Design of materials using topology optimization and energy-based homogenization approach in Matlab

Xia, Liang; Breitkopf, Piotr

doi:10.1007/s00158-015-1294-0

Cited by 301 publications

(196 citation statements)

References 42 publications

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“…2. Please refer to [1] or our recent educational paper [41] for detailed implementations of material microstructure design.…”

Section: Fe 2 -Based Concurrent Design Frameworkmentioning

confidence: 99%

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Multiscale structural topology optimization with an approximate constitutive model for local material microstructure

Xia

Breitkopf

2015

Computer Methods in Applied Mechanics and Engineering

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157

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“…2. Please refer to [1] or our recent educational paper [41] for detailed implementations of material microstructure design.…”

Section: Fe 2 -Based Concurrent Design Frameworkmentioning

confidence: 99%

“…In order to retrieve local material topologies, one just needs to perform local material topology optimizations [1,41] using the converged solution at the final converged structural topology. This two-scale design strategy requires significantly less computational efforts than the concurrent design strategy [1].…”

Section: General Design Algorithmmentioning

confidence: 99%

Multiscale structural topology optimization with an approximate constitutive model for local material microstructure

Xia

Breitkopf

2015

Computer Methods in Applied Mechanics and Engineering

Self Cite

157

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“…We have experimented with two objective functions that worked equally well for our purposes. e rst objective uses an energy based formulation [Xia and Breitkopf 2015a] to compute and optimize the elasticity tensor directly. At a high level, the optimization problem is arg min…”

Section: Continuous Optimization Of Microstructuresmentioning

confidence: 99%

“…e authors of the method developed parameter heuristics to optimize for di cult cases such as negative Poisson's ratio structures. We naturally arrive at structures with negative Poisson's ratio without the parameter varying step in [Xia and Breitkopf 2015a] since our discrete samples allow us to explore a wide variety of initial designs. e second objective is formulated using harmonic displacements [Kharevych et al 2009;Schumacher et al 2015] G instead of the elasticity tensor directly.…”

Section: Continuous Optimization Of Microstructuresmentioning

confidence: 99%

Two-Scale Topology Optimization with Microstructures

Zhu¹,

Skouras²,

Chen³

et al. 2017

ACM Trans. Graph.

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Fig. 1. Our two-scale topology optimization framework allows to optimize continuous material properties mapping to printable microstructures (le ) to fabricate high-resolution functional objects (middle) and minimum compliant structures (right).In this paper we present a novel two-scale framework to optimize the structure and the material distribution of an object given its functional specications. Our approach utilizes multi-material microstructures as low-level building blocks of the object. We start by precomputing the material property gamut -the set of bulk material properties that can be achieved with all material microstructures of a given size. We represent the boundary of this material property gamut using a level set eld. Next, we propose an e cient and general topology optimization algorithm that simultaneously computes an optimal object topology and spatially-varying material properties constrained by the precomputed gamut. Finally, we map the optimal spatially-varying material properties onto the microstructures with the corresponding properties in order to generate a high-resolution printable structure. We demonstrate the e cacy of our framework by designing, optimizing, and fabricating objects in di erent material property spaces on the level of a trillion voxels, i.e several orders of magnitude higher than what can be achieved with current systems.

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“…It is noted that the effective elasticity properties are interpreted as the summation of elastic energies of PUCs [15,19].…”

Section: Fig 1 3d Lsf and The Structural Design Domainmentioning

confidence: 99%

An effective design method for mechanical metamaterials with negative Poisson’s ratios

Xu¹,

Li²,

Xiao³

et al. 2018

EasyChair Preprints

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Abstract:In this paper, we propose a new method for the design of mechanical metamaterials by integrating the parametric level set method (PLSM) with the energy-based homogenization method (EBHM), where the topologies and shapes of material microstructures periodically distributed in the bulk material are optimized simultaneously. Firstly, material effective properties are evaluated by the EBHM under the topologies of material microstructures, where the average stress and strain theorems work as the basic theoretical framework rather than the asymptotic theory. Secondly, under the definition of the objective to seek for the negative Poisson's ratios, the PLSM is employed to evolve the topologies of microstructures until the bulk material is to be featured with negative Poisson's ratios. Several numerical examples for microstructures considering the orthotropy and isotropy are performed. A series of new and interesting material cells with negative Poisson's ratio are obtained.

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Design of materials using topology optimization and energy-based homogenization approach in Matlab

Cited by 301 publications

References 42 publications

Multiscale structural topology optimization with an approximate constitutive model for local material microstructure

Multiscale structural topology optimization with an approximate constitutive model for local material microstructure

Two-Scale Topology Optimization with Microstructures

An effective design method for mechanical metamaterials with negative Poisson’s ratios

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