Publications

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Liu, X., & Shapiro V. (2015).  Random heterogeneous materials via texture synthesis. Computational Materials Science. 99, 177-189.
Liu, X., & Shapiro V. (2016).  Homogenization of material properties in additively manufactured structures. Computer-Aided Design. 78, 71-82.
Liu, X., & Shapiro V. (2017).  Sample-based synthesis of two-scale structures with anisotropy. Computer-Aided Design. 90, 199-209.
Liu, X., & Shapiro V. (2018).  Multiscale shape–material modeling by composition. Computer-Aided Design. 102, 194-203.
Liu, X., & Shapiro V. (2016).  Sample-Based Design of Functionally Graded Material Structures. Proceedings of the ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.
Liu, X. (2019).  Distributed Design of Two-Scale Structures With Unit Cells. Proceedings of ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference.