate the meso-scale model using standard methodology and, by exploiting the meso-to-macro homogenization scaling laws, we recover bending and shear Timoshenko beam moduli. It turns out that the Timoshenko beam found in this way and the finest-scale description based on the Cauchy continuum are in excellent agreement.


Original languageEnglish
Pages (from-to)3295-3318
Number of pages24
Issue number10
Publication statusPublished - Oct 2019
MoE publication typeA1 Journal article-refereed

    Research areas

  • Variational asymptotic homogenization, beam-like square lattice structures, Timoshenko beam, multiscale description, Piola's ansatz, DOUBLE-POROSITY HOMOGENIZATION, IN-SITU EXPERIMENTS, LARGE DEFORMATIONS, STRAIN GRADIENT, PANTOGRAPHIC SHEETS, EXISTING BUILDINGS, SEISMIC ANALYSIS, ELASTICITY, MODELS, DYNAMICS

ID: 36887661