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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. (Postprint)
In: International Journal of Solids and Structures, 224, Elsevier, ISSN 0020-7683,
DOI: 10.26083/tuprints-00019874,
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Item Type: Article
Origin: Secondary publication service
Status: Postprint
Title: Numerical homogenization of second gradient, linear elastic constitutive models for cubic 3D beam-lattice metamaterials
Language: English
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.

Journal or Publication Title: International Journal of Solids and Structures
Journal volume: 224
Publisher: Elsevier
Collation: 24 Seiten
Classification DDC: 600 Technik, Medizin, angewandte Wissenschaften > 600 Technik
Divisions: 16 Department of Mechanical Engineering > Cyber-Physical Simulation (CPS)
Date Deposited: 15 Dec 2021 13:58
Last Modified: 15 Dec 2021 13:58
DOI: 10.26083/tuprints-00019874
Corresponding Links:
URN: urn:nbn:de:tuda-tuprints-198743
Additional Information:

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

URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/19874
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