Page 57 - IJAMD-1-2

International Journal of AI for
Materials and Design
AI-assisted ML monitoring in additive auxetics

for the solver formatted via Matlab code used in the design used as an input to the model. The encoder utilized multi-
generation. The mesh for the unit cell consisted of a 128 × scale kernels sized at 3 × 3, 6 × 6, and 9 × 9 to analyze
128 grid, matching the pixels, as depicted in Figure 1B(i). spatial correlations and connectivity among the solid
Considering the repetitive geometric characteristics of phases within the structure. This process allowed the
the auxetic unit cells, periodic boundary conditions were identification of diverse auxetic patterns with elevated
employed for corresponding boundary nodes, as depicted accuracy by leveraging information from multiple kernels.
in Figure 1B(ii). The solid phase was considered to be Specifically, small-sized kernels were adept at detecting
linearly elastic, with material parameters of 1,144.51 MPa immediate connectivity, whereas large-sized kernels can
for Young’s modulus (E) and 0.38 for Poisson’s ratio (v). capture broader structural correlations across the grid.
The strain field results were extracted by simulating the To further enhance the computational efficiency of the
structure’s response to tensile loading, considering plane model, convolutional feature maps were normalized based
stress conditions for two-dimensional analysis. on the number of multi-kernels applied. These feature
On the calculation of the simulation, the resulting three maps from fusion layers act as inputs for subsequent layers,
strain fields: ε , ε , and ε were extracted and used to where precise 1 × 1 pointwise convolution operations were
xx
xy
yy
42
calculate effective strain fields as follows (Equation V): employed to preserve essential structural information.
11
Within the down-sampling layers, the 2 × 2 max-pooling
2 1
ε equiv = 3  ε  xx 2 + ε + 2 yy ε − 2 zz εε − xx yy εε − yy zz ε ε + zz xx 3ε  2 xy  2 , (V) operation reduces the spatial dimensions of the feature
ν map while preserving critical structural details. The model
introduced a custom transpose convolution technique
Where ε zz = − (ε xx ε + yy ) from a plane stress
−
1
ν
condition. Furthermore, to access the NPR characteristic to aid in the reconstruction of compacted feature maps,
establishing a direct connection with the corresponding
of the designed auxetic structures, Poisson’s ratio for the feature maps in the finer layers of the encoder.
overall unit cell was calculated as the ratio between average
longitudinal and transverse strains as follows (Equation VI): Notably, the modified MNet introduced a separable
convolution approach to address the checkerboard issue,
ε
ν = − xx , a common artifact in conventional transpose convolution
unit cell
ε yy (VI) operations. The issue, characterized by distinct patterns
in CNN’s output feature maps, is effectively mitigated by
Where ( ) ⋅ denotes the volume average over the unit cell. adapting the separable approach. Mitigating checkerboard
41
Here, the y-direction is the loading direction. Therefore, issues is essential for accurate prediction of the effective
ε yy is the average longitudinal strain, whereas ε being strain fields. The training of the DL model was performed
38
xx
the average transverse strain. on a personal desktop computer equipped with a graphic
Through the process, two types of outputs were processing unit (GeForce RTX4090, Nvidia, USA).
obtained for each auxetic structure design: (i) the effective
strain fields stored as a 128 × 128 array and (ii) the 2.3. Three-dimensional printing and testing of ML
structural Poisson’s ratio value, which is a single scalar. In composite specimen
the next section, we demonstrate the data-driven model 2.3.1. Materials
architecture employed to accurately predict the effective The ML particle utilized in this study is composed of
strain fields. The dataset formulated by extracting those strontium aluminate (SAOED; SrAl O : Eu , Dy ) with
3+
2+
4
2
outputs for N designs is depicted in Figure 1B(iii). an average size of 10 µm (GSS-300FF, Nemoto and Co.,
2.2. DL model architecture Japan), which emits green photons on stressing due to the
ML effect (Figure 2A). For the 3D printing of ML-enriched
This study utilized a modified MNet DL architecture for the composites, we utilized a photocurable polymer resin
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effective mapping of auxetic structure configurations to their (AMB Med-10, 3D Systems, USA) as the matrix. The resin
respective effective strain fields, as depicted in Figure 1C. The was chosen for its transparency (ISO 10993-5 certified) to
model was equipped with an encoder-decoder framework, facilitate the visibility of ML particle emissions.
deploying a multi-kernel approach. 30,40 By integrating a
separable convolution technique within its density-populated 2.3.2. DLP-3D printing
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multi-kernel block, the model was capable of detecting To evaluate the mechanical and photonic characteristics
intricate patterns and predicting effective strain field attributes. of ML composites under tensile loading, we fabricated the
The 128 × 128 pixelized auxetic structure design, with composite specimens in dog-bone shape with the DLP 3D
“1” indicating solid phase and “0” representing void, was printing method (Figure 2B). The SAOED powder was mixed
Volume 1 Issue 2 (2024) 51 doi: 10.36922/ijamd.3539