Topological design of microstructures of cellular materials for maximum bulk or shear modulus

By Xiaodong Huang, A. Radman, Yi Min Xie. 2011

306 citations recorded by the source corpus.

This paper presents a new approach to designing periodic microstructures of cellular materials. The method is based on the bidirectional evolutionary structural optimization (BESO) technique. The optimization problem is formulated as finding a micro-structural topology with the maximum bulk or shear modulus under a prescribed volume constraint. Using the homogenization theory and finite element analysis within a periodic base cell (PBC), elemental sensitivity numbers are established for gradually removing and adding elements in PBC. Numerical examples in 2D and 3D demonstrate the effectiveness of the proposed method for achieving convergent microstructures of cellular materials with maximum bulk or shear modulus. Some interesting topological patterns have been found for guiding the cellular material design.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/28596eb7b127b475cae7da6780e56cc6a1510b1f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Liang Xia
2. Qiuling Xia
3. Xiaodong Huang
4. Yi Min Xie
5. Shiwei Zhou
6. Damiano Pasini
7. Hang Xu
8. Shanqing Xu

In Mechanics of Materials

1. Liang Xia
2. Qiuling Xia
3. Xiaodong Huang
4. Yi Min Xie
5. Shiwei Zhou
6. Damiano Pasini
7. Hang Xu
8. Shanqing Xu

Citations in the corpus

• Concurrent topology optimization of structures and their composite microstructures (2014, background): “The inverse problem is a typical topology optimization problem for the material design which seeks an optimal microstructure of the base cell with prescribed or extreme macroscopic properties [18].”
• Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review (2016, methodology): “34 Materials with maximized shear moduli in 2D/3D cases [60]”
• Topological design and additive manufacturing of porous metals for bone scaffolds and orthopaedic implants: A review. (2016, methodology): “These unit cells were obtained using the Bi-directional Evolutionar y Structural Optimization (BESO) method [101-105], wh ich shows faster convergence and unambiguous material definition [106-109].”
• 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”
• Multiscale structural topology optimization with an approximate constitutive model for local material microstructure (2015, unknown): “Following [50,51], two initial material guesses are considered for design.”
• Microstructures to control elasticity in 3D printing (2015, background): “Due to the combinatorial complexity, direct search methods are prohibitively expensive, and the problem is usually solved using a relaxed formulation with continuous material density variables [Sigmund 2009] or advanced search heuristics [Huang et al. 2011].”