Design of three dimensional isotropic microstructures for maximized stiffness and conductivity

By V. Challis, A. Roberts, Andy H. Wilkins. 2007

157 citations recorded by the source corpus.

The level-set method of topology optimization is used to design isotropic two-phase periodic multifunctional composites in three dimensions. One phase is stiff and insulating whereas the other is conductive and mechanically compliant. The optimization objective is to maximize a linear combination of the effective bulk modulus and conductivity of the composite. Composites with the Schwartz primitive and diamond minimal surfaces as the phase interface have been shown to have maximal bulk modulus and conductivity. Since these composites are not elastically isotropic their stiffness under uniaxial loading varies with the direction of the load. An isotropic composite is presented with similar conductivity which is at least 23% stiffer under uniaxial loading than the Schwartz structures when loaded uniaxially along their weakest direction. Other new near-optimal isotropic composites are presented, proving the capablities of the level-set method for microstructure design.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/3daef80d6ae9ba50830459854fa0e33f5e53decd

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Topology optimization approaches (2013, background): “So far, we have only been able to locate a few papers that treat large scale discrete topology optimization problems with multiple (non volume) constraints in a systematic manner (Challis et al. 2008; Zuo et al. 2012).”
A survey of structural and multidisciplinary continuum topology optimization: post 2000 (2014, methodology): “While not directly stress-based design, Challis et al. (2008b) provides interesting discussion regarding optimization against fracture resistance using a level set method.”
High specific strength and stiffness structures produced using selective laser melting (2014, methodology): ““optimised” unit cells at solid fractions between 7% and 20% were generated using the level set method of topology optimisation, as documented in previous work [23, 24].”
Multiscale isogeometric topology optimization for lattice materials (2017, methodology): “Gradient based schemes for topology optimization (TO), such as the solid isotropic material with penalization (SIMP) [18, 19], evolutionary methods for structural optimization (ESO) [20, 21], as well as more recent strategies, such as the level set [22, 23], have been extended to optimize the intern”
Level set topology optimization of fluids in Stokes flow (2009, methodology): “We deal with this using a simple smoothing operation, which one of the authors has used successfully in the past [55, 56].”
Current and future trends in topology optimization for additive manufacturing (2018, background): “Their main scope realizes extraordinary effective physical properties through lattice shapes such as the one close to theoretical limits [107,108], negative Poison’s ratio in elastic problem [109], negative thermal expansion [110], and acoustic negative bulk modulus [111].”