This study proposes a method to shorten the deformation simulation time of four-dimensionally printed hydrogel models using deep learning. In this method, a large number of hydrogel models with the same shape but diferent distribution of expansion ratios are first created using Abaqus, and then deformation simulations are performed using the Abaqus thermal expansion method, and a dataset is created based on the simulation results. A recurrent neural network (RNN) was created and trained on this dataset, allowing the RNN to learn model deformation features that can be used to predict the deformation of longer hydrogels under the same loading conditions. This research provides a method for eficient simulation and inverse modeling of 4D printing.
In recent years, 3D printing technology has become an important technology in the
manufacturing and engineering fields [
However, while there are many advantages to 4D printing technology, there are some
challenges and limitations to its practical application. One of these problems is related to modeling
and simulation. Simulating the deformation of long sequences of hydrogels requires a large
number of calculations, which will consume a lot of time and computational resources [
The contributions made by this study are as follows: 1.This study is the first to apply RNN models to a hydrogel modeling method based on 4D printing technology, and demonstrates the superiority in time and computational space.
2.The RNN model used in this study can be used not only for the deformation prediction of hydrogel models of the same length, but also for hydrogel models of diferent lengths with high accuracy. This advantage makes the technology not only suitable for hydrogel models, but also for the production of 4d printed models with modular structures.
The model for this study was created using software named Abaqus. As shown in Figure 1, the entire model consists of two identically shaped sections stacked above and below each other, with each section a rectangle 10 mm long, 2 mm wide, and 2 mm thick. Divide each layer into parts in millimeter increments in the longitudinal direction. The numbers "0" and "1" represent the diferent expansion rates of each part. "0" shows hydrogel with the expansion rate of 1.8938 and "1" shows the expansion of 2.1223. The Random Forest Model (RFM) generates rectangles arranged in various orders. Each part has exactly the same material properties such as density, Poisson’s ratio, Young’s modulus, specific heat, and thermal conductivity, except for the expansion coeficient.
Based on the above material properties, the hydrogel model will continuously absorb water and swell in water to produce deformation. The whole process of deformation can be clearly reflected according to the time change, while the deformation result depends on the initial swelling rate sequence of the model. It can be seen that the sequence and deformation of the hydrogel model are standard time series data. (a) Sequences schematic (b) Abaqus Model
After placing the model in water, the model is deformed by expansion due to the higher water absorption of the hydrogel, and the diferent expansion rates of the parts cause the model to bend and deform into a curvilinear shape. To simulate the deformation process, a finite element analysis is performed using Abaqus. As an equivalent substitute for water absorption and expansion, the simulated loads were set to vary in temperature from 0°C to 15°C. 2 shows the result of the simulation. At the same time, one side of the model is fixed so that the deformation of the model occurs only in the x-axis and z-axis directions, which is convenient for the final result processing. For processing the simulation results, 20 reference points are selected at 1 mm intervals in the deformed model and the coordinates of each reference point are output. In total, 400 reference points will create a curve showing the simulation results. Models with diferent expansion rates will obtain diferent deformation curves after simulation. After simulating 1000 of these diferent models, 1000 diferent curves are obtained. The data set of the hydrogel model is obtained by storing all the coordinates of the obtained curve reference points corresponding to the "0" and "1" sequence codes of the initial model in the form of a table. As shown in the ifgure 3, each row represents one of the layers in the two-layer hydrogel model, and every two rows form a piece of the hydrogel model. The 10 columns on the left side of the table encode the hydrogel "0" and "1" sequence before the deformation, while the 200 columns on the right side correspond to the coordinates of the reference points after the deformation. The first and second rows of each group represent the coordinates of the reference point in the x-axis direction and in the z-axis direction, respectively.
Recurrent Neural Network (RNN) is a neural network characterized by its ability to take into
account not only the forward flow of information but also the backward flow of information.
That is, inputs corresponding to the present point in time not only produce outputs for the
present point in time, but also outputs the efect on the subsequent point in time, which makes it
possible to react the sequence to the global efect. This property matches the material properties
of the hydrogel model, so this study chose to use RNN as the model for deep learning [
Overall, the alternate use of the LSTM layer and the fully-connected layer enables the RNN
model used in this experiment to capture the long-term dependencies in the time-series data
and to perform feature extraction and dimensionality reduction on the captured information,
which leads to a better representation of the states and features of the hydrogel model and a
more accurate prediction of the future state of the hydrogel model, and has yielded good results
in the experimental results [
As the figure 5(a) shows, the LSTM layer, as a kind of recurrent neural network, has good
memory capability, it can efectively capture the long-term dependencies in time series data
[
Second, for the four tightly packed dense layers with 64 neurons employed. As the Figure 5(b) shows, These dense layers are designed to take the output of the LSTM layer for downscaling and feature extraction to better represent the states and features of the hydrogel model. During the training process, these fully connected layers help the network better understand the structure and changing patterns of the hydrogel model by learning the relationship between the inputs and outputs of the hydrogel model. (a) LSTM model (b) Dense model
For the training part, as the figure 6 shows, the parameters of the RNN model including weights
and biases are initialized first, and the above parameters will be updated gradually during the
training process so that the model can fit the training data better. After the initialization of the
model is completed, the short sequence data with a length of 10 cm obtained from the finite
element analysis is used as the training data, which contains diferent sequence alignments as
input data and the deformed coordinates as predicted target data. After inputting the training
data into the RNN model to start training, the loss function is utilized to calculate the diference
between the predicted results of the model and the real results each time, which is called
loss. The loss results in each training session are used as a measure of model accuracy, and
the backpropagation process uses an optimization algorithm to update the parameters of the
model so that the model fits the training data better. After repeating the steps of forward
propagation to calculate the loss and backpropagation to update the parameters until the
predefined convergence threshold of the loss function is reached, the RNN model will learn the
pattern of change of the hydrogel model and try to predict the future state at each time step in
the subsequent process [
This is followed by the prediction part. As the figure 7 shows, where a short sequence of length 10cm is first used as the initial input to the RNN model. During the forward propagation of the model, the RNN model processes each time step of the input sequence sequentially. At each time step, the model generates a prediction result based on the current input sequence data with the previous hidden state. And based on the current input and prediction result, and the previous hidden state, the hidden state is updated. This hidden state will continue to be used in the next time step to help the model better understand the temporal dependencies in the sequence. After the prediction of one time is completed, the RNN model will repeat the prediction process. That is, the prediction result from the previous time step is repeatedly used as the input for the next time step, and then the forward propagation process is performed again. This process will continue until we predict the result of the entire long sequence.
The variation of the prediction results with respect to the loss function during training and prediction is shown in Figure 8. The blue curve in the figure 8(a), 8(b), 8(c)is the deformed curve obtained after simulation of the hydrogel model with a length of 15 cm sequence, i.e., the true value, and the yellow curve is the prediction curve consisting of the 300 points used as the prediction result. The training process includes a total of 80 epochs, totaling more than 30,000 iterations of training. As can be seen from the figure 8(d), the loss function decreases rapidly in the early stage of training, indicating that the training results fit the real deformation results quickly, after 10 epochs the decrease of the loss function tends to level of, but is still decreasing steadily, and after all the 80 epochs have been completed, the loss function decreases to 1.7e-7, and the training curve basically agrees with the real curve, and the RNN model has learned the deformation features of the hydrogel model with a length of 10cm. The results of the prediction of the hydrogel sequence model with a length of 15cm by this model are shown in the yellow curve in the figure 8(a), 8(b), 8(c). As can be seen from the figure 8(a) 8(b) 8(c), the change of the predicted loss function is basically the same as the change rule of the training loss function, in the first 10 epochs when the rapid fit with the real results, and then the decline gradually stabilized, and finally stayed in the vicinity of 2.2e-5, and there is still a tendency to continue to decline, if we continue to increase the number of epoch, the prediction results can also be more accurate. Compared with the training loss function, the predicted loss function is 1e2 higher, but in the comparison chart with the real results, it can be seen that the real deformation trend has been predicted, and to a large extent predicted the specific coordinates of each point. From the comparison of the predicted results with the real results, it can be seen that the RNN model has basically mastered the deformation characteristics of the hydrogel model used in this experiment, and it can use the deformation characteristics of the 10 cm model to predict the deformation of the 15 cm model. The prediction results are highly consistent with the simulation results, and the prediction accuracy can be increased with the increase of training times.
In this paper, we use deep learning to predict the deformation of hydrogel models created by 4D printing technology. We designed a Recurrent Neural Network (RNN) structure and demonstrated the utility of the method to predict the deformation of a long hydrogel based on the deformation parameters of a short model for a two-layered rectangular object created with hydrogel. In general, building and simulating complex models using the finite element method is a time-consuming task. The method submitted in this study can eficiently predict simulation results without finite element analysis, thus significantly reducing time consumption. (a) Prediction Results1 (c) Prediction Results3 (d) loss
However, at present, this experiment still sufers from the problem that the training phase of the RNN model takes a long time and the prediction accuracy is not high for models with long lengths. In the future, we will continue to improve the neural network structure and optimize the algorithm with new suitable loss function formulas to create RNN networks that allow more accurate predictions and broader applications in the 4D printing domain.