Variational asymptotic homogenization of beam-like square lattice structures

Emilio Barchiesi (Corresponding Author), Sergei Khakalo

    Research output: Contribution to journal › Article › Scientific › peer-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

    Barchiesi, Emilio ; Khakalo, Sergei. / Variational asymptotic homogenization of beam-like square lattice structures. In: Mathematics and Mechanics of Solids. 2019 ; Vol. 24, No. 10. pp. 3295-3318.
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    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.",
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    Barchiesi, E & Khakalo, S 2019, 'Variational asymptotic homogenization of beam-like square lattice structures', Mathematics and Mechanics of Solids, vol. 24, no. 10, pp. 3295-3318. https://doi.org/10.1177/1081286519843155

    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 journal › Article › Scientific › peer-review

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    AU - Khakalo, Sergei

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    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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    Barchiesi E, Khakalo S. Variational asymptotic homogenization of beam-like square lattice structures. Mathematics and Mechanics of Solids. 2019 Oct 1;24(10):3295-3318. https://doi.org/10.1177/1081286519843155

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