Emergence of elastostatic strain-gradient effects from topological optimization

0570775 - MÚ 2024 RIV FR eng J - Journal Article
Calisti, Valentin - Lebée, A. - Novotny, A. A. - Sokolowski, J.
Emergence of elastostatic strain-gradient effects from topological optimization.
European Journal of Mechanics A-Solids. Roč. 100, July-August (2023), č. článku 104979. ISSN 0997-7538. E-ISSN 1873-7285
Grant - others:AV ČR(CZ) AP2101
Program: Akademická prémie - Praemium Academiae
Institutional support: RVO:67985840
Keywords : architectured materials * higher-order homogenization * periodic homogenization
OECD category: Pure mathematics
Impact factor: 4.1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.euromechsol.2023.104979

There are very few examples of architectured materials producing significant strain-gradient effects in elastostatics. In the present paper, we generate for the first time new microstructures featuring these effects from topological optimization of two-dimensional periodic media. The optimized shape functionals depend on the first and second-order homogenized tensors, obtained from a two-scale asymptotic expansion homogenization scheme. The optimization method applied here relies on the recently rigorously derived topological derivative of the second-order homogenized tensor, measuring the strain-gradient sensitivity with respect to a small circular inclusion at the microscopic level endowed with different material property from the background. This previous theoretical work allows an accurate numerical implementation.
Permanent Link: https://hdl.handle.net/11104/0342114