Second-order homogenization of flexoelectric composites for piezoelectric behavior
Abstract
A second-order multiscale framework has been proposed for designing equivalent piezoelectric behavior by utilizing microscale flexoelectric composites. Unlike conventional homogenization approaches that neglect strain-gradient effects, the proposed method incorporates higher-order electromechanical coupling, enabling a direct and rigorous transfer of flexoelectric responses from the microscale to the macroscale. By combining isogeometric analysis with the finite cell method, a second-order computational homogenization scheme is formulated and implemented, allowing accurate analysis of complex microstructural geometries while maintaining high computational efficiency. High-order periodic boundary conditions consistent with the Hill–Mandel energy equivalence principle are enforced to ensure thermodynamic consistency across scales. Based on a perturbation analysis, closed-form macroscopic constitutive relations are systematically derived, revealing the emergence of equivalent piezoelectricity from flexoelectric composites. Numerical studies demonstrate that microscale dielectric matrices embedded with tetrahedral flexoelectric inclusions can be engineered to exhibit tunable macroscopic piezoelectric properties. A representative volume element analysis further identifies a characteristic microscale length that balances local heterogeneity and global electromechanical response. The proposed framework establishes a unified and predictive pathway for multiscale design of equivalent piezoelectric materials beyond conventional piezoelectric and homogenization theories.
Details
- Organisation(s)
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Institute of Photonics
- External Organisation(s)
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Bauhaus-Universität Weimar
Xi'an Modern Chemistry Research Institute
Tongji University
- Type
- Article
- Journal
- International Journal of Mechanical Sciences
- Volume
- 317
- ISSN
- 0020-7403
- Publication date
- 01.05.2026
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- Civil and Structural Engineering, General Materials Science, Aerospace Engineering, Condensed Matter Physics, Ocean Engineering, Mechanics of Materials, Mechanical Engineering, Applied Mathematics
- Electronic version(s)
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https://doi.org/10.1016/j.ijmecsci.2026.111494 (Access:
Closed
)
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Details in the research portal "Research@Leibniz University"
