Anisotropic strain gradient thermoelasticity for cellular structures: Plate models, homogenization and isogeometric analysis

Sergei Khakalo (Corresponding Author), Jarkko Niiranen

    Research output: Contribution to journalArticleScientificpeer-review

    Abstract

    For three-dimensional cellular plate-like structures with a triangular (extruded lattice) microarchitecture, the article develops a pair of two-scale plate models relying on the anisotropic form of Mindlin’s strain gradient thermoelasticity theory. Accordingly, a computational homogenization method is proposed for determining the constitutive parameters of the related higher-order constitutive tensors. First, a Reissner–Mindlin plate model is derived by dimension reduction from a general framework of three-dimensional orthotropic strain gradient thermoelasticity and written as a variational formulation. An isogeometric conforming Galerkin method is formulated accordingly. Second, the plate model is modified in order to reduce the number of the constitutive strain gradient parameters. These steps are then repeated by following the kinematical assumptions of the Kirchhoff plate theory. Third, in order to see the cellular microarchitecture as a homogeneous three-dimensional material with classical modulae of transversal isotropy, classical computational homogenization is accomplished for determining the corresponding material parameters. Fourth, in order to see the cellular structures as two-dimensional plates, a non-classical homogenization procedure is proposed for the identification of the strain gradient modulae of the plate models. Finally, a set of numerical examples illustrates the reliability and efficiency of the resulting plate models in homogenizing cellular plate-like structures into strain gradient plate models capturing the bending size effects induced by the microarchitecture.
    Original languageEnglish
    Article number103728
    Number of pages36
    JournalJournal of the Mechanics and Physics of Solids
    Volume134
    Early online date2019
    DOIs
    Publication statusPublished - 1 Jan 2020
    MoE publication typeA1 Journal article-refereed

    Fingerprint

    thermoelasticity
    Thermoelasticity
    homogenizing
    gradients
    Homogenization method
    Galerkin methods
    Tensors
    plate theory
    Galerkin method
    isotropy
    tensors
    formulations

    Keywords

    • Cellular plates
    • Lattice microarchitecture
    • Strain gradient thermoelasticity
    • Reissner–Mindlin plate
    • Kirchhoff plate
    • Size effectsIsogeometric analysis

    Cite this

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    abstract = "For three-dimensional cellular plate-like structures with a triangular (extruded lattice) microarchitecture, the article develops a pair of two-scale plate models relying on the anisotropic form of Mindlin’s strain gradient thermoelasticity theory. Accordingly, a computational homogenization method is proposed for determining the constitutive parameters of the related higher-order constitutive tensors. First, a Reissner–Mindlin plate model is derived by dimension reduction from a general framework of three-dimensional orthotropic strain gradient thermoelasticity and written as a variational formulation. An isogeometric conforming Galerkin method is formulated accordingly. Second, the plate model is modified in order to reduce the number of the constitutive strain gradient parameters. These steps are then repeated by following the kinematical assumptions of the Kirchhoff plate theory. Third, in order to see the cellular microarchitecture as a homogeneous three-dimensional material with classical modulae of transversal isotropy, classical computational homogenization is accomplished for determining the corresponding material parameters. Fourth, in order to see the cellular structures as two-dimensional plates, a non-classical homogenization procedure is proposed for the identification of the strain gradient modulae of the plate models. Finally, a set of numerical examples illustrates the reliability and efficiency of the resulting plate models in homogenizing cellular plate-like structures into strain gradient plate models capturing the bending size effects induced by the microarchitecture.",
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    Anisotropic strain gradient thermoelasticity for cellular structures: Plate models, homogenization and isogeometric analysis. / Khakalo, Sergei (Corresponding Author); Niiranen, Jarkko.

    In: Journal of the Mechanics and Physics of Solids, Vol. 134, 103728, 01.01.2020.

    Research output: Contribution to journalArticleScientificpeer-review

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    AU - Khakalo, Sergei

    AU - Niiranen, Jarkko

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    AB - For three-dimensional cellular plate-like structures with a triangular (extruded lattice) microarchitecture, the article develops a pair of two-scale plate models relying on the anisotropic form of Mindlin’s strain gradient thermoelasticity theory. Accordingly, a computational homogenization method is proposed for determining the constitutive parameters of the related higher-order constitutive tensors. First, a Reissner–Mindlin plate model is derived by dimension reduction from a general framework of three-dimensional orthotropic strain gradient thermoelasticity and written as a variational formulation. An isogeometric conforming Galerkin method is formulated accordingly. Second, the plate model is modified in order to reduce the number of the constitutive strain gradient parameters. These steps are then repeated by following the kinematical assumptions of the Kirchhoff plate theory. Third, in order to see the cellular microarchitecture as a homogeneous three-dimensional material with classical modulae of transversal isotropy, classical computational homogenization is accomplished for determining the corresponding material parameters. Fourth, in order to see the cellular structures as two-dimensional plates, a non-classical homogenization procedure is proposed for the identification of the strain gradient modulae of the plate models. Finally, a set of numerical examples illustrates the reliability and efficiency of the resulting plate models in homogenizing cellular plate-like structures into strain gradient plate models capturing the bending size effects induced by the microarchitecture.

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    KW - Size effectsIsogeometric analysis

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