An M-VCUT level set-based data-driven model of microstructures and optimization of two-scale structures

doi:10.1007/s11465-024-0798-y

Front. Mech. Eng.

2024, Vol. 19

Issue (4) : 26 https://doi.org/10.1007/s11465-024-0798-y

An M-VCUT level set-based data-driven model of microstructures and optimization of two-scale structures

Minjie SHAO, Tielin SHI, Qi XIA(

)

State Key Laboratory of Intelligent Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

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Abstract

The optimization of two-scale structures can adapt to the different needs of materials in various regions by reasonably arranging different microstructures at the macro scale, thereby considerably improving structural performance. Here, a multiple variable cutting (M-VCUT) level set-based data-driven model of microstructures is presented, and a method based on this model is proposed for the optimal design of two-scale structures. The geometry of the microstructure is described using the M-VCUT level set method, and the effective mechanical properties of microstructures are computed by the homogenization method. Then, a database of microstructures containing their geometric and mechanical parameters is constructed. The two sets of parameters are adopted as input and output datasets, and a mapping relationship between the two datasets is established to build the data-driven model of microstructures. During the optimization of two-scale structures, the data-driven model is used for macroscale finite element and sensitivity analyses. The efficiency of the analysis and optimization of two-scale structures is improved because the computational costs of invoking such a data-driven model are much smaller than those of homogenization.

Keywords two-scale structure structural optimization M-VCUT level set homogenization radial basis function data-driven

Corresponding Author(s): Qi XIA

About author:

^#These authors contributed equally to this work.

Issue Date: 13 August 2024

Cite this article:

Qi XIA,Tielin SHI,Minjie SHAO. An M-VCUT level set-based data-driven model of microstructures and optimization of two-scale structures[J]. Front. Mech. Eng., 2024, 19(4): 26.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-024-0798-y
https://academic.hep.com.cn/fme/EN/Y2024/V19/I4/26

Fig.1 Basic level set functions and virtual microstructures. (a–d) Four basic level set functions and cutting planes (shown in purple color). (e–h) Four virtual microstructures.

Fig.2 (a–d) Examples of the actual microstructure obtained by combining the virtual microstructures.

Fig.3 (a,b) Two virtual microstructures and (c,d) examples of the actual microstructure.

Fig.4 Schematic of radial basis function interpolation with two virtual microstructures.

Fig.5 Simple example of interpolation.

Result	Homogenization	CS 16 nodes	CS 81 nodes	MQ 81 nodes
$D 11 H$	1.0102	1.0205	1.0093	1.0090
$D 12 H$	0.2563	0.2599	0.2533	0.2539
$D 13 H$	−0.0119	−0.0118	−0.0125	−0.0124
$D 22 H$	0.8265	0.8381	0.8144	0.8170
$D 23 H$	−0.0163	−0.0155	−0.0167	−0.0164
$D 33 H$	0.3148	0.3183	0.3125	0.3128
\|\|D^H − D\|\|₁	–	0.0160	0.0155	0.0120
\|\|D^H − D\|\|₂	–	0.0146	0.0129	0.0102
Time/ms	122.9	0.1200	0.1344	0.3340

Tab.1 Comparison of the results of RBF-based interpolation^a)

Fig.6 Flowchart of offline construction of the microstructure database (in the red box) and online optimization of the two-scale structure (in the blue box).

Fig.7 Neighboring microstructures without node averaging. (a) First basic microstructure; (b) second basic microstructure; (c) actual microstructure.

Fig.8 Neighboring microstructures with node averaging. (a) First basic microstructure; (b) second basic microstructure; (c) actual microstructure.

Fig.9 Design problem of the first example.

Fig.10 (a) Initial design with 40 × 64 cells. (b) Optimized design with 40 × 64 cells and MQ-RBF. (c) Optimized design with 40 × 64 cells and CS-RBF. (d) Optimized design obtained by macroscale optimization with 1600 × 2560 elements. The compliance for (b) is 42.56, that for (c) is 42.67, and that for (d) is 53.23.

Fig.11 (a) Initial design and (b) optimized design with 40 × 64 cells with the microstructure prototype shown in Figs. 1(e) and 1(f). (c) Initial design and (d) optimized design with 40 × 64 cells with the microstructure prototype shown in Figs. 1(g) and 1(h). The compliance for (b) is 44.94 and that for (d) is 42.43.

Fig.12 Design problem of the second example.

Fig.13 (a) Initial design with 20 × 100 cells. (b) Optimized design with 20 × 100 cells and MQ-RBF. (c) Initial design with 40 × 200 cells. (d) Optimized design with 40 × 200 cells and MQ-RBF. (e) Optimized design with 20 × 100 cells and CS-RBF. (f) Optimized design obtained by macroscale optimization with 800 × 4000 elements. The compliance for (b) is 57.51, that for (d) is 57.94, that for (e) is 57.26, and that for (f) is 68.94.

Fig.14 Design problem of the third example.

Fig.15 (a) Iteration curve graph of the objective function and volume. (b) Initial design with 30 × 20 × 10 cells. (c) Optimized design by MQ-RBF. The compliance for (c) is 2.19.

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