Emergence of elastostatic strain-gradient effects from topological optimization

• Published in: European journal of mechanics, A, Solids Vol. 100; p. 104979
• Main Authors: Calisti, V., Lebée, A., Novotny, A.A., Sokolowski, J.
• Format: Journal Article
• Language: English
• Published: Elsevier Masson SAS 01.07.2023; Elsevier
• Subjects: Architectured materials; Higher-order homogenization; Mathematics; Periodic homogenization; Strain-gradient continuum; Topological optimization; Strain-gradient continuum; Periodic homogenization; Topological optimization; Higher-order homogenization; Architectured materials
• ISSN: 0997-7538; 1873-7285
• DOI: 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. •Generation of strain-gradient 2D periodic media from topological optimization.•Topological derivative based optimization.•First and second-order homogenized tensors based shape functionals.•Two-scale asymptotic expansion homogenization scheme.