Variational asymptotic homogenization of beam-like square lattice structures

Emilio Barchiesi (Corresponding Author), Sergei Khakalo

    Research output: Contribution to journalArticleScientificpeer-review

    32 Citations (Scopus)


    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
    JournalMathematics and Mechanics of Solids
    Issue number10
    Publication statusPublished - 1 Oct 2019
    MoE publication typeA1 Journal article-refereed


    This work was supported by the Academy of Finland through the project Adaptive isogeometric methods for thin-walled structures (grant numbers 270007 and 304122) and the Magnus Ehrnrooth Foundation.


    • variational asymptotic homogenization
    • beam-like square lattice structures
    • Timoshenko beam
    • multiscale description
    • Piola’s ansatz


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