Numerical simulation of upper garment pieces-body under different ease allowances based on the finite element contact model

1 Introduction

Garments deform to conform to the human body during the dressing process. This deformation is significantly affected by the ease allowance due to the difference in dressing intervals [1]. Furthermore, garment-wearing is a dynamic and continuously changing process [2]. The existing methods, such as physical measurement and graphical modeling, have limitations in capturing real-time changes and providing accurate intervals under different ease allowances. This directly influences the dressing effect, fit, and movement [3]. Therefore, it is essential to explore the interval distribution during the garment-wearing process to enhance the dressing effect and optimize garment design.

To address these challenges, some preliminary studies of the garment-wearing process have provided useful background for the present work. Methods such as graphical model [4], virtual simulation [5,6], and interactive adjustment [7] have been adopted. Although these methods could basically reflect the 2D distribution of garment deformation, they fail to represent the real-time 3D nature of the garment-wearing process. In response, the finite element method (FEM) of garment-wearing has been proposed. Unlike existing approaches, FEM provides a node-based, stepwise analysis of garment deformation, making it uniquely suited for capturing dynamic changes in real-time [8,9]. The dressing intervals could be derived at each node. For instance, Ghorbani et al. [10] established the FEM to simulate the dressing process of the compression garments-lower leg. And the dressing interval distribution was studied in different cross-sections of the lower leg. Later, the FEM of the socks-body was established to study the multiple dressing phenomenon, such as pressure distribution, displacement, and area shrinkage [11,12]. These dressing phenomena with time during the wearing process could be effectively acquired at each node. However, these studies focus on the 2D cross-section as the researcher’s object, and the overall 3D dressing effect cannot be effectively reflected.

Since then, recent studies have shifted toward numerical models of the 3D garment-wearing process based on FEM. In fact, this situation will more conform to the actual dress status, which could reflect the overall dressing information rather than focusing on the specific parts. Yu et al. [13] advanced this concept by simulating a 3D glove-wearing process based on the FEM based on contact theory (FECM). The pressure magnitudes and distribution over the hand dorsum, as given by a pressure glove, were measured. Liang et al. [14,15] extended this research by establishing a numerical FEM of the sports bra-body to simulate the static and dynamic contact conditions. Yu et al. [16] considered the dressing interval under the motion phase as the research object and established the FECM of the vest-body for achieving dressing simulation. These studies not only demonstrate the effectiveness of the 3D dressing simulation based on FECM but also provide a better understanding of the contact for our study.

Despite these successes, limitations remain. Most existing FECM-based studies of garment-body primarily focus on compress or tight-fitting garments [14,15,16]. Few reports comprehensively describe how the garments with different ease allowances affect the garment-wearing process. Due to the differences in supporting points during the dressing process, the dressing effects are significantly different. Thus, a comprehensive understanding of how garments with different ease allowances behave during the wearing process is still lacking.

To overcome these shortcomings, the present study focuses on simulating the garment-wearing process using the FECM, with an emphasis on garment pieces constructed with different ease allowances. Among them, the garment pieces are defined as the individual components of a complete garment that are sewn together to form its final shape [17]. Later, the FECM of the garment pieces-body was established to simulate the dressing process under gravity. Subsequently, the 3D dressing process and interval distribution were calculated. This study provides a better understanding of the dressing process under the different dressing periods and ease allowances, offering useful information for enhancing the dressing effect and optimizing garment design.

2 FECM theory of garment pieces-body

The garment pieces-body system is a complex 3D nonlinear system. To simplify the calculation, the body is described as a geometric entity composed of an undeformable torso (rigid body) and a deformable soft tissue layer (flexible body) [18]. The garment piece is considered a geometrically nonlinear elastic shell with large deformation. The dressing interval is considered a dynamic sliding interface without mutual penetration. Figure 1 illustrates the time-dependent contact coordinate system ( x i ) . In this system, the garment piece and the human body are considered as the domain ( Ω n ) , where n represents the geometric entity objects. Among them, n = 1 for the garment piece, n = 2 for the soft tissue, and n = 3 for the torso, respectively. The contact elastic-mechanical could be described by the kinematical equations (equation (2)), the constitutive equations (equation (3)), and the boundary conditions (equations (4) and (5)) [19].

Figure 1

The time-dependent contact coordinate system.

At time t = 0 , the garment piece and body do not exert any force. Thus, the garment piece occupies domain Ω 0 1 , and the body occupies domains Ω 0 2 for the soft tissue and Ω 0 3 for the torso, respectively. From t > 0 , the garment piece starts to move from the shoulder to the hem to fit the body under the gravity. It occupies new domains Ω t 1 and contacts the domain Ω t 2 of the soft tissue that corresponds to the domain Ω t 3 . In addition, three geometric entities do not penetrate each other, satisfying the physical constraint (equation (1)):

where ∅ represents the empty set, indicating that there is no mutual penetration, and Ω t 1 , Ω t 2 , and Ω t 3 represent the geometric entities at time t .

1. Kinematical equations. Assuming that µ(x) is the displacement field with respect to time t , a ( x ) is the acceleration field. Equation (2) shows the kinematical equations of elastomers:

   (2) ∂ σ ji ( x ) ∂ x j + q gi ( x ) = ρ a i ( x ) , x ∈ Ω t n , n , i , j = 1,2,3 ,

   where σ ji ( x ) represents the Cauchy stress component that gives the actual traction on the imaginary plane ij within object n , q g i ( x ) is the body force vector q g ( x ) of object n in the i direction, ρ is the density (kg/m³), and a i ( x ) is the acceleration vector within object n in the i direction.

2. Constitutive equations. According to Dan [11,12,13,14] and Yeung [19], the soft tissue in the human body can be assumed as an isotropic linear elastic material. Thus, the constitutive equations can be derived from Hooke’s law as follows:

   (3) ε 1 = 1 E ( σ x − v ( σ y + σ z ) ) , γ 1 = τ xy 2 G ε 2 = 1 E ( σ y − v ( σ x + σ z ) ) , γ 2 = τ xz 2 G ε 3 = 1 E ( σ z − v ( σ x + σ y ) ) , γ 3 = τ yz 2 G .

   Here, ε 1 , ε 2 , and ε 3 represent the linear strains at a point of elastomers in the coordinate system (%), γ 1 , γ 2 , and γ 3 are the shear strains at a point of elastomers, E is the elastic modulus (MPa), G is the shear stiffness (MPa), and v represents the Poisson’s ratio.

3. Boundary conditions. The boundary conditions of the garment pieces-body contact system include gravity and contact force. Among them, the gravity extracted on the object n is expressed as follows:

where q g n represents the gravity of object n , g is the gravity acceleration, and ρ represents the density (kg/m³) of object n .

Then, the contact force can be expressed as follows:

where q c i n represents the contact force of object n in the i direction and N i n is the unit normal vector of object n in the i direction.

3 Experimental section

In this study, the commercial FEM software ABAQUS (SIMULIA, France) was used to simulate the garment pieces-wearing process under gravity. First, the geometric models of the body and garment pieces with different ease allowances were constructed. Second, the material attributes of geometric models were defined. Then, the geometric models were assembled according to the dressing process. The appropriate element types were used to mesh. Later, the numerical processing of the dressing process was carried out by defining the boundary condition and exerting the loading to obtain the numerical solution. The real-time changes and dressing intervals were thus acquired at each node and analysis step. Figure 2 illustrates the construction producers of FECM.

Figure 2

Construction producers of FECM.

3.1 Geometric model

In this study, we applied reverse engineering technology to construct the geometric model. The method conforms to the “point-curve-surface,” which primarily follows Chen’s study [20].

3.1.1 Geometric model of the human body

To meet the requirements of body morphology characteristics, we selected the 170/92A male mannequin. The 3D scanner ([TC]², USA) was used to acquire the 3D point cloud in accordance with the ISO 20685-1:2018(E). The mean value of three-time-repeated scanning was used to reduce systematic error. Furthermore, the body point cloud was imported into reverse engineering (Geomagic Studio 2021, Raindrop, USA) to develop the geometric model. The producers were “point cloud encapsulation-curvature filling-triangular mesh refinement.” Anatomically, the body is attached to a torso with subcutaneous tissue around it. Since the torso is inside the body, the soft tissue and the torso do not penetrate each other. Thus, a “Boolean” was performed to assemble them into the torso geometric model. Figure 4(a) and (b) shows the geometric models.

3.1.2 Geometric model of the garment piece

In this study, the straight men’s jacket was chosen as the garment style, while the garment pieces had different ease allowances. Since this study focuses solely on the influence of ease allowance, the plain woven fabric was selected as the material. To ensure that the garment style remained unchanged, the shoulder width, bust, waist, and hem circumferences were graded with ease allowances of 1, 4, 4, and 4 cm, respectively, in accordance with Ancutiene and Lage [21]. The ease allowances setting was referenced to Zhang [22], covering garment pieces with different ease allowances ranging from close-fit to loose. Table 1 shows the specification data.

Table 1

Specification data

	Shoulder (cm)	Bust (cm)	Waist (cm)	Hem (cm)	Back length (cm)
Body dimension	44	92	76	86	40
Basic piece	46.8	112	110	106	40
Piece 1	44	100	98	94	40
Piece 2	44.8	104	102	98	40
Piece 3	45.8	108	106	102	40
Piece 4	47.8	116	114	110	40

To acquire the garment pieces with different ease allowances, an offset method based on the human body was applied [13,16]. This method was chosen for two main reasons: ① Due to the non-rigid deformation of the garment pieces, it is difficult to obtain the complete shape of the real garment through 3D scanning. ② It enables the garment piece that conforms to the body shape and garment structure characteristics, without the need to make the actual garment, achieving a similar effect to 3D scanning. This is also one of the advantages of FEM simulation.

The ease allowance represents the difference in the circumference direction, while the point cloud offset represents the radial distance deviation. Therefore, it is necessary to establish a mapping relationship between the point cloud offset and ease allowances. Figure 3 shows the correlation analysis results. It was observed that the point cloud offset was significantly positively correlated with the ease allowance, with coefficients (R ²) all greater than 0.987. Then, the mapping equations were established according to the correlation analysis. The deviation values (Table 2) were obtained through the mapping equations.

Figure 3

Relationship between the point offset and ease allowance.

Table 2

Point offset values

Body parts	Shoulder (mm)	Offset (mm)	Bust (mm)	Offset (mm)	Waist (mm)	Offset (mm)	Hem (mm)	Offset (mm)
Basic piece	28	8	200	27	340	53.6	200	31.4
Piece 1	0	0	80	12	240	34.7	80	12.5
Piece 2	8	2.5	120	17	260	41	120	18.8
Piece 3	18	5	160	22	300	47.3	160	25.1
Piece 4	38	10.8	240	32	380	59.9	240	37.7

Following this, the construction producers for the garment piece geometric model were the same as the human body model of the “point-curve-surface” approach. Specifically, the garment piece points were acquired based on the cloud-offset (Point phase). Then, these points were connected based on the human curvature to form structural lines of the garment piece (Line phase). Finally, the “boundary blending” was applied to fill the surface successively to obtain the geometric model (Surface phase). However, although this method could achieve the specifications, the body presents an irregular surface, particularly in the bust and scapula regions, producing a floating surplus. Direct construction will lead to a “penetration” phenomenon, causing the garment pieces’ surface to be lower than the human body during the assembly [23]. To address the above problem, the application of curvature subdivision was proposed. Then, the non-fluid surface with large curvatures was converted into multiple surfaces with gentle curvatures to solve the “penetration” phenomenon. Considering the symmetry of the garment, the front and back pieces were selected in this study. The geometric models of the garment pieces are shown in Figure 4(c) and (d).

Figure 4

Geometric models: (a) body geometric, (b) torso geometric, (c) front piece, and (d) back piece.

4 Results and discussion

4.1 3D garment-wearing simulation results based on FECM

To clearly describe the garment-wearing process, simulation results were analyzed in the time domain. Taking the basic garment piece as an example, the initial contact time between the garment pieces and body at 0.035 s, full contact was achieved at 0.06, and the dynamic equilibrium was reached by 0.1 s. Figure 5 presents the displacement magnitude nephogram of the garment pieces in the analysis step of 0.02 s. Here, the magnitude is the resultant displacement of the node of garment pieces in the X, Y, and Z directions.

Figure 5

Displacements in garment pieces in the garment-wearing process.

As depicted in Figure 5, substantial deformation occurred throughout the dressing process, particularly during the full contact and equilibrium phases. Notably, displacements of different body parts were inconsistent. As the garment piece-wearing process, the dynamic changes in the shoulder gradually increase from small displacements, while the opposite occurs in the waist and hem parts. In the full contact phase, the largest displacements were observed in the waist and hem (12.74 mm), followed by the bust (11.67 mm) and shoulder (8.47 mm). This is primarily due to the differences in surface contact areas: the shoulder’s large contact surface supports the garment pieces early and restricts excessive deformation, while the hem’s limited support leads to more significant movement. During the equilibrium phase, the displacement change was exactly the opposite. The reason for the above phenomenon is that the shoulder region is used to support the whole garment piece, resulting in the largest deformation. However, the waist and hem parts supported less, the deformation was small, and the corresponding displacement change was also small.

To better explore the displacement changes in the front and back pieces, a new path was created based on the piece’s structure line (front center line, back center line, and side seam line) at the full contact phase (0.06 s), where the displacement is at its maximum, as shown in Figure 6. It was observed that the displacement changes were basically consistent, with gradually increasing from the shoulder to the bust and hem, and the displacements followed side seam > back centerline > front centerline. This indicated that during the dressing process, the bust muscles provided a better support for the garment pieces compared to the back muscles, making it more conforming to the front of the body. Compared to the bust muscle support at the front centerline, the back centerline had support from the back muscles. However, at the side seam line, there was no effective support, and the armhole curve was in an open area, causing the garment pieces in this region to be mostly in a free state. Therefore, the displacement changes on the side were significantly greater than those on the front and back of the garment pieces.

Figure 6

Displacements of garment pieces of the structure line.

4.2 Dressing interval simulation results based on the FECM

In this study, the dressing interval is defined as the radial distance difference between the garment pieces and the body [4]. To quantify the dressing interval at different positions, the bust cross-section was selected as the research object, with the interval extracted at 15° increments.

4.2.1 Dressing interval distribution during the dressing period

Figure 7 shows the interval distribution over the time domain. The results showed that the dressing intervals of the back piece were larger than those of the front piece, with the side seam having the smallest intervals. The reasons for the above phenomenon could be attributed to differences in the anatomical support and fabric behavior. This also indicated that during the dressing process, specifically during the garment-wearing process, the bust muscles provided a better support for the garment pieces compared to the back muscles, making it more conforming to the front of the body. This is consistent with the displacement simulation results of the above dresses. Meanwhile, the side seam serves as a convergence zone for lateral fabric tension, resulting in a tighter fit and minimal intervals. This distribution phenomenon is consistent with the related studies on garment pressure and ease allowance around the torso [24].

Figure 7

Dressing interval during the dressing cycle.

Notably, the dressing intervals do not reduce to zero over the time domain. This situation is a certain discrepancy from the human body is in contact with a garment, mainly due to the limitations in the simulation precision and effectiveness. Furthermore, in the male mannequin used in this study (170/92A), the garment is predominantly supported by the shoulder region rather than the chest, further contributing to the observed non-contact in the simulation results. Figure 8 illustrates the dressing interval change. It was seen that there were significant changes at different positions. They could be divided into two different tendencies. In front and side pieces, the tendency showed that the maximum intervals were observed during the full contact phase. In contrast, another tendency was that the maximum dressing interval for the back piece occurred in the initial phase, along the back centerline. During the initial contact phase, due to the bust support, the front piece first came into contact with the body, while the back remained in a free state, leading to a significant accumulation of dressing intervals in the back piece. Meanwhile, in the full contact phase, the shoulder gradually replaced the bust as the primary support, causing the garment pieces to move away from the bust area, resulting in a larger dressing interval.

Figure 8

Dressing interval change tendency during the dressing cycle.

4.2.2 Dressing interval change tendency under different ease allowances

As illustrated in Figure 9, the bust intervals at the full contact phase were selected. It was evident that a clear positive correlation existed between the dressing intervals and ease allowances. Furthermore, as the ease allowance increased, the bust intervals gradually shifted from the back to the front. This shift reflects the changes in body support areas with different ease allowances; the main reason was that the bust protrusion weakened, with the back muscles gradually replacing the pectoral muscles. This also indicates that the ease allowance directly influences the 3D dressing effects.

Figure 9

Dressing interval under different ease allowances.

4.3 Validation of the FECM simulation results

The results calculated by the actual basic garment and simulated by the FECM are shown in Figure 10. The mean difference and root mean square error are used to characterize the difference between the simulation and measurement results. The Pearson correlations between simulation and measurement results are about 0.81. This demonstrates the effectiveness of the dressing intervals predicted by the FECM to some extent. However, the inconsistencies mainly occurred in the front piece due to two main reasons. On the one hand, during the simulation, the front piece is fixed at the front center, but this cannot be effectively achieved in actual wear. On the other hand, the accuracy of the FECM simulation is affected by the mesh density, contact functions, etc. In this study, these factors were not refined, resulting in the largest error in the front region.

Figure 10

Validation of the FECM simulation results.

5 Conclusion

This study proposed the 3D dressing simulation of garment pieces-body with different ease allowances based on the FECM. The displacement changes and interval distribution under the dressing period and ease allowances were analyzed. The main conclusions were as follows:

1. Experiments showed that a 3D dressing simulation based on the FECM was successfully established. The displacements of the garment pieces mainly occurred in the full contact and equilibrium phases during the dressing phase. The dynamic changes in the shoulder gradually increased from small displacements, while the waist and hem areas exhibited the opposite trend. The maximum displacement occurred in the full contact phase, and the displacements followed waist > bust > shoulders because of the change in the supporting parts.

2. According to the interval simulation results under dressing periods and ease allowances, the back piece reaches its maximum dressing interval during the initial phase. Meanwhile, the front piece and side seam reach their maximum during the full contact phase. As the ease allowance increased, the dressing interval gradually shifted from the back to the front piece.

Next, we plan to optimize the mesh refinement in high-curvature areas and refine the contact algorithm in FECM to better simulate realistic pressure/contact behaviors during the garment-wearing process. This will provide an effective and scientific approach to enhance the 3D dressing effect.