Variational asymptotic homogenization of beam-like square lattice structures

Emilio Barchiesi (Corresponding Author), Sergei Khakalo

    Research output: Contribution to journalArticleScientificpeer-review

    7 Citations (Scopus)

    Abstract

    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
    Volume24
    Issue number10
    DOIs
    Publication statusPublished - 1 Oct 2019
    MoE publication typeA1 Journal article-refereed

    Fingerprint

    Timoshenko Beam
    Lattice Structure
    Square Lattice
    Homogenization
    Macros
    Cauchy
    Continuum
    Plane Strain
    Scaling Laws
    Standard Model
    Scaling laws
    Modulus
    Benchmark
    Methodology

    Keywords

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

    Cite this

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    title = "Variational asymptotic homogenization of beam-like square lattice structures",
    abstract = "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.",
    keywords = "variational asymptotic homogenization, beam-like square lattice structures, Timoshenko beam, multiscale description, Piola’s ansatz",
    author = "Emilio Barchiesi and Sergei Khakalo",
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    doi = "10.1177/1081286519843155",
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    Variational asymptotic homogenization of beam-like square lattice structures. / Barchiesi, Emilio (Corresponding Author); Khakalo, Sergei.

    In: Mathematics and Mechanics of Solids, Vol. 24, No. 10, 01.10.2019, p. 3295-3318.

    Research output: Contribution to journalArticleScientificpeer-review

    TY - JOUR

    T1 - Variational asymptotic homogenization of beam-like square lattice structures

    AU - Barchiesi, Emilio

    AU - Khakalo, Sergei

    PY - 2019/10/1

    Y1 - 2019/10/1

    N2 - 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.

    AB - 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.

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    KW - beam-like square lattice structures

    KW - Timoshenko beam

    KW - multiscale description

    KW - Piola’s ansatz

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