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Numerical homogenization of second gradient, linear elastic constitutive models for cubic 3D beam-lattice metamaterials

Weeger, Oliver (2021)
Numerical homogenization of second gradient, linear elastic constitutive models for cubic 3D beam-lattice metamaterials.
In: International Journal of Solids and Structures, 2021, 224
doi: 10.26083/tuprints-00019874
Article, Secondary publication, Postprint

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Item Type: Article
Type of entry: Secondary publication
Title: Numerical homogenization of second gradient, linear elastic constitutive models for cubic 3D beam-lattice metamaterials
Language: English
Date: 2021
Place of Publication: Darmstadt
Year of primary publication: 2021
Publisher: Elsevier
Journal or Publication Title: International Journal of Solids and Structures
Volume of the journal: 224
Collation: 24 Seiten
DOI: 10.26083/tuprints-00019874
Corresponding Links:
Origin: Secondary publication service
Abstract:

Generalized continuum mechanical theories such as second gradient elasticity can consider size and localization effects, which motivates their use for multiscale modeling of periodic lattice structures and metamaterials. For this purpose, a numerical homogenization method for computing the effective second gradient constitutive models of cubic lattice metamaterials in the infinitesimal deformation regime is introduced here. Based on the modeling of lattice unit cells as shear-deformable 3D beam structures, the relationship between effective macroscopic strain and stress measures and the microscopic boundary deformations and rotations is derived. From this Hill–Mandel condition, admissible kinematic boundary conditions for the homogenization are concluded. The method is numerically verified and applied to various lattice unit cell types, where the influence of cell type, cell size and aspect ratio on the effective constitutive parameters of the linear elastic second gradient model is investigated and discussed. To facilitate their use in multiscale simulations with second gradient linear elasticity, these effective constitutive coefficients are parameterized in terms of the aspect ratio of the lattices structures.

Status: Postprint
URN: urn:nbn:de:tuda-tuprints-198743
Additional Information:

Numerical homogenization, Generalized continuum mechanics, Second gradient linear elasticity, Lattice metamaterials, Multiscale simulation

Classification DDC: 600 Technology, medicine, applied sciences > 600 Technology
Divisions: 16 Department of Mechanical Engineering > Cyber-Physical Simulation (CPS)
Date Deposited: 15 Dec 2021 13:58
Last Modified: 16 Aug 2023 05:49
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19874
PPN: 510629989
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