Variational asymptotic homogenization of beam-like square lattice structures

Emilio Barchiesi (Corresponding Author), Sergei Khakalo

Research output: Contribution to journalArticleScientificpeer-review

4 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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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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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

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