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Published October 2018 | Supplemental Material
Journal Article Open

Microstructural patterns with tunable mechanical anisotropy obtained by simulating anisotropic spinodal decomposition


The generation of mechanical metamaterials with tailored effective properties through carefully engineered microstructures requires avenues to predict optimal microstructural architectures. Phase separation in heterogeneous systems naturally produces complex microstructural patterns whose effective response depends on the underlying process of spinodal decomposition. During this process, anisotropy may arise due to advection, diffusive chemical gradients or crystallographic interface energy, leading to anisotropic patterns with strongly directional effective properties. We explore the link between anisotropic surface energies during spinodal decomposition, the resulting microstructures and, ultimately, the anisotropic elastic moduli of the resulting medium. We simulate the formation of anisotropic patterns within representative volume elements, using recently developed stabilized spectral techniques that circumvent further regularization, and present a powerful alternative to current numerical techniques. The interface morphology of representative phase-separated microstructures is shown to strongly depend on surface anisotropy. The effective elastic moduli of the thus-obtained porous media are identified by periodic homogenization, and directionality is demonstrated through elastic surfaces. Our approach not only improves upon numerical tools to simulate phase separation; it also offers an avenue to generate tailored microstructures with tunable resulting elastic anisotropy.

Additional Information

© 2018 The Author(s). Published by the Royal Society. Received: 2 February 2018; Accepted: 31 August 2018. The authors acknowledge motivating and stimulating discussions with Prof. Lorenzo Valdevit. Data accessibility: The data supporting this article, including numerical codes used to generate the presented results and videos of anisotropic spinodal decomposition, have been uploaded as part of the electronic supplementary material. Author's contributions: A.V. and S.K. developed the computational code and conducted all simulations. All three authors conceived of and designed this study and drafted the manuscript. All the authors gave their final approval for publication. We declare we have no competing interests. A.V. acknowledges support from the Army Research Laboratory under Cooperative Agreement no. W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein.

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August 19, 2023
October 19, 2023