Gan Transistor Converter Matlab

DogLayout: Denoising Diffusion GAN for Discrete and Continuous Layout

Abstract

Layout Generation aims to synthesize plausible arrangements from given elements. Currently, the predominant methods in layout generation are Generative Adversarial Networks (GANs) and diffusion models, each presenting its own set of challenges. GANs typically struggle with handling discrete data due to their requirement for differentiable generated samples and have historically circumvented the direct gen- eration of discrete labels by treating them as fixed conditions.

Conversely, diffusion-based models, despite achieving state- of-the-art performance across several metrics, require exten- sive sampling steps which lead to significant time costs. To address these limitations, we propose DogLayout (Denoising Diffusion GAN Layout model), which integrates a diffusion process into GANs to enable the generation of discrete label data and significantly reduce diffusion’s sampling time. Ex- periments demonstrate that DogLayout considerably reduces sampling costs by up to 175 times and cuts overlap from 16.43 to 9.59 compared to existing diffusion models, while also surpassing GAN based and other layout methods. Code is available at https://github.com/deadsmither5/DogLayout.

Introduction

Creating aesthetic layouts is an essential method for convey- ing important information to viewers and plays a critical role in various applications such as UI design (Deka et al. 2017), advertisement poster synthesis (Guo et al. 2021), and editing in printed media (Zhong, Tang, and Yepes 2019). Tradition- ally reliant on manual design processes, the scalability and efficiency demands of modern digital content creation ne- cessitate automated solutions using generative models.

In the layout generation task, each layout element is char- acterized by discrete labels along with continuous size and position attributes. Besides conditioning on the label types, sizes, and positions, there are two other important layout generation tasks: 1) Unconditional generation, which in- volves generating layouts without predefined constraints or elements’ attributes, such as randomly designing a game lay- out. 2) Completion, which involves filling in missing layout elements based on partially known elements and can be used to complete layouts forgotten by human designers.

In both unconditional generation and completion, gen- erating the discrete label is inevitable. However, previous GAN-based layout models (Li et al. 2020; Kikuchi et al.

Figure 1: Visualization of DogLayout’s inference process. During inference, we first obtain the noisy layout from stan- dard gaussian. Then the generator takes it as input to output the predicted clean layout. Subsequently, we derive the less noisy layout by adding noise to the predicted clean layout.

Repeat the above process to achieve the final clean layout. 2021) can only generate the continuous sizes or positions conditioned on the label. Given a one-hot encoded label, GAN-based layout models fail to generate discrete data for two reasons: 1) Given the generator’s probabilistic outputs, the discriminator’s task is overly simplified as it only needs to identify a single non-zero element in the data’s one- hot vector representation. 2) Using the non-differentiable argmax function to convert the generator’s probabilistic out- puts into discrete formats leads to vanishing gradients.

On the other hand, existing diffusion models (Inoue et al. 2023) focus too much on improving automatic evaluation indicators and ignore the importance of sampling speed in practical applications. To maintain the posterior distribution in a Gaussian form, diffusion models (Ho, Jain, and Abbeel 2020) always involve thousands of sampling timesteps. Al- though some works like LACE (Chen et al. 2024) use DDIM (Song, Meng, and Ermon 2020) to accelerate the sampling process, the time cost is still significant. In scenarios where quick response is required, the high time cost is unafford- able. Additionally, the layouts generated by diffusion mod- els, such as LayoutDM (Inoue et al. 2023), still suffer from

Arxiv:2412.00381V1 [Cs.Cv] 30 Nov 2024

excessive overlap, which is highly noticeable to humans. In this study, we propose the DogLayout (shown in Fig- ure 2) to expand Layout GAN models’ ability to handle un- conditional generation and completion while maintaining a high sampling speed. By adding a diffusion process to GAN, we propose a new method for GANs to deal with discrete label data: 1) All operations on the Generator’s output are differentiable. 2) The discriminator does not directly see the generator’s output and cannot distinguish real denoised lay- out from predicted denoised layout based solely on the pres- ence of a single non-zero element. Moreover, by using GAN to fit the non-Gaussian denoising distribution (Xiao, Kreis, and Vahdat 2021), we significantly reduce the number of sampling steps and achieve a sampling speed that is up to 175 times faster than current diffusion-based layout models and also improved the overlap from 16.43 to 9.59.

We Summarize Our Contributions As Follows:

• By adding a diffusion process to GANs, we propose a new method to generate discrete label data, which main- tains the differentiability of the generator’s output and prevents the discriminator from distinguishing real from fake data by detecting a single non-zero element.

• We expanded the capabilities of previous layout GAN models, which were limited to conditional tasks, to in- clude unconditional and completion tasks, thereby im- proving the quality of generated layouts by up to 2.5 times compared to LayoutGAN++ (Kikuchi et al. 2021).

• Through extensive experiments, our model outperforms non-diffusion-based layout models in most tasks and re- duces the time cost of layout generation by up to 175 times compared to diffusion-based layout models, while maintaining competitive performance. User studies indi- cate that our model is more favored by real users.

Layout Generation

Automatically generating layouts is a long-researched topic in graphic design (Hurst, Li, and Marriott 2009). Early stud- ies optimize layouts by manually designing energy func- tions with constraints. Recent works have begun to use deep generative models to learn plausible layouts. LayoutVAE (Jyothi et al. 2019) introduces two conditional Variational Autoencoders (VAE). NDN-none (Lee et al. 2020) is also a VAE-based model for conditional layout generation using graph neural networks. BLT (Kong et al. 2022) proposes a hierarchical sampling policy with bidirectional layout trans- former. As for the generative adversarial networks (GANs, (Goodfellow et al. 2014)) based models, LayoutGAN (Li et al. 2020) can synthesize graphic layouts conditioned on different element attributes. LayoutGAN++ (Kikuchi et al.

2021) builds a transformer-based gan and formulates the lay- out generation as a constrained optimization problem. How- ever traditional GAN can’t deal with categorical data (Hjelm et al. 2017), previous GAN based layout model is all lim- ited to condition on the discrete labels. Recently, diffusion- based models have begun to be used. LayoutDM (Inoue et al.

2023), LayoutDiffusion (Zhang et al. 2023) and (Hui et al. 2023) use the Discrete Diffusion Models (Austin et al. 2021) in a similar way to handle the structured layout data in the discrete representation, their works also expand the condi- tional layout generation to unconditional situation. LACE (Chen et al. 2024) proposed a novel align loss and also uti- lizes unconditional layout generation. Although diffusion- based layout models show strong capabilities in terms of di- versity, the time cost and overlap in the generated layouts are non-negligible. Our work proposes a new way to enable GANs to generate discrete labels with minimal time cost.

Gans For Discrete Data

Challenges with Discrete Data in GANs.

Generative Ad-

versarial Networks (GANs) face two main challenges when applied to discrete data. The generator transforms a la- tent vector into an output, while the discriminator evaluates whether this output resembles the actual discrete data, typi- cally represented as a one-hot vector. The first challenge is that discriminator’s task becomes straightforward—it only needs to detect the presence of a single non-zero element in the real one-hot discrete data. This simplicity contrasts sharply with generator’s output, which often spreads non- zero probabilities across multiple dimensions. The second challenge arises when attempting to address the first: using argmax on generator’s output to provide one-hot form input for discriminator leads to a gradient vanishing problem due to the non-differentiability of the argmax operation.

Existing solutions.

Several Studies Seek To Address These

challenges. Gumbel GAN(Kusner and Hern´andez-Lobato 2016) employs the Gumbel reparameterization technique (Jang, Gu, and Poole 2016), which enables gradient back- propagation from discriminator to generator. However, this approach introduces a new challenge: discriminator only ob- serves the one-hot transformed output from generator, not the output itself, limiting it’s ability to effectively guide gen- erator’s gradient optimization. BGAN (Hjelm et al. 2017) addresses this by exploring the boundaries of data distribu- tions, yet accurately defining and identifying these bound- aries remains challenging. Seq-GAN (Yu et al. 2017) uses discriminator as a reward function employing policy gradi- ents, but designing an effective reward function that accu- rately evaluates the quality of generated layouts proves dif- ficult. Figure 5 shows that using LayoutGAN++ directly to model discrete label data results in gradient vanishing.

Preliminary

Problem Formulation.

Following Previous Studies (Chen

et al. 2024; Kikuchi et al. 2021), we define a layout l with M elements and as {(c1, b1), . . , (cM, bM)}, where (ci, bi) represents the i-th elements in l. ci ∈{0, . , N −1} is the discrete label in a range of N classes such as the Text or Title and bi = (xi, yi, wi, hi) ∈[0, 1]4 is the corresponding center coordinates (x, y) and size ratio (w, h).

Diffusion Models.

A Standard Diffusion Model Contains A

forward diffusion process and reverse diffusion process. In diffusion’s forward process, given x0 ∼q(x0), each data xt is corrupted gradually by adding Gaussian noise to xt−1.

Figure 2: Overview of our method. (a) During training, we first obtain the noisy layout xt−1, then generate xt by directly adding noise to xt−1. The generator then takes xt and an additional latent dimension z as inputs to output the predicted clean layout

0. Subsequently, We Derive The Predicted X′

t−1 using 2. For the real data, the discriminator evaluates the real noisy layout xt and xt−1 to determine whether xt−1 is the true denoised layout of xt. An additional decoder then takes the global context token h from the discriminator and reconstructs x0, which forces the discriminator to learn the meaningful attributes of the layout.

For the fake data, the discriminator assesses the real noisy layout xt and the predicted layout x′

T−1

is the true denoised layout of xt. The model architectures are shown in (b), (c) and (d). In reverse process , the goal is to train a network pθ to pre- dict xt−1 from xt and the whole training objective could be

Lt−1

.

(1)

In a standard diffusion process, when forward timestep is large enough q(xT |x0) and pθ(xT ) will both follows a standard normal distribution N(0, 1) and the LT term will be nearly equal to zero. L0 is the reconstruct loss from x1 to x0. Lt−1 means to train a neural network pθ(xt−1|xt) to fit the true distribution q(xt−1|xt). In order to trace q(xt−1|xt) , DDPM (Ho, Jain, and Abbeel 2020) use q(xt−1|xt, x0) to

Q(Xt|X0)

.

Overview And Model Architecture

DogLayout builds on Diffusion GAN models (Xiao, Kreis, and Vahdat 2021; Gong et al. 2024). In this chapter, we will first introduce the model architecture of DogLayout, then discuss the details of our framework and the methods used to reduce sampling time costs by integrating a GAN into the diffusion process, and explain how this integration enables GANs to handle discrete data.

Conditional and Unconditional Generation.

Condi-

tional generation involves creating an entire layout from a partially known layout xp. Let m represent the mask, where 1 and 0 indicate known and unknown layout attributes, re- spectively. The conditional information is incorporated as follows: xt−1 = (1 −m) ⊙˜xt−1 + m ⊙xp, where ˜xt−1 ∼ pθ(xt−1|xt). Unconditional generation refers to the process of generating a layout initially from standard Gaussian.

Generator.

To Process The Input Noise Layout Xt, We Utilize

a fully-connected layer to expand its dimensions to the em- bedding dimension. The latent variable z is initially sampled from a standard Gaussian distribution, subsequently resized to the specified latent dimension through a fully-connected layer. while temporal embedding is not explicitly incorpo- rated. The core processing unit comprises a transformer- encoder (Vaswani et al. 2017) Finally, the transformer- encoder’s output is adjusted back to the input’s dimensions

X′

0 = fF C(h3).

(3)

In the above notations, fF C represents the fully-connected layer, and fT F −ENC represents the transformer-encoder layer. xt is sampled from N(xt; √1 −βtxt−1, βtI) and con- dition is injected from known layout xp.

Discriminator.

T−1, Depending On

whether the data is real or generated. This combined input is then passed through a fully-connected layer to expand its di- mensions to match the embedding dimension. Position em- bedding is injected via a trainable embedding layer, while time embedding is not included. The core unit consists a transformer-encoder which includes a learnable special to- ken hs to get global context token h. Then a fully-connected layer processes h to produce the probability logits:

[H, H2] = Ft F −Enc(H1, Hs),

p = fF C(h).

(4)

Here, p presents the probability that whether xt−1 or x

T−1 Is

the true denoised layout of xt. Decoder.

When The Discriminator Processes Real Inputs Xt

and xt−1, it employs a transformer-encoder and a fully- connected layer to reconstruct the initial layout x0 from the

X′

d0 = fF C(h1).

X′

d0 is the reconstruction results of decoder. This reconstruc- tion process enables the discriminator to learn the meaning- ful attributes of the layout effectively, which enables the dis- criminator to effectively distinguish between real and gener- ated layouts based on their meaningful attributes.

Doglayout

The key to reducing sampling time in the diffusion process is to decrease the timesteps. Using Bayes’ rule, the real denois- ing distribution q(xt−1|xt) = q(xt|xt−1)q(xt−1)/q(xt), when T is sufficiently large, the noise added between each adjacent step is small enough that the ratio q(xt−1)/q(xt) ≈ 1. Consequently, both q(xt|xt−1) and q(xt−1|xt) can be as- sumed to follow Gaussian distributions.

To reduce the timestep T to a smaller number (e.g., T = 4), we can use a GAN to match the non-Gaussian distribu- tion q(xt−1|xt). When T is small, DDGAN (Xiao, Kreis, and Vahdat 2021) proposes using a conditional generative adversarial network to minimize the distance between these two distributions instead of the original KL Divergence de- scribed in Equation 1. Given the noisy layout xt to both the generator and discriminator, the generator pθ(xt−1|xt) aims to reconstruct the cleaner layout xt−1 that is indistinguish- able from the real xt−1. The discriminator aims to maximize its ability to distinguish between the real cleaner layout xt−1 and the predicted xt−1 ∼pθ(xt−1|xt). This training pro- cess can be regarded as minimizing the following expres- sion, where Dadv represents a metric for calculating the dis- tance between two distributions (e.g., Wasserstein distance

T≥1

Eq(xt)[Dadv(q(xt−1|xt), pθ(xt−1|xt))].

(6)

We choose the softened reverse KL as the Dadv. We pro- pose not to inject time into the generator and discriminator due to the fact that the timestep t is implicitly included in the noise strength of the given xt. The generator will take an additional N-dimensional latent variable z to enhance diver- sity and directly output the predicted version of the layout x0 = Gθ(xt, z). Then, xt−1 is sampled using Equation 2.

The denoising distribution pθ(xt−1|xt) can be written as:

Z

p(z)q(xt−1|xt, x0 = Gθ(xt, z)) dz.

(7)

Inspired by the self-supervised learning method of (Liu et al. 2020), when trained with real xt−1 and xt, another decoder takes the global context token h from the discrimi- nator and reconstructs the layout x0 = De(h). With such a constraint, we can ensure that the discriminator has learned effective layout features. The training objective for the dis-

Eq(Xt−1|Xt)[−Log(D(Xt−1, Xt))]+

Eq(x0|xt)[Lrec(x0, De(h))]].

(8)

DogLayout for Discrete Data.

We Are The First To Discover

that adding a diffusion process to GANs enables the gener- ation of discrete data. The introduction of the diffusion pro- cess addresses two challenges that GANs face with discrete

Data, For Two Specific Reasons:

1. All operations on the generator’s output x0 = G(xt, z) are differentiable. Instead of applying an argmax to x0, we use Equation 2 to compute the predicted noisy lay- out xt−1. Meanwhile, the operations of the discriminator are all on xt−1, ensuring that the gradient flows normally towards the generator after back-propagation.

2. The discriminator no longer directly sees the output of the generator, except when T = 1. Since all noisy layouts

Deployment In Out-Of-Position Situations

D. Bendjaballah1, A. Bouchoucha1, M. L. Sahli1,2* and J-C. Gelin2

Abstract

Side-impact collisions represent the second greatest cause of fatality in motor vehicle accidents. Side-impact airbags have been installed in recent model year vehicle due to its effectiveness in reducing passengers’ injuries and fatality rates. In meeting these requirements, simulations of folding and deploying airbags are very useful and are widely used. The paper presents a simulation method for the deploying airbags using three materials in different working conditions. Finite element analysis is primarily used to evaluate this concept. In these simulations, the gas flow is described by the conservation laws of mass, momentum, and energy. The numerical results indicate that the FE method in this paper is capable of capturing airbag deploying process accurately.

Keywords: Airbag simulations, Out-of-position, Crash, Modeling, Out-of-position

Background

The passive safety of cars has become a very high prior- ity issue for the automotive industry. Today, there are not only one or two airbags in a car; certain models have ten times more than that. With the increasing usage of airbags, the number of accidents where the airbag itself can cause an injury to the occupant also increases

(Augenstein Et Al. 2003; Gabauer And Gabler 2010;

Audrey et al. 2011). As is well known, safety belts are also now devices designed to provide protection to the users of vehicles during crash events, minimizing the loads necessary to adapt their movement to the move- ment of the car (Freesmeier and Butler 1999; Schmitt et al. 1997). In general, the seat belt is designed to restrain the occupant in the vehicle and prevent the

Occupant From Having Harsh Contacts With Interior

surfaces of the vehicles. The airbag acts to cushion any impact with vehicle structure and has positive internal pressure, which can exert distributed restraining forces over the head and face. As a safety component of auto- mobile, an airbag decreases occupants’ injury likelihood effectively in case of an accident (Ruff et al. 2007). These safety elements can reduce the death rates on the roads, and its protection effects have been widely approved (Crandall et al. 2001; Teru and Ishikawa 2003). With computational tools such as finite element methods designed for dynamic contact problems, crashworthiness simulations can now be used with reliable accuracy to evaluate occupant protection in various collision condi- tions with safety metric/parameters such as acceleration, head injury criteria, intrusion distance, intrusion vel- ocity, and neck forces (neck injury risk or whiplash).

Thus, new types of airbag products are being developed to handle different collision scenarios.

Become Standard Equipment On Most New Passenger

vehicles (Braver and Kyrychenko 2004; Teng et al. 2007; Yoganandan et al. 2007). The airbag cushion is com- posed of a woven fabric which is rapidly inflated during a car crash. The airbag dissipates the passenger’s kinetic energy thereby reducing injury through biaxial stretching of the fabric bag and escaping gas through vents. There- fore, the performance of the airbag is greatly influenced by the mechanical properties of the fabric. Generally, air bags are designed to deploy in a crash that is equivalent to a vehicle crashing into a solid wall at 8 to 14 mph.

Air bags most often deploy when a vehicle collides with another vehicle or with a solid object like a tree. There are various types of airbags: frontal, side-impact, and curtain airbags. In general, the passenger side airbags are usually larger than the driver airbags (see Fig. 1).

Besançon, France

© The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Bendjaballah et al. International Journal of Mechanical

Doi 10.1186/S40712-016-0070-2

Extensive studies have shown that the airbag deploy- ment in load cases consists of two occupant loading phases: a punch-out effect where the airbag bursts out of its container with the airbag and airbag module cover accelerating towards the occupant and a second loading phase during which the airbag is taking on its deployed shape and volume (membrane-loading effect). Bankdak et al. (2002) developed an experimental airbag test system to study airbag-occupant interactions during close proximity deployment. The results provided insight for simulating the effect of inflation energy and mass flow on target response. Bedard et al. (2002) found that while left-side (driver-side) impacts accounted for only 13.5% of all crashes, the fatality rate among these

Crashes Was 68.3% In Comparison To Front Impact

(48.3%), right-side impact (31.3%), and rear impact (38.4%). These studies underscore the importance of oc- cupant safety during side-impact collisions. In the last years, the current market requested to reduce the time and cost airbag development. In order to achieve this result, virtual simulations play an important role since they allow to minimize the number of experimental tests (Pei et al. 2013; Cao et al. 2014). Several simulation models of airbag were established (Wang et al. 2007). It is feasible to optimize the parameters of airbag deploy- ment using simulation technology. Experimental and numerical studies have quantified injury risks to close- proximity occupants from deploying side airbags. These studies have focused on the prevention of the most ad- verse effects of airbag deployment (Duma et al. 2003).

Other studies have proposed airbag characteristics to minimize particular biomechanical responses (Haland and Pipkorn 1996). In a more recent study, Marklund and Nilsson (2003) compared deformation patterns with experimental data as well as the computational costs associated with three different airbag deployment simu- lation methods; they concluded that the SPH method is relatively inexpensive and produces incremental deform- ation patterns that compare most closely to the experi- mental results. The process of inflation of an airbag is one of the determining factors in saving lives. The duration from the initial impact of the crash to the full inflation of an airbag is about 40 ms, and during this time, the airbag goes from being in a folded state to a fully inflated state, with a high internal pressure. After achieving this state, the airbag begins to deflate, thus providing a nice cushion for the body impacting it.

Ideally, the person in the crash should come into contact with the airbag at this time. In the present study, a large volume passenger side airbag model is developed to handle different collision scenarios. The main aim is evaluate the performance of deploying of passenger side airbag using finite element methods (FEM).

Materials

The tensile specimens were made in different airbags (P: Peugeot, R: Renault, and VW: Volkswagen) with a length of 200 mm long and a width of 40 mm. Table 1 shows the mechanical properties of the airbag.

Tensile Tests

To determine the mechanical properties of the material of airbag used in the test pieces, tensile tests were performed on Lloyd EZ20 universal testing machine in Constantine. These tests were conducted using rect- angular samples. The axial force and axial displacement acquired during a test are converted into stress and the strain in order to be used for the fabric material model.

The continuous recording of the stress-strain data was performed during both the load and unload phases. A minimum of five samples were made in order to check the repeatability of the measurements. All the data was collected by using a PC-based data acquisition system and analyzed by commercial software. The picture frame test device that is made for this study is shown in Fig. 2.

Fig. 1 a Frontal and side airbags. b Oblique view of facet occupant model in sitting posture following airbag deployment (Lim et al. 2014)

0.150

Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

Page 2 Of 9

Figure 3 shows the stress-strain relationship of the airbag sample under axial tensile loads. The results are showing a linear increase in extension with the increas- ing stresses. This is an expected output and it confirms with the theoretical behavior of a sample subjected to tensile stress. The rupture strain values for different airbags (R/P/VW) were 0.322, 0.441, and 0.472, respect- ively. The measured elastic parameters (i.e., Young’s modulus E and initial yield strength) and Poisson’s ratio are summarized in Table 2. The tensile tests of the woven fabrics can show differences on mechanical prop- erties because woven fabrics can resist in-plane shear loads once the yarn lock-up angle has been reached. The differences of material property on material direction can affect the shape of fully deployed bag (see Fig. 3b).

Theoretical Background

Numerical simulations of airbags use very complex and techniques such as an orthotropic model to identify the mechanical behaviors during the airbag inflation and the fluid mechanics (gas flow) to describe the inflator gas flow (pressure gradient) and improve the representation of the pressures within the airbag. To model the airbag as an orthotropic model, three material constants have to be provided. Assuming a plane stress condition, the

Ð1Þ

where σ is the normal stress and τ is the shear stress, the subscript refers to the principal material directions, i.e., the fill and warp directions. Also, ε and γ are the strain components. The material elastic constants Qij are

Ð2Þ

where E1 and E2 are the Young’s modulus in the fill and wrap directions and G12 is the shear modulus of the fabric material. νij is the Poisson ratio of the material.

The gas exerts a pressure load on the airbag causing it to expand. This expansion puts the airbag under tensile stress lowering the expansion rate. In this study, heat conduction and heat transfer is not taken into account.

Fig. 2 A photograph of Lloyd EZ20 universal testing Fig. 3 Stress versus strain using Lloyd EZ20 machine for a three different airbags at 0° and 90° and b VW airbag test specimens at

Different Angles

Table 2 Physical and mechanical properties of the airbag

Page 3 Of 9

In the deployment of an airbag, an inflator supplies high velocity gas into an airbag causing it to expand rapidly. The gas inside the airbag is assumed to be ideal, to be of constant entropy, and to satisfy the equation of state:

Ð3Þ

Here p, ρ, and e are respectively the pressure, density, and specific internal energy, and γ is the ratio of the heat capacities of the gas. The gas flow is described by the conservation laws for mass, momentum, and energy that

Ð4Þ

here, V is a volume, A is the boundary of this volume,

N Is The Normal Vector Along The Surface A, And U

denotes the velocity vector in the volume. Applying Bernoulli’s equation in the case of an ideal gas with

Ð5Þ

Here, the subscript ex denotes quantities at the throat of the tube. Furthermore u, p, and ρ denote the quan- tities inside that part of the tube that is supplying mass.

Materials And Boundary Conditions

The airbag system mainly consists of three parts: the airbag itself, the inflator unit, and the crash sensor or diagnostic unit. Thus, to study the behavior of the airbag using FE simulations, we need to have an FE model of the airbag in the folded position. A FE model of the airbag was used to simulate the test condition as shown in Fig. 5. LS-DYNA® material model FABRIC (MAT_34) is used to simulate the airbag material. It is a variation of the layered orthotropic material model. Additionally, in the LS-DYNA® material model, fabric leakage can be accounted for. However, for this CAB material, the leak- age is almost negligible and therefore no leakage is specified. The mechanical properties can be determined from the physical test. Typical material properties for airbag fabrics are taken as given in Chawla et al. (2004a) (Table 3). These properties are used to simulate inflation process of airbag (see Table 1). The car dashboard is modeled as the rectangular thin plate using a MAT_RI-

Gid Material, And The Degrees Of Freedom Are Con-

strained in all the directions. The similar properties of thermoplastic polymer are assigned for contact purposes. The porosity of the fabric is assumed zero. The nitro- gen gas is taken for inflating the airbag. Properties of nitrogen gas and initial bag conditions are shown in Table 4. The example on which we perform the study is a typical passenger side airbag. The geometric de- tails have been measured from a commercially avail- able airbag. The initial state of the airbag is a closed rectangular whose sides are to be finished to 482 × 635 mm2 and is shown in Fig. 4.

Table 3 Material properties of airbag and rigid plate used in FE

–

Table 4 Initial values used for FE simulation of the swelling of

3.33 × 10−4

Fig. 4 The initial airbag geometry in the form of a rectangular Bendjaballah et al. International Journal of Mechanical and Materials Engineering (2017) 12:12

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