Measurement of local shear deformation in fabric drape using three-dimensional scanning

Abstract

We propose a measuring method of shear deformation in drape using three-dimensional (3D) scanning. We measured the local shear angles in fabric drape based on the Fabric Research Laboratories (FRL) drape test for woven fabrics using the proposed method. We investigate the effects of the relative positions of the node to the center grainlines that cross at the fabric center, and the bending and shear properties of fabric on the shear angles. To measure the local shear deformation, we obtained 3D drape shapes of four different fabrics with three to six nodes. We covered the obtained drape shapes using a fabric model composed of square cells that allowed shear deformation. By calculating the shear angles of the cells, we obtained the local shear deformation. We found that the FRL drape can be characterized by three areas, except for the flat areas of the support disks: (a) areas along the center grainlines with zero or small shear angles within 3°, which could result from single curvature bending; (b) areas in the bias directions with relatively large shear angles over 3°, which could result from double curvature bending; and (c) polygon edges connected by tangents of the support disk with relatively larger shear angles than their surroundings, which could result from both bending and shear deformation, such as folding and wrinkles. By investigating the relationships between areas with large shear angles and the bending rigidity/shear stiffness, we clarified that the bending rigidity indirectly affects the local shear deformation of drape.

Keywords

fabric drape shear deformation three-dimensional scanning double curvature

Drape is the large three-dimensional (3D) deformation of fabric that results from gravity and the mechanical properties of fabric. The drapability of fabric is important to a garment's appearance and thus the selection of fabric. The relationship between the drapability and mechanical properties of fabric has been studied since the 1950s. In 1950, Chu et al.¹ proposed the Fabric Research Laboratories (FRL) drape test and defined the drape coefficient (DC), which is an index widely used to evaluate drapability quantitatively. In 1960, they reported that the drapability of fabric was affected by the fabric weight, Young’s modulus and the moment of inertia of area, the product of which is the bending rigidity.² Cusick³ investigated the dependence of drape on the bending rigidity and shear stiffness by statistically analyzing the relationship between the DC and those mechanical properties. He showed that both bending and shear properties affect drape where the drape has curvature in more than one direction. Morooka and Niwa⁴ investigated the effect of the bending rigidity of fabric on drape in the warp, weft and 45° bias directions. They conducted multiple regressions to express the DC using the bending rigidity and weight. Niwa and Seto⁵ examined the DC using both shear and bending properties, and indicated the effect of shear and bending hysteresis on the DC. Nagai et al.⁶ investigated the effects of shear and bending on fabric drape and showed the effect of the weight and Young’s modulus in the 45° bias direction, which represents the shear stiffness. These studies revealed that drape deformation is affected by the bending rigidity, shear stiffness and weight. Drape should thus be composed of bending and shear deformation. Whenever bending occurs in more than one direction, because of the double curvature in drape, shear deformation definitely occurs and the deformation could be unequal.⁷ Thus, it is necessary to discuss the effects of bending and shear on fabric drape simultaneously.

These effects on fabric drape have been theoretically analyzed using numerical calculation under appropriate assumptions and restrictions. Cusick⁸ calculated the DC using the bending deformation model of a strip cantilever under the conditions of infinite and zero shear stiffness. Yang et al.⁹ analyzed the effect of the fabric dimension on drape deformation using the model of a circular segment cantilever for infinite shear stiffness and the deflection of strip cantilevers in radial directions for zero shear stiffness. Although they showed the effect of shear deformation on drape, it was only discussed for two cases – infinite shear stiffness and zero shear stiffness – because of the limitation of theoretical analysis.

To overcome this limitation, many researchers have analyzed fabric drape using the finite element method (FEM) with the measured and/or assumed mechanical properties of fabric. Imaoka et al.¹⁰ and Kang and Yu¹¹ calculated drape deformation using the FEM with the measured or estimated tensile and shear modulus, bending rigidity and Poisson’s ratio. They compared the shapes and contour lines of experimental and calculated drapes. Teng et al.¹² and Hu et al.¹³ simulated fabric drape behavior over circular pedestals and compared the simulated drape shape with the experimental shape. Although these researchers were able to calculate drape shape, neither study discussed the local deformation on drape.

By contrast, a particle method using a mass-spring model has also been used to simulate fabric drape for modeling and animation. Lafleur et al.¹⁴ were pioneers of clothing animation using a particle model. Breen et al.¹⁵ conducted drape simulation with approximated bending and shear curves derived from bending and shear properties. Based on their method, many researchers have developed fabric drape models by considering the mechanical properties of fabric. Mitsui et al.¹⁶ calculated fabric drape considering the nonlinearity and anisotropy of fabric. They compared their results with Breen’s method from the perspective of bending and shear recovering forces. Dai et al.¹⁷ simulated fabric drape from a drape model by reflecting the mechanical properties of fabric. In addition to bending and shear properties, Dai et al.¹⁸ accounted for fabric twist and the force and displacement relationships of various types of deformation. They simulated fabric in heart-loop tests and compared it with actual fabric. However, they showed agreement of only the shape and essential features, and local deformation in drape was not verified because of the lack of a measurement method for local shear deformation.

The drape simulations were conducted based on the measured or estimated mechanical properties. By contrast, some researchers have estimated fabric deformation theoretically or geometrically. Mack and Taylor,¹⁹ Shinohara and Uchida²⁰ and Moriguchi and Sato²¹ presented fitting equations based on the shearing behavior of woven fabric on spherical surfaces. For other 3D deformation of fabric, some researchers have proposed algorithms for covering or fitting 3D objects, such as spherical and tubular surfaces, considering the shear deformation of fabric. Heisey et al.^22,23 proposed a projection method by projecting a known 3D fabric surface onto a two-dimensional surface. Van Der Weeën²⁴ introduced algorithms for drape fabrics on doubly curved surfaces. Potluri et al.²⁵ developed a comprehensive drape model for 3D tubular surfaces using existing drape algorithms, but not the fabric drape. Vanclooster et al.²⁶ conducted forming simulations of woven textile composites using an explicit FEM. Cho et al.²⁷ proposed a 3D covering algorithm for individual pattern making. Mohammed et al.²⁸ and Kim et al.²⁹ investigated the shear deformation of fabric on a spherical surface. Despite many researchers^22–29 proposing calculating algorithms for shear deformation to form composites or for pattern making for garments, the applicability of these algorithms to fabric drape has not been verified.

By applying these algorithms to drape shapes, it will be possible to measure the local deformation of draped fabric. However, researchers have focused on the outline of the drape shape and, to the best of our knowledge, there have been no studies on the measurement of local deformation on draped fabric. To compare the shape of simulated and actual drape, May-Plumlee et al.,³⁰ Kenkare et al.³¹ and Pandurangan et al.³² measured 3D drape shape using 3D scanning technologies. Although they compared the shapes, they focused on the outline of the drape shape and did not discuss the local deformation on drape.

To clarify the effects of shear deformation on drape, in the present paper, we investigate local shear deformation in drape by measuring shear deformation in drape quantitatively, adopting 3D scanning and geometrical covering. Our fabric model covers the scanned 3D drape geometrically to allow shear and bending (out-of-plane pin-joint rotation) deformation. We calculate the shear angles in the fabric model.^27,33 By adopting this method, we managed to measure local shear angles in FRL drape, which had not been measured yet. We clarified the locations where the angle of shear deformation occurs in drapes. We also investigated the effects of the relative positions of the node to grainlines that cross at the fabric center (center grainlines), and the bending and shear properties of fabric on local shear deformation. Through this study, we can clarify the local shear deformation and effect of shear deformation on FRL drape.

Calculating method for shear deformation

The method for calculating shear deformation is based on the 3D fitting of a woven fabric model to a surface proposed by Cho et al.²⁷ A 3D scanned surface composed of triangle patches is covered with a fabric model, which is composed of square cells at an interval of r₁. To construct the fabric model that covers the surface, two crossing grainlines are assigned on the surface. From the crossing point of the two grainlines, the cells start to be constructed by allowing trellis (pin-joint) shear deformation, without elongation in the yarn direction. Because compared with shear deformation, the deformation of a woven fabric in the yarn direction under low tension is negligible, we assumed no elongation in the yarn direction in our method.⁷ Then, the construction of cells repeats at a regular interval of r₁ along the grainlines. This can be used as the covering fabric model. Consequently, the fabric model that covers the surface can be obtained by setting the two grainlines. The fitting algorithm is as follows: consider a triangle patch ΔABC of a 3D scanned surface that has the vertices A, B and C in 3D space, as shown in Figure 1. The assigned grainlines provide three points, P₀, P₁ and P₂, on the surface, where P₀ is the intersection of the two grainlines and P₁ and P₂ are given by points along each grainline with a distance r₁ from P₀. To create a cell on ΔABC, it is necessary to determine a point P₃ that meets the following conditions: (a) it is at an equal distance r₁ from P₁ and P₂; and (b) it is located in ΔABC.

Figure 1.

Fitting method.

To determine P₃, we assume two spheres of center points P₁ and P₂, with radius r₁. These two spheres intersect with a plane including P₀. The intersection plane is called Plane Π. This plane includes a circle with the center point Q and radius r₂. Then, P₃ is determined to be a point located on the circle except P₀. The position vector Q of Q can then be expressed using the position vectors P ₁ and P ₂ of points P₁ and P₂

Q = \frac{P_{1} + P_{2}}{2} = \frac{2 P_{1} + P_{12}}{2}, P_{12} = P_{2} - P_{1}

(1)

where P ₁₂ is a normal vector to Plane Π.

To investigate which edge of ΔABC intersects Plane Π, the scalar products of the vectors $QA$ , $QB$ and $QC$ , with P ₁₂, are introduced.

Three conditions need to be discussed

I: $QA$ ċ P ₁₂ ≥ 0

II: $QB$ ċ P ₁₂ ≥ 0

III: $QC$ ċ P ₁₂ ≥ 0

Either condition I is satisfied or condition II and condition III both are satisfied. Here, ΔABC is separated by Plane Π, with A on one side and B, C on the other side; that is, edges AB and AC intersect Plane Π.

Either condition II is satisfied or condition I and condition III both are satisfied. Here, ΔABC is separated by Plane Π, with B on one side and A, C on the other side; that is, edges AB and BC intersect Plane Π.

Either condition III is satisfied or condition I and condition II both are satisfied. Here, ΔABC is separated by Plane Π with C on one side and A, B on the other side; that is, edges AC and BC intersect Plane Π.

Otherwise, ΔABC is parallel to Plane Π; that is, no edge intersects Plane Π.

Based on the above conditions, two intersections E, F of ΔABC and Plane Π are defined.³⁴ Thus, if we want to confirm whether P₃ is located in ΔABC, it is necessary to investigate whether P₃ is located on line EF.

Because the point F is unknown, to find F, we introduce direction vector L and position vector E of E to express $EF$ as follows

EF = E + L t

(2)

where t is located at a distance r₂ from Q.

Thus, if P₃ is on EF, it needs to meet the condition that the distance from Q to line EF is r₂. Therefore, the position of P₃ on the surface is determined if the point meets the condition. Then, the cell can be fitted to the curved surface. By repeating the process, a fabric model is obtained that covers the entire surface. The covering process stops when P₃ cannot be found on the surface.

With the obtained fabric model, the shear angle of each cell can be calculated. Regarding the calculation of the shear deformation of one cell, because trellis shear is assumed, the shear angle θ of each fabric model cell is defined, as shown in Figure 2. Among the four angles of each fabric model cell, shear angle θ close to the crossing position of the center grainline is obtained.

Figure 2.

Calculation of shear angle θ.

To calculate shear angle θ, let P ₀, P ₂, P _3o and P _1o be the position vectors of the vertices for the initial state of a fabric model cell. When P _3o and P _1o of the cell are deformed to P ₃ and P ₁, shear angle θ at P ₀ is obtained according to the scalar products of two vectors as

cos (\frac{π}{2} - θ) = \frac{(P_{1} - P_{0}) \cdot (P_{2} - P_{0})}{| P_{1} - P_{0} | | P_{2} - P_{0} |}

(3)

When θ ≥ 0, the cell has shear deformation with elongation in the P ₀ $-$ P ₃ direction, as shown in Figure 2; when θ < 0, the cell has shear deformation with elongation in the P ₂ $-$ P ₁ direction.

The absolute value of shear angle θ is used to represent the shear deformation of each fabric cell. The elongated direction is indicated in each cell using its diagonal line.

Experimental method and validation of the proposed method

Validation experiment 1: comparison of the square cell deformation and position for the calculation and fabric

To confirm the validity of the proposed method, the FRL drape test was performed when the node number (n) was 4 for a woven fabric of wool gabardine, as shown in Table 1. In the FRL drape test, the fabric radius (R) of 14 cm and disk radius (r) of 7 cm were used according to Yang et al.⁹

Table 1.

Sample specifications

Sample	Material	Weave	Thickness (mm)	Area density w (g m⁻²)	Bending rigidity B (10⁻⁴ cN m² m⁻¹)				Shear stiffness G (cN m⁻¹ degree^–1)
Sample	Material	Weave	Thickness (mm)	Area density w (g m⁻²)	Warpwise	Weftwise	Bias (45°)	Mean	Sliding in warp direction	Sliding in weft direction	Mean
Gabardine	Wool 100%	Twill	0.509	188	8.91	5.33	6.74	6.99	54.9	75.5	65.2
Broadcloth	Cotton 100%	Plain	0.431	112	5.23	4.01	3.47	4.24	68.6	91.1	79.9
Taffeta	Polyester 100%	Plain	0.199	82.6	11.1	10.0	6.05	6.50	227	175	201
Satin	Polyester 100%	Satin	0.435	187	10.6	67.0	19.4	32.3	139	110	125
Denim	Cotton 100%	Twill	1.07	226	13.2	2.83	4.74	6.91	109	124	116

The warp and weft grainlines of the circular sample fabrics were traced as crossing at the center. These grainlines are defined as the center grainlines. Square cells with dimensions of 1 cm × 1 cm were drawn on the fabric parallelly along the center grainlines. The fabric was sandwiched between two disks with the radius of 7 cm. Then, draped fabric with drawn lattices was obtained.

Figure 3 shows the coordinate system and the measuring method of drape. The draped shape of the sample was scanned using a portable structured light 3D scanner (Artec Eva Lite, Artec 3D, Luxembourg, Luxembourg).³⁵ The scanner had two geometry-capturing cameras, one texture-capturing camera and one light generator. The structured light pattern generated by the light generator was projected onto an object. Then, the two geometry cameras captured the object image with the deformed light pattern, and the texture camera captured the object photo image without the light pattern, which is called the texture. The triangulation of the object was performed using a structured light tracking algorithm based on the captured images. The ability of a scanning system to resolve detail in the scanned object was up to 0.5 mm.

Figure 3.

Drape test and three-dimensional (3D) scanning.

Scanning was conducted from multiple directions by moving the scanner around the drape shape manually, as shown in Figure 3. A 3D polygon mesh of drape (drape mesh) with texture (photographic image of the surface) was obtained using Artec Studio v9.2 software (Artec 3D, Luxembourg, Luxembourg). At this stage, the obtained drape mesh could not be used because of noise on the surface. To remove noise, a smoothing process was applied to the drape mesh and a new smoothed drape mesh was obtained, but the texture disappeared. To set the grainlines on the smoothed 3D drape mesh, it was necessary to confirm the position of the grainlines using the texture on the smoothed drape mesh. Thus, screen images of the drape mesh with texture were captured from multiple angles in advance and the captured images were superposed on the surface of the smoothed drape mesh at the same scale. A smooth drape mesh with texture was thus obtained. The unnecessary thickness of the disk was removed. By tracing the center grainlines on the texture, the center grainlines on the smoothed drape mesh were set. Then, the obtained drape mesh was covered with the fabric model, which had a cell size of 1 cm × 1 cm. Simultaneously, the shear angle of each fabric model cell was calculated.

Then to evaluate the accuracy of fitting of the square fabric model cells on the 3D drape mesh, the lattices marked on the drape mesh and the fabric model cells were compared in terms of shape and position. We compared the coordinates of crossing points of the lattice on the scanned 3D drape mesh and crossing points of the square cells in the fabric model in the areas of the four nodes where the texture can be clearly obtained. We calculated the root mean square deviation (RMSD) of the coordinates and the distances of the corresponded points to evaluate the error.

Results

Figure 4(a) shows the 3D drape mesh with lattices after the disk was cut. Figure 4(b) shows the superposed results of lattices marked on the 3D drape mesh and the fabric model cells. Figure 4(c) shows the proposed fabric model, with colors representing the shear angle in each cell. As shown in Figure 4(b), the fabric model cells coincide with the lattices drawn on the fabric in terms of both the deformed shape and position.

Figure 4.

Lattice marked on the fabric and square fabric model cells. (Color online only.)

Using the x, y, z coordinate system shown in Figure 3, we obtained 203 sets of coordinate values for the crossing points of the lattice on the scanned 3D drape mesh and compared them with the corresponded coordinate values for the crossing points of square fabric cells. Figure 5 shows the comparison of the coordinate values. The results showed a good agreement between the points of scanned 3D drape mesh and the points of square fabric cells. In terms of x, y and z coordinate values, all of them had high coefficients of determination of 0.99. Those average differences of the x, y and z components are 0.60, 0.98 and 0.59 mm, respectively. The RMSDs are 0.30, 0.70 and 0.30, respectively. The average distance between the corresponded points is 0.86 mm. The RSMD is 0.93. Their deviation is considered to be due to the error of the 3D scanner (0.5 mm). Thus, the validity of the method is demonstrated. Therefore, by determining two center grainlines on the drape surface, local shear deformation was obtained.

Figure 5.

Comparison of the coordinate values for the crossing points of marked lattice on the scanned three-dimensional (3D) drape mesh and the corresponding points on square fabric cells: (a) x-coordinate; (b) y-coordinate; (c) z-coordinate.

Validation experiment 2: effect of the cell size on the fabric model calculation

To evaluate the effect of the square cell size, the calculated shear angles of cotton broadcloth as shown in Table 1 were compared for n = 3, but with different cell sizes of 3, 5 and 10 mm. The difference between shear angles for different cell sizes was evaluated using the shear angle ratio of each angle range, defined as follows

\begin{matrix} Shearangleratioinagivenanglerange (%) \\ = \frac{Number of cells in the given angle range}{{\begin{matrix} Total number of cells \\ - Number of square cells in the disk area \end{matrix}}} \times 100 \end{matrix}

(4)

Because the shear angle of the fabric was considered to be below 10°, the shear angle range was divided into 10 groups.

Results

Figure 6 shows a comparison of the obtained shear angle ratio for the same sample but with different cell sizes. The average of three sizes and the standard deviation among the obtained shear angle ratio for the three cell sizes are also shown. The maximum standard deviation was 2.31% for shear angles in the range of 1°–2°, which means that the difference caused by the linear approximation of a cell was small.

Figure 6.

Comparison of the shear angle ratio for broadcloth (n = 3) but with different square cell sizes in the fabric model.

Measurement of local shear deformation on Fabric Research Laboratories drape for various node numbers

Because we demonstrated the validity of the proposed method, we investigated the local shear deformation on FRL drape using the proposed method.

FRL drape tests were performed using four types of woven fabric (broadcloth, taffeta, satin and denim) to measure the shear angle of draped fabrics. The experimental conditions for the radii of the fabric sample and disks were the same as those in Validation experiment 1. The node number (n) in the tests was manually set to 3, 4, 5 or 6.⁹ To investigate the effect of the grainline direction on local shear deformation, the node locations of n = 4 were controlled with respect to the grainlines; that is, along the center grainline directions and in the bias directions. Then, the scanning process was conducted to obtain the drape mesh.

The obtained drape mesh was covered with the fabric model, which had cell sizes of 0.5 cm × 0.5 cm. Simultaneously, the shear angle of each fabric model cell was calculated. To investigate local shear deformation, the shear angle ratios for each drape mesh were calculated for the same nine groups using Equation (4).

The sample properties are presented in Table 1. The bending rigidity and shear stiffness of the samples were measured using the Kawabata Evaluation System for Fabrics (KES-FB, Kato Tech., Kyoto).³⁶

Results and discussion

Local shear deformation in FRL drape

Figure 7 shows colored cells according to the calculated shear angles of the sample fabrics in drapes and those depicted on the initial flattened patterns for various node numbers (n). The shear angle range was divided into 10 groups with an interval of 1° using the same method used in Validation experiment 2. Figure 8 shows the shear angle ratio of the samples binned with a shear interval of 1° for different node numbers.

Figure 7.

Calculated shear angles for draped broadcloth and those depicted on the initial flattened patterns for various node numbers (n). (Color online only.)

Figure 8.

Shear distributions for different samples: (a) broadcloth; (b) taffeta; (c) satin; (d) denim.

Figure 8 shows that the shear angle ratio in the shear angle range 0°–1° was highest: over 40% for all fabrics, except denim, which was over 30%. Then, the shear angle ratio decreased as the shear angle ranges increased for all samples. Relatively large shear angles over 3° were below 16% for all samples. Among the same shear angle ranges for different node numbers for a shear angle ratio for shear angles >1°, no obvious increase nor decrease was observed. However, the shear angle ratio in the range 0°–1° increased from n = 3 to n = 4 and then decreased from n = 4 to n = 6. The percentage of node numbers along the center grainlines for all nodes when n = 4 in the center grainlines (4/4 = 100%) was higher than that when n = 3 (1/3 = 33%), 5 (1/5 = 20%) and 6 (2/6 = 33%). Therefore, the shear angle ratio is related to the node position relative to the center grainlines.

From Figure 7, irrespective of the value of n and the fabric, most of the shear deformation with shear angles in the range 0°–3° was observed in the areas along the center grainlines, such as the two sides of a single node and the depressed area between adjacent nodes along those directions. Shear deformation with a shear angle >3° occurred for nodes and the depressed area in the bias directions, and along the tangents to the support disk. The results demonstrated that discontinuous deformation occurred in these areas of drape, such as buckling wrinkles. In Figure 7(b-2), larger shear angles over 7° occurred on the edges of the fabric circle. This could be because of the large depression at the edge by double curvature.

From the observations obtained from Figure 7, a drape surface is classified into four areas for shear deformation, as shown in Figure 9.

Area a: area without deformation; that is, the area of the support disk plane such that there is no bending nor shear deformation.

Polygon edge b: polygonal edges connected with tangents to the support disk with a relatively large shear deformation. There is a sudden change of fabric deformation, such as wrinkling, which could lead to discontinuous shear and bending deformation.

Area c1: areas along the center grainlines with relatively low shear angle deformation. These areas are not planar, so they could deform with single curvature bending, which is bending deformation with zero Gaussian curvature. These areas are divided into two areas, Area c1-c and Area c1-d, which are the convex area of the node and the depressed area between adjacent nodes, respectively.

Area c2: areas not along the center grainlines with non-uniform and relatively large shear angle deformation. It could deform with double curvature bending and is not in a developable surface that requires elongation and/or contraction to form. Therefore, fabric could be elongated in the bias directions because it is easy to shear. These areas are also divided into two areas: Area c2-c and Area c2-d, which are the convex area of the node and the depressed area between two adjacent nodes, respectively.

Figure 9.

Areas for bending and shear deformation in drape.

From these local shear deformations, the results demonstrate that drape deformation is characterized by four areas according to shear deformation. Consequently, the results clarify that the relative node positions along the center grainlines affect local shear deformation.

Effects of mechanical properties on local shear deformation

To clarify the relationship between shear deformation and mechanical properties, the relationships between the obtained shear angles and bending rigidity and shear stiffness of fabrics were investigated. Yang et al.⁹ and many researchers have shown that the mechanical parameter (B/w)^1/3 is a fundamental parameter related to the drape test. Niwa and Seto⁵ added the mechanical parameter (G/w)^1/3 to investigate the relationship between the drape test and mechanical properties from the analogy of (B/w)^1/3. Thus, the relationships between the shear angle ratio for shear angle >3 ° to (G/w)^1/3 in Figure 10 and to (B/w)^1/3 in Figure 11, respectively, were investigated. For G and B, the mean values of the shear stiffness and bending rigidity of the sample fabrics shown in Table 1 were used. The regression equations and corresponding coefficients of determination of the shear angle ratio for shear angle >3° to (G/w)^1/3 and (B/w)^1/3 are shown in Table 2. Figure 10, for n = 3, 5 and 6, shows that the higher the shear stiffness, the lower the shear angle ratio for shear angle >3°. This means that fabrics with high shear stiffness were less deformed by large shear angles. However, for n = 4, irrespective of the node positions and the center grainline direction, no apparent relationship between the shear angle ratio for shear angle >3° and shear rigidity was observed. This is because drape shapes can be formed without large shear deformation and are less related to the shear stiffness. It could be more related to the bending rigidity. As shown in Figure 11, irrespective of n, the higher the bending rigidity, the lower the shear angle ratio for shear angle >3°. Therefore, it is clarified that local shear deformation in drape is affected by not only the shear stiffness, but also the bending rigidity.

Figure 10.

Relationships between the shear angle ratio for shear angle >3° and (G/w)^1/3.

Figure 11.

Relationships between the shear angle ratio for shear angle >3° and (B/w)^1/3.

Table 2.

Regression equations and coefficients of determination for shear angle ratio for shear angle >3° and mechanical parameters

Relationships Number of nodes	Shear angle ratio for shear angle >3° (y) and (G/w)^1/3 (x)		Shear angle ratio for shear angle >3° (y) and (B/w)^1/3 (x)
Relationships Number of nodes	Regression equation	Coefficient of determination	Regression equation	Coefficient of determination
n = 3	y = –4.26x + 20.10	0.60	y =−5.96x + 27.0	0.43
n = 4 (Node in the center grainline direction)	y = –0.334x + 3.90	0.027	y = –3.02x + 9.47	0.80
n = 4 (Node in the bias direction)	y = 1.05x + 8.00	0.16	y = –3.00x + 15.1	0.32
n = 5	y = –6.70x + 22.5	0.45	y = –13.8x + 42.0	0.75
n = 6	y = –3.43x + 14.0	0.60	y = –6.06 + 21.9	0.68

Conclusion

We investigated the relationship between the local shear angles in drapes, the node numbers and the mechanical properties of fabric by measuring the local shear angles in FRL drape tests for four different fabrics with three to six nodes using the proposed method.. The findings are summarized below.

Place and type of deformation in drape

FRL drape can be characterized by three areas, except for the flat areas of the support disks:

areas along the center grainlines with zero or small shear angles within 3°, which could result from single curvature bending;

areas along the bias directions with relatively large shear angles over 3°, which could result from double curvature bending;

polygon edges connected with tangents of the support disk in the FRL drape test with a relatively larger shear angle than the surroundings, which could result from both bending and shear deformations, such as folding and wrinkles.

Relationship between the shear angle and the node position relative to the center grainlines

Node areas along the center grainline had smaller shear angles than the nodes in the bias direction. Therefore, we found that local shear deformation in drape is affected by the relative position of the node to the center grainline of fabric, regardless of the node numbers.

Relationship between shear deformation and mechanical properties

When n was 3, 5 and 6, the shear angles were related to both the shear stiffness and bending rigidity. Fabric with high shear stiffness and high bending rigidity forms drape without large shear angles. However, when n was 4, the large shear angles occurred with small bending rigidity, regardless of the shear stiffness. Thus, the bending rigidity indirectly affects shear deformation in drape.

Consequently, using the proposed method, we successfully measured local shear deformation in FRL drape of woven fabrics, which has not been measured yet. We also clarified the effects of the node positions relative to the center grainlines and the mechanical properties of fabric on local shear deformation. The advantage of the proposed method is that by tracing the loci of the two center grainlines, the shear deformation of the entire surface can be measured. The method provides a new means for analyzing the complicated deformation of woven fabrics. However, because the method is based on the assumption that fabric does not stretch along the yarn direction, for fabric that can stretch regardless of shear deformation, such as knitted fabric, this method cannot be applied.

Footnotes

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship and/or publication of this article: This work was supported by a Grant-in-Aid for the Shinshu University Advanced Leading Graduate Program by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. This work was also supported by JSPS KAKENHI Grant No. 17H01955.

ORCID iDs

Liu Yang

KyoungOk Kim

Masayuki Takatera

References

Chu

Cummings

Teixeira

. Mechanics of elastic performance of textile materials: Part V: a study of the factors affecting the drape of fabrics—the development of a drape meter. Text Res J 1950; 20: 539–548.

Chu

Platt

Hamburger

. Investigation of the factors affecting the drapeability of fabrics. Text Res J 1960; 30: 66–67.

Cusick

. 46—The dependence of fabric drape on bending and shear stiffness. J Text Inst Trans 1965; 56: T596–T606.

Morooka

Niwa

. Relation between drape coefficients and mechanical properties of fabrics. J Text Mach Soc Japan 1976; 22: 67–73.

Niwa

Seto

. Relationship between drapability and mechanical properties of fabrics. J Text Mach Soc Japan 1986; 39: T161–T168.

Nagai

Suda

Inagaki

. Applicability of the evaluation method of isotropic sheets drapability to that of textile fabrics. J Jpn Res Assoc Text End-Uses 2008; 49: 413–420.

Hearle

JWS

Grosberg

Backer

. Structural mechanics of fibers, yarns, and fabrics Volume 1, New York: Wiley-Interscience, 1969.

Cusick GE. A study of fabric drape. PhD Thesis, The University of Manchester, UK, 1962.

Yang

Kim

Takatera

. Effect of the fabric dimension on limits of the drape coefficient. Text Res J 2020; 90: 442–459.

10.

Imaoka

Okabe

Tomiha

, et al. Prediction of three-dimensional shapes of garments from two-dimensional paper patterns. Sen'i Gakkaishi 1989; 45: 420–426.

11.

Kang

. Drape simulation of woven fabric by using the finite-element method. J Text Inst 1995; 86: 635–648.

12.

Teng

Chen

. A finite-volume method for deformation analysis of woven fabrics. Int J Numer Meth Eng 1999; 46: 2061–2098.

13.

Chen

S-F

Teng

. Numerical drape behavior of circular fabric sheets over circular pedestals. Text Res J 2000; 70: 593–603.

14.

Lafleur B, Magnenat-Thalmann N and Thalmann D. Cloth animation with self-collision detection. In: Tosiyasu L. KUNII (ed) Modeling in computer graphics. Tokyo: Springer, 1991, pp.179–187.

15.

Breen

House

Wozny

. A particle-based model for simulating the draping behavior of woven cloth. Text Res J 1994; 64: 663–685.

16.

Mitsui

Komai

Dai

, et al. Particle model reflecting non-linearity and anisotropy of the mechanical properties of cloth and its collision and repulsion mechanism. J Inst Image Informat Televis Eng 2000; 54: 1762–1770.

17.

Dai

Furukawa

Mitsui

, et al. Drape formation based on geometric constraints and its application to skirt modelling. Int J Cloth Sci Tech 2001; 13: 23–37.

18.

Dai

Zhang

. Simulating anisotropic woven fabric deformation with a new particle model. Text Res J 2003; 73: 1091–1099.

19.

Mack

Taylor

. 39—The fitting of woven cloth to surfaces. J Text Inst Trans 1956; 47: T477–T488.

20.

Shinohara

Uchida

. The surface fitness of textile fabrics. J Tex Mach Soc Japan 1966; 19: T17–T23.

21.

Moriguchi

Sato

. Nunoji no kikagaku (geometry of fabrics). Suugaku Seminaa 1972; 8: 55–59.

22.

Heisey

Brown

Johnson

. Three-dimensional pattern drafting: Part I: projection. Text Res J 1990; 60: 690–696.

23.

Heisey

Brown

Johnson

. Three-dimensional pattern drafting: Part II: garment modeling. Text Res J 1990; 60: 731–737.

24.

Van Der Weeën

. Algorithms for draping fabrics on doubly-curved surfaces. Int J Numer Meth Eng 1991; 31: 1415–1426.

25.

Potluri

Sharma

Ramgulam

. Comprehensive drape modelling for moulding 3D textile preforms. Compos Part A-Appl S 2001; 32: 1415–1424.

26.

Vanclooster

Lomov

Verpoest

. Experimental validation of forming simulations of fabric reinforced polymers using an unsymmetrical mould configuration. Compos Part A-Appl S 2009; 40: 530–539.

27.

Cho

Komatsu

Inui

, et al. Individual pattern making using computerized draping method for clothing. Text Res J 2006; 76: 646–654.

28.

Mohammed

Lekakou

Bader

. Experimental studies and analysis of the draping of woven fabrics. Compos Part A-Appl S 2000; 31: 1409–1420.

29.

Kim

Suzuki

Takatera

. Measurements and prediction of fabric surface fitting ability under low tension. Text Res J 2018; 88: 1413–1425.

30.

May-Plumlee T, Eischen J, Kenkare N, et al. Evaluating 3D drape simulations: methods and metrics. In: international textile design and engineering conference (INT-EDEC), Edinburgh/Galashiels, UK, 22–24 September, 2003.

31.

Kenkare

Lamar

TAM

Pandurangan

, et al. Enhancing accuracy of drape simulation. Part I: investigation of drape variability via 3D scanning. J Text Inst 2008; 99: 211–218.

32.

Pandurangan

Eischen

Kenkare

, et al. Enhancing accuracy of drape simulation. Part II: optimized drape simulation using industry-specific software. J Text Inst 2008; 99: 219–226.

33.

Yang L, Kim K and Takatera M. Measurement of fabric shear in drape using three-dimensional scanning. Li Y, Zhang K, Pan Z, Li G (eds.) In: Textile Bioengineering and Informatics Symposium Proceedings (2019), Suzhou, China, 9–11 September 2019, paper no. 41, pp.303–309. Hongkong: TBIS.

34.

Bigliani R and Eischen JW. Collision detection in cloth modeling. In: House DH and Breen DE (eds) Cloth modeling and animation. Wellesley, PA: A. K. Peters, Ltd, 2000, pp.199–205.

35.

Artec Studio 9. User's guide/manual, August 2013.

36.

Kawabata S. The standardization and analysis of hand evaluation. 2nd ed. Osaka: The Textile Machinery Society Japan, 1980.