Effective strain gradient continuum model of metamaterials and size effects analysis

In this paper, a strain gradient continuum model for a metamaterial with a periodic lattice substructure is considered. A second gradient constitutive law is postulated at the macroscopic level. The effective classical and strain gradient stiffness tensors are obtained based on asymptotic homogeniza...

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Published in:Continuum mechanics and thermodynamics 2023-05, Vol.35 (3), p.775-797
Main Authors: Yang, Hua, Timofeev, Dmitry, Giorgio, Ivan, Müller, Wolfgang H.
Format: Article
Language:English
Subjects:
Accuracy
Cantilever beams
Classical and Continuum Physics
Continuum modeling
Engineering Thermodynamics
Finite element method
Fourier transforms
Heat and Mass Transfer
Homogenization
Mathematical analysis
Mechanics
Metamaterials
Methods
Microbalances
Microstructure
Original Article
Physics
Physics and Astronomy
Size effects
Stiffness
Structural Materials
Tensors
Theoretical and Applied Mechanics
Unit cell
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container_title Continuum mechanics and thermodynamics
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creator Yang, Hua
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description In this paper, a strain gradient continuum model for a metamaterial with a periodic lattice substructure is considered. A second gradient constitutive law is postulated at the macroscopic level. The effective classical and strain gradient stiffness tensors are obtained based on asymptotic homogenization techniques using the equivalence of energy at the macro- and microscales within a so-called representative volume element. Numerical studies by means of finite element analysis were performed to investigate the effects of changing volume ratio and characteristic length for a single unit cell of the metamaterial as well as changing properties of the underlying material. It is also shown that the size effects occurring in a cantilever beam made of a periodic metamaterial can be captured with appropriate accuracy by using the identified effective stiffness tensors.
doi_str_mv 10.1007/s00161-020-00910-3
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subjects Accuracy
Cantilever beams
Classical and Continuum Physics
Continuum modeling
Engineering Thermodynamics
Finite element method
Fourier transforms
Heat and Mass Transfer
Homogenization
Mathematical analysis
Mechanics
Metamaterials
Methods
Microbalances
Microstructure
Original Article
Physics
Physics and Astronomy
Size effects
Stiffness
Structural Materials
Tensors
Theoretical and Applied Mechanics
Unit cell
title Effective strain gradient continuum model of metamaterials and size effects analysis
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