Compression Property of TPEE-3D Fibrous Material and Its Application in Mattress Structural Layer

Thermoplastic poly(ether/ester) elastomer (TPEE) has great potential as a mattress material due to its high resilience, breathability, and light weight. This study aimed to evaluate the feasibility of TPEE-3D fibrous material (T3DF), a three-dimensional block material made of TPEE fibers randomly aligned and loop-connected, for mattress application. After testing the compression properties of T3DF, the effects of T3DF structural layers on mattress firmness were investigated. The results showed that T3DF had good energy absorption capacity, broad indentation hardness range (126.94–333.82 N), and high compression deflection coefficient (2.79–4.39). The thickness and density of T3DF were the main factors influencing mattress firmness, and the impact of thickness was more significant (p < 0.05). Owing to the hard and soft segments contained in TPEE, T3DF could be used for both the padding and core layers of the mattress. The hardness value and Dsurface of the mattress with a T3DF padding layer increased with T3DF density but decreased with T3DF thickness. Moreover, the hardness value and Dsurface of the mattress with a T3DF core layer increased with T3DF density, while with T3DF thickness, its Dsurface increased and Dbottom decreased. Therefore, the thick and low-density T3DF padding layer could improve the comfort of the mattress surface, a thin T3DF core layer could satisfy both the softer surface and the firmer bottom of the mattress.


Introduction
Thermoplastic poly(ether/ester) elastomer (TPEE) is a block copolymer with a microphaseseparated structure consisting of alternately arranged poly(butylene terephthalate) (PBT) rigid blocks and poly(tetramethylene glycol) (PTMG) flexible blocks linked by ester linkages [1,2] (Figure 1).The rigid segment gives TPEE the same processing properties as thermoplastic; the soft segment gives the good elasticity of rubber.By adjusting the ratio of ester/ether segments, the hardness or other properties of TPEE can be changed to meet specific requirements.In addition, TPEE has excellent durability, heat resistance, and light weight [3].Due to its multi-functional versatility, TPEE is widely used in automotive, electronic, transportation, and medical devices, such as shock-absorbing pads for high-speed railway tracks, hydraulic hoses, and artificial heart valves, making it an ideal material for multi-cycle load application conditions [4][5][6][7].Among them, the three-dimensional TPEE fibrous material (abbreviated as T 3D F) formed by the random arrangement of TPEE fibers in a loop connection has also brought innovation to the mattress industry (Beathair ® by Toyobo (Osaka, Japan), airfiber ® by Airweave (Tokyo, Japan); fullair ® by Keyi (Wuxi, China)) (Figure 2).
Mattresses are the direct support for human sleep and rest; the characteristics of the mattress have an enormous impact on sleep [8][9][10][11].Mattress materials are the basic building blocks of a mattress.From the point of view of mattress structure, mattress materials are mainly divided into core layer materials and padding layer materials.Common core layer materials include spring, hard foam, palm, etc., while padding layer materials include polyurethane foam, natural latex, slow rebound foam, etc. [12,13].Some researchers developed new constructions of hybrid springs for mattresses and demonstrated that they could achieve the desired progressive stiffness characteristics [14,15].Chen studied the compression properties of luffa mattresses and found that compressing the LCs to the densification stage increased the firmness of the low-density luffa mattresses [16,17].Compared to polyurethane mattresses, latex mattresses reduced peak body pressure and achieved a more even distribution of pressure [18], while significantly alleviating back pain and sclerosis in humans [19,20], attributed to the superior cushioning and resilience properties of latex.Moreover, variation in material parameters also affects mattress performance.Yu-Chi found that a 30 mm thickness of padding layer on the mattress was the most appropriate [21].It is clear that the properties of a material depend largely on its response to loading, that better material properties could optimize mattress performance, and that mattress performance is significantly related to the type of materials, the choice of their parameters, and the way they are combined.Mattresses are the direct support for human sleep and rest; the characteristics of the mattress have an enormous impact on sleep [8][9][10][11].Mattress materials are the basic building blocks of a mattress.From the point of view of mattress structure, mattress materials are mainly divided into core layer materials and padding layer materials.Common core Mattresses are the direct support for human sleep and rest; the characteristics of the mattress have an enormous impact on sleep [8][9][10][11].Mattress materials are the basic building blocks of a mattress.From the point of view of mattress structure, mattress materials are mainly divided into core layer materials and padding layer materials.Common core T 3D F has the potential to be a good mattress material because it not only retains the high elasticity and durability of TPEE, but also the large amount of pore space in its structure makes it highly breathable and easier to clean than ordinary polyurethane foam.Previous studies have shown that T 3D F used in mattresses could improve pressure dispersion, facilitate turning movements and blood flow [22], and reduce the risk of pressure ulcers in long-term bedridden groups [23,24].Moreover, these types of mattresses were found to be effective in lowering the body temperature of subjects during sleep, allowing the body to enter deep sleep earlier [25].These studies aimed to evaluate the performance of this mattress at the human-mattress interface, often by comparing it to mattresses made from other materials to quantify sleep comfort after using T 3D F. However, the results were far from conclusive, in part because they did not fully consider mattress performance, particularly the mattress firmness, which in turn affects the comfort of the human-bed interface.For this reason, further systematic research is needed to determine whether T 3D F meets the design requirements for mattress firmness and whether it has more performance advantages than conventional structural layer materials.
Therefore, this study analyzed T 3D F with different densities and thicknesses.Firstly, the compression properties of T 3D F with different parameters were characterized.Secondly, the effect of T 3D F on mattress firmness was investigated when used as a padding layer or a core layer.Meanwhile, a comparative analysis of mattress firmness was carried out by combining the commonly used pocketed spring, polyurethane foam, and latex.This study can provide a theoretical basis for the reasonable application of T 3D F in mattresses.

Material and Combination of Mattress
The structure of the experimental mattresses was composed of three parts from top to bottom: a composite fabric layer, a padding layer, and a core layer.The composite fabric layer was identical for all mattresses and consisted of textile fabric, wadding fibers, and nonwoven fabric quilting, with a thickness of 20 mm.The padding layer was a single layer of material selected from TPEE-3D fibrous material (T 3D F), latex foam (LF), and polyurethane foam (PU).Two materials, T 3D F and pocketed spring (PS), were used in the core layer respectively.In addition, T 3D F was available in four densities and four thicknesses, PS was available in two spring parameters, while LF and PU were both available in one size.In total, 44 mattresses were combined.The sectional view of the mattresses is shown in Figure 3 and the detailed material parameters are listed in Table 1.layer of material selected from TPEE-3D fibrous material (T3DF), latex foam (LF), and pol-yurethane foam (PU).Two materials, T3DF and pocketed spring (PS), were used in the core layer respectively.In addition, T3DF was available in four densities and four thicknesses, PS was available in two spring parameters, while LF and PU were both available in one size.In total, 44 mattresses were combined.The sectional view of the mattresses is shown in Figure 3 and the detailed material parameters are listed in Table 1.The pocketed spring factors 2.0 60 6 refer to the wire diameter, diameter, and the number of turns of the spring, respectively.

Testing of Material Properties
(1) Quasi-static compression In order to determine the mechanical parameters of the different materials in the case of quasi-static behavior, a series of uniaxial compression experiments were carried out using an AG-X20KN universal mechanical testing machine (Shimadzu, Kyoto, Japan) (Figure 4).The loading pad was cylindrical in shape with a diameter of 100 mm and was pressed into the sample at a rate of 3 mm•min −1 to 80% of its thickness [26].To ensure reliable and statistical results, the sample size was 80 mm × 80 mm × 80 mm.Five speci-

Testing of Material Properties (1) Quasi-static compression
In order to determine the mechanical parameters of the different materials in the case of quasi-static behavior, a series of uniaxial compression experiments were carried out using an AG-X20KN universal mechanical testing machine (Shimadzu, Kyoto, Japan) (Figure 4).The loading pad was cylindrical in shape with a diameter of 100 mm and was pressed into the sample at a rate of 3 mm•min −1 to 80% of its thickness [26].To ensure reliable and statistical results, the sample size was 80 mm × 80 mm × 80 mm.Five specimens were used for each type of material and each specimen was compressed only once.It has been found that environmental conditions have a major influence on the mechanical behaviors of materials [26,27].In this study, all specimens used were tested in the same environment of 25 • C and 50% humidity, and each specimen was required to remain in this environment for 24 h prior to testing.The Young's modulus reflects the ability of a material to resist elastic deformation, the higher the value, the greater the stiffness of the material.The Young's modulus (E) of a material is derived from a linear fit of the stress-strain data for each specimen using the linear regression method [28].
The energy absorption capacity of the material is an important aspect that affects its cushioning performance when used in mattresses, which is mainly assessed by the two indices of absorbed energy and energy absorption efficiency.During compression, the area between the stress-strain curve and the strain axis of the material is the absorbed energy by the material, expressed in Equation ( 1) [29].The energy absorption efficiency (E ea ) is the ratio of the absorbed energy by the material to the corresponding stress, given by Equation (2) [30,31].
Polymers 2023, 15, 3681 5 of 21 where W is the absorbed energy (J); E ea is the energy absorption efficiency (%); ε a is the compaction strain; ε is the arbitrary strain; σ(ε) is the stress corresponding to the strain (MPa); σ a is the stress corresponding to the compaction strain (MPa).The Young's modulus reflects the ability of a material the higher the value, the greater the stiffness of the material.a material is derived from a linear fit of the stress-strain data linear regression method [28].
The energy absorption capacity of the material is an imp cushioning performance when used in mattresses, which is indices of absorbed energy and energy absorption efficienc area between the stress-strain curve and the strain axis of energy by the material, expressed in Equation ( 1) [29].The (Eea) is the ratio of the absorbed energy by the material to the by Equation (2) [30,31].
where W is the absorbed energy (J);   is the energy absorp compaction strain;  is the arbitrary strain; σ(ε) is the stress (2) Indentation property of the material The indentation property of the material was measured according to ISO 2439:2008(E) [32].The test was performed using the same machine (AG-X20KN) with a cylindrical indenter of 200 mm diameter.The loading speed was 100 mm•min −1 and the maximum compression was 75% of the initial thickness.The sample size was 400 mm × 400 mm × 50 mm, with 5 duplicate samples for each material.The indentation hardness and the compressive deflection coefficient (S f ) of the material were determined from the load-deflection curve obtained from the test.a.
Indentation hardness: the corresponding force after maintaining for the 30 s when the sample was indented to 40% of its thickness.b.
Compressive deflection coefficient: S f = F65/F25, is the ratio of the force at 65% and 25% indentation in compression.

Testing of Mattress Firmness
(1) Total firmness of the mattress The total firmness of the mattress was tested according to the ISO 23769: 2021 standard [33].The testing machine was the same as described above.The loading pad was a ball-capped rigid object with a diameter of 355 mm and a contact area of 1000 cm 2 (Figure 5).The loading speed was 90 mm•min −1 and the force range was 0-1000 N. The mattress sample had a width dimension of 500 mm × 500 mm and 5 replicates per mattress.Prior to the test, the mattress had to be kept at room temperature of 25  to the test, the mattress had to be kept at room temperature of 2 for 24 h.(2) Multilevel firmness of the mattress After 24 h in place, the mattress samples were tested on a u chine (AG-X20KN) using a 100 mm diameter cylindrical indente 250 N at a constant speed of 100 mm min −1 .Based on the load-de from the tests, the approximate modulus calculation method wa multilevel firmness of the mattress [17]: surface firmness ( Firmness rating: a number (1 decimal) from 1 to 10 characterizes the degree of firmness of the mattress, from firm to soft, as calculated in Equations ( 4) and (5) [33].
(2) Multilevel firmness of the mattress After 24 h in place, the mattress samples were tested on a universal mechanical machine (AG-X20KN) using a 100 mm diameter cylindrical indenter.The load range was 0-250 N at a constant speed of 100 mm min −1 .Based on the load-deflection curves obtained from the tests, the approximate modulus calculation method was used to determine the multilevel firmness of the mattress [17]: surface firmness (D sur f ace ), core firmness (D core ), and bottom firmness (D bottom ), as shown in Equations ( 6)- (8), in MPa.
where D sur f ace , D core , and D bottom represent the modulus between 4 and 40 N (surface), 40 and 200 N (core), 200 N and 250 N (bottom); ε represents the strain at 4 N, 40 N, 200 N, and 250 N; S is the bottom area of the indenter.

Statistical Analysis
For the data obtained from the tests, the normal distribution was first analyzed for significance using the Kolmogorov-Smirnov test (sig.> 0.05).One-way analysis of variance (ANOVA) was used to analyze the differences in each index between T 3D F of different densities and between other materials.In addition, a two-way ANOVA was used to determine the main effects of density and thickness on mattress firmness and their interactions when T 3D F was used for the mattress structural layer.Duncan's test was performed separately to determine significant differences in mattress firmness within the density and thickness groups.Mattress firmness was also compared between the use of T 3D F and the use of other regular materials.Statistical analyses were performed using SPSS 20.0 statistics software (Chicago, IL, USA) at the 5% level of significance.

TPEE-3D Fibrous Material
The non-linear curves showed the viscoelasticity of T 3D F (Figure 6a).The compression curves gradually transitioned from the elastic deformation phase (phase I) to the plastic strengthening phase (phase II) and compacting phase (phase III), which deviated from Hooke's law gradually.The mesh skeleton of T 3D F, the main stressed part, first underwent elastic deformation.Due to the small strain range in this phase (0-0.13),T 3D F would return to its original state after stress relief.The compressive E of T 3D F ranged from 0.016 MPa to 0.044 MPa, which increased with increasing density (Figure 6b), and the difference in E between any two densities was statistically significant (p < 0.001).

Statistical Analysis
For the data obtained from the tests, the normal distribution was first analyzed for significance using the Kolmogorov-Smirnov test (sig.> 0.05).One-way analysis of variance (ANOVA) was used to analyze the differences in each index between T3DF of different densities and between other materials.In addition, a two-way ANOVA was used to determine the main effects of density and thickness on mattress firmness and their interactions when T3DF was used for the mattress structural layer.Duncan's test was performed separately to determine significant differences in mattress firmness within the density and thickness groups.Mattress firmness was also compared between the use of T3DF and the use of other regular materials.Statistical analyses were performed using SPSS 20.0 statistics software (Chicago, IL, USA) at the 5% level of significance.

TPEE-3D Fibrous Material
The non-linear curves showed the viscoelasticity of T3DF (Figure 6a).The compression curves gradually transitioned from the elastic deformation phase (phase I) to the plastic strengthening phase (phase II) and compacting phase (phase III), which deviated from Hooke's law gradually.The mesh skeleton of T3DF, the main stressed part, first underwent elastic deformation.Due to the small strain range in this phase (0-0.13),T3DF would return to its original state after stress relief.The compressive E of T3DF ranged from 0.016 MPa to 0.044 MPa, which increased with increasing density (Figure 6b), and the difference in E between any two densities was statistically significant (p < 0.001).In phase II, the T3DF mesh skeleton underwent partial plastic deformation due to the high stress, and its polyester fibers began to be stressed simultaneously.During the deformation process, some of the stress was consumed, resulting in a rapid increase in strain and a relatively small increase in stress.When the compressive stress on T3DF reached a Figure 6.Results of quasi-static compression of T 3D F. (a) Stress-strain curve.The stress-strain curve of T 3D F during compression consists of three distinct phases: the elastic deformation phase (phase I), the plastic strengthening phase (phase II), and the compacting phase (phase III).(b) Young's modulus (E).Variation of E of T 3D F with its four densities.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).In phase II, the T 3D F mesh skeleton underwent partial plastic deformation due to the high stress, and its polyester fibers began to be stressed simultaneously.During the deformation process, some of the stress was consumed, resulting in a rapid increase in strain and a relatively small increase in stress.When the compressive stress on T 3D F reached a certain value, the mesh skeleton was completely deformed, the stress increased sharply with the strain, the pores within the skeleton were compacted, and the curve entered phase III.Moreover, the strain range of phase II decreased as the density of T 3D F increased, meaning that the denser T 3D F entered phase III earlier.At the same strain, the compressive stress gradually increased with increasing T 3D F density, indicating that the denser T 3D F was stiffer, i.e., the polyester fibers forming the skeleton were stiffer and could withstand greater stress.
Figure 7a shows that the absorbed energy of T 3D F decreased with increasing density in the stress range of 0-0.005MPa and gradually increased when the stress exceeded 0.009 MPa.However, there was no regularity in the variation of absorbed energy with density among the stress range of 0.005-0.009MPa.Due to the large strain range (0.13-0.63), phase II was the main phase of energy absorption and the increments of T 3D F stress and absorbed energy were calculated in Figure 7b.At the same strain of T 3D F, the higher the stress, the more energy was absorbed, so 75 kg m −3 T 3D F (referred to as T 3D F 75) absorbed the most energy in phase II with an increase of 0.0038 J.
Polymers 2023, 15, x FOR PEER REVIEW 8 of 21 certain value, the mesh skeleton was completely deformed, the stress increased sharply with the strain, the pores within the skeleton were compacted, and the curve entered phase III.Moreover, the strain range of phase II decreased as the density of T3DF increased, meaning that the denser T3DF entered phase III earlier.At the same strain, the compressive stress gradually increased with increasing T3DF density, indicating that the denser T3DF was stiffer, i.e., the polyester fibers forming the skeleton were stiffer and could withstand greater stress.Figure 7a shows that the absorbed energy of T3DF decreased with increasing density in the stress range of 0-0.005MPa and gradually increased when the stress exceeded 0.009 MPa.However, there was no regularity in the variation of absorbed energy with density among the stress range of 0.005-0.009MPa.Due to the large strain range (0.13-0.63), phase II was the main phase of energy absorption and the increments of T3DF stress and absorbed energy were calculated in Figure 7b.At the same strain of T3DF, the higher the stress, the more energy was absorbed, so 75 kg m −3 T3DF (referred to as T3DF 75) absorbed the most energy in phase II with an increase of 0.0038 J.
The Eea values of T3DF tended to increase and then decrease with the stress (Figure 7c), suggesting the existence of a peak value at which the energy absorption capacity of T3DF was optimal.Figure 7d shows that the maximum Eea value of T3DF increased with density, and the stresses corresponding to the maximum Eea values for four densities of T3DF (45-75 kg•m −3 ) were 0.004 MPa, 0.007 MPa, 0.008 MPa, and 0.011 MPa, respectively.The E ea values of T 3D F tended to increase and then decrease with the stress (Figure 7c), suggesting the existence of a peak value at which the energy absorption capacity of T 3D F was optimal.Figure 7d shows that the maximum E ea value of T 3D F increased with density, and the stresses corresponding to the maximum E ea values for four densities of T 3D F (45-75 kg•m −3 ) were 0.004 MPa, 0.007 MPa, 0.008 MPa, and 0.011 MPa, respectively.
Table 2 lists the results of the indentation properties of T 3D F. The indentation hardness ranged from 126.94 N to 333.82 N and increased with density.T 3D F 45 was the softest, in agreement with the quasi-static compression results described above.The S f value characterized the deformation resistance of the material, and a higher S f value indicated a softer surface or harder base.The S f value of T 3D F decreased with increasing density and all S f values were greater than 2.5.Therefore, the surface of low-density T 3D F was softer and the base of high-density T 3D F was harder. 1 IFD is the indentation force deflection at n% compression. 2S f is compression deflection coefficient. 3Data are mean ± standard deviation (SD).

Comparison of the Properties between T 3D F and Other Materials
The stress-strain curves of PU, LF, and T 3D F 45 (Figure 8a) all correspond to the three phases of compression of porous materials: phase I, elastic deformation; phase II, plastic strengthening; and phase III, compaction.However, the change in each material during compression was not uniform and at the same strain, the materials could be in different phases of deformation.The three phases of the PU curve were the easiest to distinguish, particularly phase II, where the curve converged to a horizontal line, with a smaller increase in stress but a greater deformation in compression, in contrast to the other two materials.For the curves of LF and T 3D F 45, both phases I were present only in small strain segments, while the stresses in phase II were relatively more variable.Specifically, when the strain was less than 0.28, the PU could withstand more stress at the same strain.In the strain range of 0.28-0.36,T 3D F 45 maintained a high stress level.Then, the stress of LF remained higher after strain exceeded 0.36.In addition, the E of PU was significantly higher than that of T 3D F 45 and LF (p < 0.001), whereas there was no significant difference between the E of T 3D F 45 and LF (p = 0.065) (Figure 8b).
Figure 9a indicates that the energy absorbed by the materials varied with the stress.LF absorbed the most energy when the stress was less than 0.0023 MPa, whereas in the range 0.0023-0.0072MPa, the comparison of energy absorbed was PU > T 3D F 45 > LF.The pattern of E ea was consistent with the energy absorbed (Figure 9b).PU had the highest E ea (0.44%) at the stress of 0.0033 MPa, followed by T 3D F 45 with a peak E ea of 0.32%.The results implied that the maximum E ea of PU was the highest, but it occurred at lower stresses.In contrast, T 3D F could absorb more energy at higher stress and more energy could be absorbed at higher density (Figure 7a), implying that the energy absorption capacity of T 3D F was significantly better than that of PU and LF.
As shown in Table 3, the indentation hardness of PU was the highest, followed by LF, while that of T 3D F 45 was the lowest (126.94N).In addition, LF had the highest S f value and 25% lower compression force (69.33 N), meaning that LF had the softest surface.ANOVA showed that the difference in S f values between T 3D F 45 and LF was not significant (p = 0.082), but both were significantly greater than PU (p < 0.05), indicating that the S f value of T 3D F 45 was comparable to that of LF and superior to that of PU. segments, while the stresses in phase II were relatively more variable.Specifically, when the strain was less than 0.28, the PU could withstand more stress at the same strain.In the strain range of 0.28-0.36,T3DF 45 maintained a high stress level.Then, the stress of LF remained higher after strain exceeded 0.36.In addition, the E of PU was significantly higher than that of T3DF 45 and LF (p < 0.001), whereas there was no significant difference between the E of T3DF 45 and LF (p = 0.065) (Figure 8b). Figure 9a indicates that the energy absorbed by the materials varied with the stress.LF absorbed the most energy when the stress was less than 0.0023 MPa, whereas in the range 0.0023-0.0072MPa, the comparison of energy absorbed was PU > T3DF 45 > LF.The pattern of Eea was consistent with the energy absorbed (Figure 9b).PU had the highest Eea (0.44%) at the stress of 0.0033 MPa, followed by T3DF 45 with a peak Eea of 0.32%.The results implied that the maximum Eea of PU was the highest, but it occurred at lower stresses.
In contrast, T3DF could absorb more energy at higher stress and more energy could be absorbed at higher density (Figure 7a), implying that the energy absorption capacity of T3DF was significantly better than that of PU and LF.As shown in Table 3, the indentation hardness of PU was the highest, followed by LF, while that of T3DF 45 was the lowest (126.94N).In LF had the highest Sf value and 25% lower compression force (69.33 N), meaning that LF had the softest surface.ANOVA showed that the difference in Sf values between T3DF 45 and LF was not significant (p = 0.082), but both were significantly greater than PU (p < 0.05), indicating that the Sf value of T3DF 45 was comparable to that of LF and superior to that of PU.    4 shows that the density and thickness of the T 3D F padding layer had a significant effect on mattress firmness (p < 0.05), but there was no interaction between them (p = 0.148), i.e., the influence of thickness on mattress firmness did not differ between densities.From the F-value, the influence of thickness on mattress firmness was greater than that of density, indicating the importance of thickness selection in the structure of the mattress padding layer.As shown by the between-subjects effect test (Table 5), both density and thickness of T 3D F had a significant effect (p < 0.05) on the hardness value, firmness rating, D sur f ace , and D bottom of the mattress, while the greatest influence was found on D sur f ace (F D = 9.834, F T = 14.849).Therefore, the effects of the thickness and density of the T 3D F padding layers on the mattress firmness were compared according to the mean of their main effects.Under the T 3D F padding layer of different densities, the mattress firmness is shown in Figure 10.As the density increased, the hardness value increased and the firmness rating decreased (Figure 10a), the mattress became firmer.The difference between the low-density (45-55 kg•m −3 ) and high-density (65-75 kg•m −3 ) T 3D F padding layer was significant (p < 0.05) for both indices.In addition, the firmness rating of mattresses ranged from 2.3 to 5.3, indicating that with the same core layer (PS: 2.0 60 6/80), the mattress could be configured with different firmness, from moderately soft to firm, with the available density of T 3D F padding layers.

TPEE-3D Fibrous Material for Mattress Padding Layers
The multilevel firmness of the mattress gradually increased from the surface to the bottom (Figure 10b).As the density of the T 3D F padding layer increased, the D sur f ace of the mattress increased, while the D core and D bottom decreased.The mattress with the T 3D F 45 padding layer had the softest D sur f ace and the firmest D core and D bottom , which could be influenced by the compression process of the mattress.The softer the surface (T 3D F 45), the greater the deformation of the mattress; after continued compression, the indenter came into contact with the spring core layer zone in advance, making the compressible thickness of the mattress smaller; and the spring's resistance to deformation increased with the force, making the mattress require more force to deform.Duncan's test revealed that the D sur f ace of the mattress with T 3D F 45 padding layer was significantly lower than that of T 3D F 65 and T 3D F 75 (p = 0.020, p = 0.000), and the difference between the D sur f ace of T 3D F 55 and T 3D F 75 was also significant (p = 0.005).However, there was no significant difference between D bottom of T 3D F 55 and T 3D F 65 (p = 0.919), while the remaining two densities were significantly different (p < 0.05).
Figure 11 shows the mattress firmness between two thicknesses of the T 3D F padding layer.As the thickness increased from 20 mm to 40 mm, the hardness value decreased and the firmness rating increased (Figure 11a), indicating that the total firmness decreased with the padding thickness and there was a significant difference in hardness values between two thicknesses (p = 0.009).Moreover, D sur f ace and D bottom decreased significantly with thickness (p = 0.006, p = 0.039), while D core was similar (p = 0.176) (Figure 10b).In general, increasing the thickness of the padding layer enhanced the softness of the mattress. 1Values in bold indicate the maximum F-value in the same column.
Under the T3DF padding layer of different densities, the mattress firmness is shown in Figure 10.As the density increased, the hardness value increased and the firmness rating decreased (Figure 10a), the mattress became firmer.The difference between the lowdensity (45-55 kg•m −3 ) and high-density (65-75 kg•m −3 ) T3DF padding layer was significant (p < 0.05) for both indices.In addition, the firmness rating of mattresses ranged from 2.3 to 5.3, indicating that with the same core layer (PS: 2.0 60 6/80), the mattress could be configured with different firmness, from moderately soft to firm, with the available density of T3DF padding layers.The multilevel firmness of the mattress gradually increased from the surface to the bottom (Figure 10b).As the density of the T3DF padding layer increased, the   of the mattress increased, while the   and   decreased.The mattress with the T3DF 45 padding layer had the softest   and the firmest   and   , which could be influenced by the compression process of the mattress.The softer the surface (T3DF 45), the greater the deformation of the mattress; after continued compression, the indenter came into contact with the spring core layer zone in advance, making the compressible thickness of the mattress smaller; and the spring's resistance to deformation increased with the force, making the mattress require more force to deform.Duncan's test revealed that the   of the mattress with T3DF 45 padding layer was significantly lower than that of T3DF 65 and T3DF 75 (p = 0.020, p = 0.000), and the difference between the   of T3DF 55 and T3DF 75 was also significant (p = 0.005).However, there was no significant difference between   of T3DF 55 and T3DF 65 (p = 0.919), while the remaining two densities were significantly different (p < 0.05).
Figure 11 shows the mattress firmness between two thicknesses of the T3DF padding layer.As the thickness increased from 20 mm to 40 mm, the hardness value decreased and the firmness rating increased (Figure 11a), indicating that the total firmness decreased with the padding thickness and there was a significant difference in hardness values between two thicknesses (p = 0.009).Moreover,   and   decreased significantly with thickness (p = 0.006, p = 0.039), while   was similar (p = 0.176) (Figure 10b).In general, increasing the thickness of the padding layer enhanced the softness of the mattress.

Comparison of Mattress Firmness between T3DF and Other Padding Materials
The differences in mattress firmness between single material PU, LF, and T3DF padding layers are illustrated in Figure 12 when the core layers were all PS (2.0 60 6).The hardness value was T3DF 75 > PU > LF > T3DF 45, with the firmness rating reversed (Figure 12a).This indicated that the mattress with the T3DF 45 padding layer had the lowest total firmness and belonged to the medium-firm mattresses (Hs = 5.8).The ANOVA showed that the differences in total firmness between the different padding materials were significant (p < 0.05), except for LF and PU (p > 0.05).

Comparison of Mattress Firmness between T 3D F and Other Padding Materials
The differences in mattress firmness between single material PU, LF, and T 3D F padding layers are illustrated in Figure 12 when the core layers were all PS (2.0 60 6).The hardness value was T 3D F 75 > PU > LF > T 3D F 45, with the firmness rating reversed (Figure 12a).This indicated that the mattress with the T 3D F 45 padding layer had the lowest total firmness and belonged to the medium-firm mattresses (H s = 5.8).The ANOVA showed that the differences in total firmness between the different padding materials were significant (p < 0.05), except for LF and PU (p > 0.05).Figure 12b shows that the   of the mattress between different padding materials was PU > T3DF 75 > LF > T3DF 45; the   of the mattress with PU padding layer was 2.02 times higher than that of T3DF 45 and was significantly different from other padding layers (p < 0.05).In addition, the   of the mattress was comparable between T3DF 75 and LF padding layer, and the   of the mattress with T3DF 45 padding layer was significantly lower than that of LF (p = 0.009).Therefore, the use of the T3DF padding layer could significantly reduce the   of the spring mattress, and the mattress surface was softer than LF when low-density T3DF was used.
The   of the mattresses with different padding materials was T3DF 45 > LF > T3DF 75 > PU, and the   of the mattress with T3DF 45 padding layer was significantly higher than that of the PU (p = 0.017), which was influenced by the   .The softer surface resulted in more deformation, so that more force was required to deform the mattress further, whereas the deformation of the mattress was relatively less for the same force, i.e., the mattress was firmer.The change in   was similar to that of   .On the other hand, T3DF 45 was an excellent material for the padding layer, even superior to LF.

Effect of the T3DF Core Layer on Mattress Firmness
When T3DF was used for the mattress core layer, the density, thickness, and their interaction all had a significant effect on mattress firmness (p < 0.05) (Table 6), and the influence of thickness was greater than that of density (F = 208.981).This meant that thickness was an important factor and the effect of thickness on mattress firmness varied across densities.Further checking the results of the main effects (Table 7), thickness and density had a significant effect on all indicators of mattress firmness (p < 0.05), while the interaction only had a significant effect on   and   (p < 0.05).In addition, the F-value shows that thickness and density had the greatest effect on   , while the interaction had the greatest effect on   .Therefore, the effects of density and thickness on hardness value, firmness rating, and   were directly based on mean comparisons of main effects, while their effects on   and   were analyzed by means of their individual effects.Figure 12b shows that the D sur f ace of the mattress between different padding materials was PU > T 3D F 75 > LF > T 3D F 45; the D sur f ace of the mattress with PU padding layer was 2.02 times higher than that of T 3D F 45 and was significantly different from other padding layers (p < 0.05).In addition, the D sur f ace of the mattress was comparable between T 3D F 75 and LF padding layer, and the D sur f ace of the mattress with T 3D F 45 padding layer was significantly lower than that of LF (p = 0.009).Therefore, the use of the T 3D F padding layer could significantly reduce the D sur f ace of the spring mattress, and the mattress surface was softer than LF when low-density T 3D F was used.
The D core of the mattresses with different padding materials was T 3D F 45 > LF > T 3D F 75 > PU, and the D core of the mattress with T 3D F 45 padding layer was significantly higher than that of the PU (p = 0.017), which was influenced by the D sur f ace .The softer surface resulted in more deformation, so that more force was required to deform the mattress further, whereas the deformation of the mattress was relatively less for the same force, i.e., the mattress was firmer.The change in D bottom was similar to that of D core .On the other hand, T 3D F 45 was an excellent material for the padding layer, even superior to LF.

Effect of the T 3D F Core Layer on Mattress Firmness
When T 3D F was used for the mattress core layer, the density, thickness, and their interaction all had a significant effect on mattress firmness (p < 0.05) (Table 6), and the influence of thickness was greater than that of density (F = 208.981).This meant that thickness was an important factor and the effect of thickness on mattress firmness varied across densities.Further checking the results of the main effects (Table 7), thickness and density had a significant effect on all indicators of mattress firmness (p < 0.05), while the interaction only had a significant effect on D core and D bottom (p < 0.05).In addition, the F-value shows that thickness and density had the greatest effect on D bottom , while the interaction had the greatest effect on D core .Therefore, the effects of density and thickness on hardness value, firmness rating, and D sur f ace were directly based on mean comparisons of main effects, while their effects on D core and D bottom were analyzed by means of their individual effects.Figure 13 shows the effect of the density and thickness of T 3D F core layer on the hardness value, firmness rating, and D sur f ace .As the density increased, the hardness value and D sur f ace increased while the firmness rating decreased, i.e., the mattress's total firmness became firmer (Figure 13a).The differences in hardness value or D sur f ace between four densities were not significant (p = 0.062, p = 0.499).However, the mattress with T 3D F 45 core layer had a significantly higher firmness rating than the others (p < 0.05).Furthermore, as the thickness of the T 3D F core layer increased, the hardness value decreased while the firmness rating and D sur f ace increased (Figure 13b).All three indices were significantly different between different thicknesses (p < 0.05).This indicates that the thicker the T 3D F core layer, the softer the total firmness and the firmer the mattress surface.Moreover, the mattresses with a T 3D F core layer were all classified as firm mattresses (H s : 0-2).Figure 13 shows the effect of the density and thickness of T3DF core layer on the hardness value, firmness rating, and   .As the density increased, the hardness value and   increased while the firmness rating decreased, i.e., the mattress's total firmness became firmer (Figure 13a).The differences in hardness value or   between four densities were not significant (p = 0.062, p = 0.499).However, the mattress with T3DF 45 core layer had a significantly higher firmness rating than the others (p < 0.05).Furthermore, as the thickness of the T3DF core layer increased, the hardness value decreased while the firmness rating and   increased (Figure 13b).All three indices were significantly different between different thicknesses (p < 0.05).This indicates that the thicker the T3DF core layer, the softer the total firmness and the firmer the mattress surface.Moreover, the mattresses with a T3DF core layer were all classified as firm mattresses (Hs: 0-2).When the T3DF density ranged from 45 kg•m −3 to 75 kg•m −3 , the differences in   and   of mattresses with three thicknesses of T3DF core layers are shown in Figure 14.In the case of T3DF 45 core layer,   and   decreased with increasing thickness, indicating that the mattress with the thicker core layer had a softer core and bottom, When the T 3D F density ranged from 45 kg•m −3 to 75 kg•m −3 , the differences in D core and D bottom of mattresses with three thicknesses of T 3D F core layers are shown in Figure 14.In the case of T 3D F 45 core layer, D core and D bottom decreased with increasing thickness, indicating that the mattress with the thicker core layer had a softer core and bottom, while for other densities, only D bottom was negatively correlated with thickness.The comparisons showed that all D core and D bottom of the mattresses were significantly different between the core layer thicknesses (p < 0.05), except for the D core of the T 3D F 55 core layer (p > 0.05).
Polymers 2023, 15, x FOR PEER REVIEW 15 of 21 while for other densities, only   was negatively correlated with thickness.The comparisons showed that all   and   of the mattresses were significantly different between the core layer thicknesses (p < 0.05), except for the   of the T3DF 55 core layer (p > 0.05).Figure 15 shows the variation of   and   of the mattress among the four densities of T3DF core layers at each thickness.When the core layer thickness was 80 mm, the   of the mattress gradually increased with the density, and there were significant differences among the four densities (p < 0.05) (Figure 15a).However, when the thickness was 40 or 60 mm, the effect of the density of the core layer on   of the mattress was not remarkable (p > 0.05).This could be influenced by the structure of T3DF, which consisted of strips of hollow filaments arranged in a random longitudinal and horizontal pattern; when T3DF was cut into different thicknesses, the size and distribution of the pores on different cross-sections were different (Figure 2), which led to the uneven density distribution of T3DF, and the smaller the thickness, the greater the porosity, which in turn affected the hardness of the material and its mattress firmness.Therefore, the influence of the core layer density on the mattress decreases as the thickness decreases.Figure 15 shows the variation of D core and D bottom of the mattress among the four densities of T 3D F core layers at each thickness.When the core layer thickness was 80 mm, the D core of the mattress gradually increased with the density, and there were significant differences among the four densities (p < 0.05) (Figure 15a).However, when the thickness was 40 or 60 mm, the effect of the density of the core layer on D core of the mattress was not remarkable (p > 0.05).This could be influenced by the structure of T 3D F, which consisted of strips of hollow filaments arranged in a random longitudinal and horizontal pattern; when T 3D F was cut into different thicknesses, the size and distribution of the pores on different cross-sections were different (Figure 2), which led to the uneven density distribution of T 3D F, and the smaller the thickness, the greater the porosity, which in turn affected the hardness of the material and its mattress firmness.Therefore, the influence of the core layer density on the mattress decreases as the thickness decreases.
The D bottom (Figure 15b) of the mattress decreased with increasing density at thicknesses of 40 mm and 60 mm, but it does not have a linear law with the change in density at thickness of 80 mm, which could be influenced by the D bottom .ANOVA showed that the effect of density on D bottom was statistically significant at all thicknesses (p < 0.05).Moreover, the mattress always had the highest D bottom in the T 3D F 45 core layer, which was consistent with the results for the T 3D F padding layer.

Comparison of Mattress Firmness between T 3D F and Other Core Materials
The mattress firmness of the different core layers (PS versus T 3D F) was compared at the same padding layers (LF, 40 mm) (Figure 16).The comparison of the hardness value showed T 3D F 75 > PS 2.18 > T 3D F 45 > PS 2.08, with the firmness rating reversed.The total firmness of the mattress differed significantly (p < 0.05) between the core layers.
Regarding the multilevel firmness of the mattress, the D sur f ace of the four core layers was similar, while the D core and D bottom were significantly different (p < 0.05).The D core of the T 3D F 75 core layer mattress was significantly higher (p < 0.05), which may be influenced by the hardness of the core layer material.Due to the change in strain of the mattress during the compression process, the D bottom was the lowest.
Polymers 2023, 15, 3681 16 of 21  not remarkable (p > 0.05).This could be influenced by the structure of T3DF, which consisted of strips of hollow filaments arranged in a random longitudinal and horizontal pattern; when T3DF was cut into different thicknesses, the size and distribution of the pores on different cross-sections were different (Figure 2), which led to the uneven density distribution of T3DF, and the smaller the thickness, the greater the porosity, which in turn affected the hardness of the material and its mattress firmness.Therefore, the influence of the core layer density on the mattress decreases as the thickness decreases.The   (Figure 15b) of the mattress decreased with increasing density at thicknesses of 40 mm and 60 mm, but it does not have a linear law with the change in density at thickness of 80 mm, which could be influenced by the   .ANOVA showed that the effect of density on   was statistically significant at all thicknesses (p < 0.05).Moreover, the mattress always had the highest   in the T3DF 45 core layer, which was consistent with the results for the T3DF padding layer.

Comparison of Mattress Firmness between T3DF and Other Core Materials
The mattress firmness of the different core layers (PS versus T3DF) was compared at the same padding layers (LF, 40 mm) (Figure 16).The comparison of the hardness value showed T3DF 75 > PS 2.18 > T3DF 45 > PS 2.08, with the firmness rating reversed.The total firmness of the mattress differed significantly (p < 0.05) between the core layers.
Regarding the multilevel firmness of the mattress, the   of the four core layers was similar, while the   and   were significantly different (p < 0.05).The   of the T3DF 75 core layer mattress was significantly higher (p < 0.05), which may be influenced by the hardness of the core layer material.Due to the change in strain of the mattress during the compression process, the   was the lowest.

Discussion
The mattress structure, the material of the mattress and its combination, directly affects the firmness of the mattress, which is an important aspect affecting the comfort of the human-mattress interface [34].In this study, T3DF was introduced as the structural layer material of the mattress.Taking advantage of the good energy absorption capacity and larger compression deflection coefficient (Sf) of T3DF, it performed well in both the mattress padding and core layers.Experiments suggested that a reasonable choice of T3DF thickness and the structural layer used for it could better regulate the mattress firmness.Thus, T3DF was a preferable substitute for mattress material.With the progress of science and the continuous improvement of material properties, the application of T3DF in mattresses will be continuously expanded.

Discussion
The mattress structure, the material of the mattress and its combination, directly affects the firmness of the mattress, which is an important aspect affecting the comfort of the human-mattress interface [34].In this study, T 3D F was introduced as the structural layer material of the mattress.Taking advantage of the good energy absorption capacity and larger compression deflection coefficient (S f ) of T 3D F, it performed well in both the mattress padding and core layers.Experiments suggested that a reasonable choice of T 3D F thickness and the structural layer used for it could better regulate the mattress firmness.Thus, T 3D F was a preferable substitute for mattress material.With the progress of science and the continuous improvement of material properties, the application of T 3D F in mattresses will be continuously expanded.
Energy absorption capacity is an important parameter that visually reflects the cushioning performance of the material.Mattress materials with better cushioning performance can absorb more impact energy and keep the stress transmitted to the body at a lower threshold [35,36].This study revealed that the peak energy absorption of T 3D F ranged from 0.0028 to 0.0085 J and increased with increasing density (Figure 7a).The best energy absorption of T 3D F was found when the stress range was 0.004-0.011MPa (Figure 7c).The difference in energy absorption of the material was related to its deformation mechanism.When T 3D F was compressed, as the density increased, the greater the strength of the individual fibers that formed the T 3D F mesh skeleton, the greater the stress it could withstand and the higher the energy absorption capacity.Through the energy absorption diagram, T 3D F with the optimum energy absorption capacity could be selected for different stress limits.
In addition, the energy absorption capacity of T 3D F was significantly higher than PU and better than LF, except for T 3D F 45 (Figure 9), which was mainly attributed to the large amount of pore space in the T 3D F structure [37].From loofah, which also contained many pores, it was found that the low-density loofah could absorb higher energy in the range of 0.01-0.035MPa with a maximum E ea of about 0.4 [17].However, the loofah treated with compression absorbed more energy due to its higher stress (0-0.56MPa).In contrast, the stress range of loofah was almost seven times higher than that of T 3D F, but the maximum E ea increased by only 25% (0.32 versus 0.4), indicating that the energy absorption capacity of T 3D F remained superior for the same stress range.On the other hand, T 3D F can also be recovered and degraded for recycling, reducing plastic emissions, and ensuring environmental sustainability.
A higher S f value indicated a softer surface or a harder bottom of the material, which was directly related to the support capacity at different load levels [38,39].The S f values of T 3D F ranged from 2.9 to 4.3 and decreased with increasing density (Table 2).This meant that when T 3D F was used for the mattress, its performance in reducing body pressure gradually decreased with density, but the resistance of the mattress to the bottom gradually increased after loading.Therefore, T 3D F could be used not only as a padding layer to meet the softness requirement in contact with the human body, but also as a core layer with sufficient hardness to provide good body support.
Compared to PU and LF, the S f value of T 3D F 45 was comparable to LF and significantly higher than PU (Table 3).Scarfato found the S f value of PU to be 2.7 [39], similar to the present study.Thus, the low-density of T 3D F was more suitable for use as a padding layer, the same as the LF, providing a softer surface for mattresses than that of PU.
The mattress padding layer was in close contact with the human body and soft padding materials were usually used to improve comfort, reduce pressure on bony prominences, and prevent pressure sores [40].When T 3D F was used as the padding layer, its density and thickness were important factors influencing mattress firmness (Table 5), with a greater effect of thickness, especially on the D sur f ace .A moderate increase in the thickness of the padding layer would result in a softer mattress surface [21], which was consistent with the results of this study.In addition, the strain range of the tested surface firmness was 0-0.25, which was still within the range of the padding thickness; thus, the padding layer was the main load-bearing area.As the density increased, the indentation hardness of T 3D F (Table 2) and the D sur f ace of the mattress both increased (Figure 10b), implying that there was a correlation between the D sur f ace of the mattress and the indentation hardness of the material.
Comparing different materials, the mattress containing T 3D F 75 padding layer had the highest D sur f ace , owing to the highest indentation hardness of T 3D F 75.The D sur f ace of the mattress with T 3D F padding layer covered the range between PU and LF, and the D sur f ace of T 3D F 45 padding layer was softer than that of LF.Ren showed that the use of softer padding materials could effectively conform to the body and facilitate better shoulder and hip coverage [41].Others found that the addition of a latex padding layer could effectively reduce mattress firmness compared to a firmer palm mattress [28].Therefore, thick and low-density T 3D F was more suitable as a padding layer to enhance the comfort of the mattress surface.Furthermore, the mattress with T 3D F padding layer offered a wide range of firmness adjustments to meet the needs of different weight groups.
The core layer of the mattress was an important structural layer to support the human body, which not only required high firmness, but also needed good elasticity to mitigate the vibrations caused by the bed frame [42].This study confirmed that the thickness of the T 3D F core layer was the primary factor influencing the D bottom of the mattress, followed by T 3D F density, and their interaction notably affected D core (Tables 6 and 7).Increasing thickness of the core layer led to a gradual decrease in D bottom .When a core layer with a thickness of 40 mm was used, the mattress had the lowest D sur f ace and the highest D bottom (Figures 13a and 15).Thus, the thickness of the core layer of the mattress does not appear to relate to better properties.A 40 mm T 3D F core layer was sufficient for the mattress with a soft surface and a firm bottom.
When the thickness was 80 mm, the D core of the mattress increased with the density of the T 3D F core layer (Figure 15a).Upon comparison with the pocketed spring, the mattress firmness was similar to that of PS 2.08 at T 3D F 45 core layer, while T 3D F 75 was greater than PS 2.18 (Figure 16).The results indicate that T 3D F, when used as a mattress core layer, was comparable to the hardness range of the spring mattress and could meet the needs of the mattress firmness design.In addition, the mattress with a T 3D F core layer displayed superior deformation performance compared to spring mattresses.This makes it suitable for a variety of bed sets or frames, particularly multifunctional ones that require high levels of mattress softness.It also aided in offering reasonable support to the human body in various sitting, lying, or semi-lying positions.
Based on the analysis of the compression properties of T 3D F and their impact on mattress firmness, a design strategy was proposed to meet the demand for regulating mattress firmness using T 3D F. Firstly, the thickness of a mattress was the main factor affecting its firmness.The choice of thickness was influenced by the mattress structure layer.If T 3D F is used as a padding layer, a moderate increase in thickness can lead to a softer surface and more even pressure dispersion.In the forthcoming studies on human-mattress interaction, the impact of T 3D F thickness on interface pressure will be probed to identify the optimal configuration for padding thickness and mattress firmness.Furthermore, a thin T 3D F core layer satisfied both the softest surface and the firmest bottom of the mattress.This design also increased the economic and practical benefits of the T 3D F mattress.Moreover, to reduce the firmness rating of the mattress with a T 3D F core layer, a softer padding material such as a slow rebound gel could be utilized in subsequent studies.
Secondly, the T 3D F density was also an important parameter in mattress design that cannot be ignored.When the density ranges from 45 kg•m −3 to 75 kg•m −3 , the E, indentation hardness, and S f values displayed significant differences across the four densities.If T 3D F is used for the mattress padding layer, low-density T 3D F with lower indentation hardness, higher energy absorption capacity, and higher S f value can be considered to make a mattress surface with better softness and cushioning.If T 3D F is used as a core layer of the mattress, it will result in a firm mattress regardless of its density.Additionally, the mattress will significantly improve in terms of support and cushioning.In addition, the pressure at the human-mattress interface depended not only on the mattress firmness, but also on the weight of the individual [42,43].Therefore, incorporating the weight of the participant in future studies would aid in the selection of a suitable density for the T 3D F core layer.

Conclusions
To fully comprehend the properties of T 3D F and its impact on mattress firmness, four densities and four thicknesses of T 3D F were incorporated for analysis.The mattress firmness was measured when T 3D F was used as the padding layer and the core layer separately.The conclusions obtained are as follows:

Figure 3 .
Figure 3. Construction of the mattresses.(a) TPEE-3D fibrous material (T 3D F) used as a padding layer, (b) T 3D F used as a core layer.

Figure 5 .
Figure 5. Setup for testing of mattress's Total firmness.

Figure 5 .
Figure 5. Setup for testing of mattress's Total firmness.The hardness value (H) and the firmness rating (H s ) are two indicators of the total firmness of a mattress, both determined from measured load-deflection curves.a. Hardness value: the average of the slopes of the load-deflection curves at 210 N, 275 N, and 340 N, as shown in Equation (3) [33], the unit is N/mm.H = C 210 + C 275 + C 340 3 (3) b.Firmness rating: a number (1 decimal) from 1 to 10 characterizes the degree of firmness of the mattress, from firm to soft, as calculated in Equations (4) and(5) [33].

Figure 6 .
Figure 6.Results of quasi-static compression of T3DF.(a) Stress-strain curve.The stress-strain curve of T3DF during compression consists of three distinct phases: the elastic deformation phase (phase Ⅰ), the plastic strengthening phase (phase II), and the compacting phase (phase Ⅲ).(b) Young's modulus (E).Variation of E of T3DF with its four densities.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 7 .
Figure 7. Energy absorption capacity of T3DF.(a) Absorbed energy; (b) Increment of stress and absorbed energy in phase II; (c) Energy absorption efficiency (Eea); (d) Variation of maximum Eea value with T3DF density.

Figure 7 .
Figure 7. Energy absorption capacity of T 3D F. (a) Absorbed energy; (b) Increment of stress and absorbed energy in phase II; (c) Energy absorption efficiency (E ea ); (d) Variation of maximum E ea value with T 3D F density.

Figure 8 .
Figure 8. Test results of quasi-static compression of the material.(a) Stress-strain curve; (b) Young's modulus (E).Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 8 .
Figure 8. Test results of quasi-static compression of the material.(a) Stress-strain curve; (b) Young's modulus (E).Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 10 .
Figure 10.Mattress firmness of the T3DF padding layer at different densities.(a) Total firmness, (b) Multilevel firmness.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 10 .
Figure 10.Mattress firmness of the T 3D F padding layer at different densities.(a) Total firmness, (b) Multilevel firmness.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 11 .
Figure 11.Mattress firmness of the T3DF padding layer at two different thicknesses.(a) Total firmness, (b) Multilevel firmness.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 11 .
Figure 11.Mattress firmness of the T 3D F padding layer at two different thicknesses.(a) Total firmness, (b) Multilevel firmness.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 12 .
Figure 12.Mattress firmness of different padding layers.(a) Total firmness, (b) Multilevel firmness.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 12 .
Figure 12.Mattress firmness of different padding layers.(a) Total firmness, (b) Multilevel firmness.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 13 .
Figure 13.Effect of core density (a) and thickness (b) on hardness value, firmness rating, and   of the mattress.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 13 .
Figure 13.Effect of core density (a) and thickness (b) on hardness value, firmness rating, and D sur f ace of the mattress.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 14 .
Figure 14.Effect of core layer thickness on the   (a) and   (b) of the mattress at different densities.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 14 .
Figure 14.Effect of core layer thickness on the D core (a) and D bottom (b) of the mattress at different densities.Significant differences between different letters in the graph are the result of multiple (p < 0.05).

Figure 15 . 21 Figure 15 .
Figure 15.Effect of core layer density on D core (a) and D bottom (b) of the mattress under different Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 16 .
Figure 16.Mattress firmness of different core layers.(a) Total firmness, (b) Multilevel firmness.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Figure 16 .
Figure 16.Mattress firmness of different core layers.(a) Total firmness, (b) Multilevel firmness.Significant differences between different letters in the graph are the result of multiple comparisons (p < 0.05).

Table 1 .
Parameters of mattress materials.

Table 1 .
Parameters of mattress materials.

Table 2 .
Indentation properties of T 3D F.

Table 3 .
Indentation properties of the materials.
1Significant difference between different letters in the same column were the result of multiple comparisons (p < 0.05).

Table 3 .
Indentation properties of the materials.

Table 4 .
Summary of analysis of variance (ANOVA) results for mattress firmness performed on the density and thickness of T 3D F padding layers.

Table 5 .
Results of main effects of density and thickness of T 3D F padding layers on each mattress firmness index.
1Values in bold indicate the maximum F-value in the same column.

Table 6 .
Summary of analysis of variance (ANOVA) results for mattress firmness performed on the density and thickness of the T 3D F core layer.

Table 7 .
Results of the main effects of density and thickness of the T 3D F core layer on each mattress firmness index.
1Values in bold indicate the maximum F-value in the same column.

Table 6 .
Summary of analysis of variance (ANOVA) results for mattress firmness performed on the density and thickness of the T3DF core layer.

Table 7 .
Results of the main effects of density and thickness of the T3DF core layer on each mattress firmness index.
1Values in bold indicate the maximum F-value in the same column.