Mechanical properties of polyolefin elastomer and its effect on pressure distribution of mattress body

doi:10.19491/j.issn.1001-9278.2023.11.004

Abstract

Abstract:

In this paper， polyolefin elastomer （POE） was selected as the core material for the mattress. Through the static and fatigue durability tests towards POE specimens， the loading deformation curves of each specimen were compared and analyzed， and the influencing factors of POE on their anti⁃fatigue compression and support performance were discussed. Meanwhile， the nonlinear mechanical behavior of POE was characterized by choosing the 2nd⁃order Ogden model and the 3rd⁃parameter Mooney⁃Rivlin model to simplify the human⁃bed interface contact process. The pressure⁃reducing performance of the POE mattress was evaluated through finite elements. The results indicated that there was no apparent geometric relationship between the thickness and hardness loss of POE， which seems not to increase significantly with an increase in the density. The density had little effect on the minimum static buffer coefficient. The compression coefficient of POE was greater than 2.8， and the hardness pressure reached 0.77 N/cm². These results can meet the support requirements of people with different weights for mattress materials. The 2nd⁃order Ogden model and the 3⁃parameter Mooney⁃Rivlin model have an ability to predict the large deformation of POE materials. However， the 3⁃parameter Mooney⁃Rivlin model is insufficient in describing the small deformation range. The POE mattress with two densities was more uniform and hierarchical in stress transmission than the natural latex/palm fiber mattress. The peak pressure decompression percentage was as high as 94.11 % and 94.23 %， which was enough to meet the requirement of daily production and life.

Key words: polyolefin elastomer, mechanical property, hyperelastic model, finite element simulation, decompression performance

CLC Number:

TQ325.1

PAN Hongyang, CHEN Zongyong, LIAO Tingmao, YUAN Hong. Mechanical properties of polyolefin elastomer and its effect on pressure distribution of mattress body[J]. China Plastics, 2023, 37(11): 24-34.

Figures/Tables 17

Fig.1. MTS 831.10 material testing machine

POE试件	C⁃1	C⁃2	C⁃3	平均值	标准差
低密度	73.56	73.62	73.64	73.61	0.04
高密度	75.30	77.76	76.28	77.11	1.59

Tab.1. Statistical table of POE specimens of two densities kg·m-3

试件编号	质量/g	密度/kg·m^-3	d₁-d₂/mm	$Δ d$ /%	H₁/N	H₂/N	$Δ H$ /%
D1⁃1	526.38	72.91	5.67	11.34	442.59	142.03	67.91
D1⁃2	524.97	72.71	7.62	15.24	299.13	129.32	56.77
平均值	525.68	72.81	6.65	13.29	370.86	135.68	62.34
标准差	1.00	0.14	1.38	2.76	101.44	8.99	7.88
D2⁃1	574.91	79.63	6.78	13.56	377.97	123.04	67.45
D2⁃2	584.25	80.92	5.63	11.26	396.15	159.76	59.67
D2⁃3	579.39	80.25	5.61	11.22	407.08	161.19	60.40
平均值	579.52	80.27	6.01	12.01	393.73	148.00	62.51
标准差	4.67	0.65	0.67	1.34	14.70	21.62	4.30

试件编号	质量/g	密度/kg·m^-3	d₁-d₂/mm	$Δ d$ /%	H₁/N	H₂/N	$Δ H$ /%
D1⁃1	526.38	72.91	5.67	11.34	442.59	142.03	67.91
D1⁃2	524.97	72.71	7.62	15.24	299.13	129.32	56.77
平均值	525.68	72.81	6.65	13.29	370.86	135.68	62.34
标准差	1.00	0.14	1.38	2.76	101.44	8.99	7.88
D2⁃1	574.91	79.63	6.78	13.56	377.97	123.04	67.45
D2⁃2	584.25	80.92	5.63	11.26	396.15	159.76	59.67
D2⁃3	579.39	80.25	5.61	11.22	407.08	161.19	60.40
平均值	579.52	80.27	6.01	12.01	393.73	148.00	62.51
标准差	4.67	0.65	0.67	1.34	14.70	21.62	4.30

Tab.2. Thickness and hardness loss percentage of POE with different density under fatigue test

Fig.2. Force⁃displacement curves of the HC hardness test

样品编号	M_n	S_f	HA_{40 %/30 s}/N	HB_{40 %/0 s}/N	HC_{25 %/30 s}/N	HC_{40 %/30 s}/N	HC_{65 %/30 s}/N
D1⁃1	13.13	3.36	292.06	313.25	257.85	381.94	825.65
D1⁃2	13.05	4.19	312.96	335.05	243.09	365.98	849.16
D1⁃3	13.44	3.86	320.55	346.49	273.96	424.39	931.39
D2⁃1	13.66	3.46	454.50	492.16	402.12	595.66	1 377.76
D2⁃2	13.39	3.40	502.48	542.12	447.57	662.68	1 414.88
D2⁃3	11.30	3.29	411.52	443.06	361.63	559.22	1 176.62

Tab.3. Mechanical properties of the POEs

Fig.3. Static buffer curves of the POEs

Fig.4. POE mean stress⁃strain curve

Fig.5. Comparison of Mooney⁃Rivlin model fitting results with experimental data

Fig.6. Comparison of Ogden model fitting results with experimental data

Fig.7. Comparison of Yeoh model fitting results with experimental data

超弹性模型	Mooney⁃Rivlin（三参数）				Ogden（N=2）					Yeoh（N=3）
拟合参数	C₁₀	C₀₁	C₁₁	R²	u₁	α₁	u₂	α₂	R²	C₁₀	C₂₀	C₃₀	R²
低密度试件	7 051.0	-3 126.0	253.0	0.980 8	10 200.0	7.05	9 743.0	-3.55	0.999 2	3 067.0	-1 169.0	235.7	0.973 3
高密度试件	9 830.0	-4 264.0	344.8	0.988 1	13 950.0	6.36	13 140.0	-3.21	0.999 8	4 408.0	-1 609.0	324.0	0.982 4

Tab.4. Fitting coefficient of the hyperelastic constitutive model

Fig.8. POE finite element model

Fig.9. Comparison of finite element result and experiment data

Fig.10. Simplified human⁃bed interface contact model

材料

E_z/

MPa

υ_z

E_xy/

MPa

υ_xy

MPa

ρ/

kg·m^-3

Tab.5. Finite element model parameters of the natural latex/palm fiber

Fig.11. Simulation cloud map of the natural latex/palm fiber mattress

超弹性模型	低密度试件		高密度试件
超弹性模型	体压分布	定向变形	体压分布	定向变形
三参数Mooney⁃Rivlin模型
二阶Ogden模型

Tab.6. Finite element simulation results of two hyperelastic models of the POE specimens

References 42

1	Tonetti L， Martoni M， Natale V. Effects of different mattresses on sleep quality in healthy subjects： an actigraphic study［J］. Biological Rhythm Research， 2011， 42（2）： 89⁃97.
2	Yu Hyunsoo， Oh⁃Soon Shin， Kim Sayup， et al. Effect of an inflatable air mattress with variable rigidity on sleep quality［J］. Sensors， 2020， 20（18）： 5317.
3	Rebecca Robbins， Mahmoud Affouf， Azizi Seixas， et al. Four⁃year trends in sleep duration and quality： a longitudinal study using data from a commercially available sleep tracker［J］. Journal of Medical Internet Research， 2020， 22： 14735.
4	Scott Jonathon P R， McNaughton Lars R， Polman Remco C J. Effects of sleep deprivation and exercise on cognitive， motor performance and mood［J］. Physiology & Behavior， 2006， 87（2）： 396⁃408.
5	Chen Zongyong， Li Yuqian， Liu Rong， et al. Effects of interface pressure distribution on human sleep quality［J］. PLOS One， 2014， 9（6）： 99969.
6	Se Jin Park， Min Seung Nam， Murali Subramaniyam， et al. The evaluation of compatibility between human and mattress using EMG［C］//Advances in Human Aspects of Healthcare： Kraków， Poland， AHFE International， 2021：8 347⁃8 352.
7	Jacobson Bert H， Tia Wallace， Hugh Gemmell. Subjective rating of perceived back pain， stiffness and sleep quality following introduction of medium⁃firm bedding systems［J］. Journal of Chiropractic Medicine， 2006， 5（4）： 128⁃134.
8	Lee Hyunja， Sejin Park. Quantitative effects of mattress types （comfortable vs. uncomfortable） on sleep quality through polysomnography and skin temperature［J］. International Journal of Industrial Ergonomics， 2006， 36（11）： 943⁃949.
9	赵欢，申黎明. 空气纤维材料床垫对人⁃床界面温度及人体热舒适的影响［J］. 家具， 2019， 40（4）： 103⁃108.
	ZHAO H， SHEN L M. The effect of air fiber materials mattress on human⁃mattress interface temperature and thermal comfort of human body［J］. Furniture， 2019， 40（4）： 103⁃108.
10	王静，史永森，李亚玲，等. 聚烯烃弹性体催化剂研究进展［J］. 分子催化， 2020， 34（6）： 579⁃591.
	WANG J， SHI Y S， LI Y L， et al. The development of catalysts for polyolefin⁃based elastomer［J］. Journal of Molecular Catalysis（China）， 2020， 34（6）： 579⁃591.
11	Zhao Xin⁃Tong， Yong⁃Feng Men. Fractionation of polyolefin elastomer by a modified SSA technique［J］. Chinese Journal of Polymer Science， 2022， 40（10）： 1 252⁃1 258.
12	Zhang Heng， Meng Yuan， Cao Yufeng， et al. Form⁃stable phase change materials based on polyolefin elastomer and octadecylamine⁃functionalized graphene for thermal energy storage［J］. Nanotechnology， 2020， 31（24）： 245402.
13	吴薇，贾珺博，王文燕，等. 聚烯烃弹性体研究进展［J］. 弹性体， 2022， 32（4）： 90⁃94.
	WU W， JIA J B， WANG W Y， et al. Research progress of polyolefin elastomers［J］. China Elastomerics， 2022， 32（4）： 90⁃94.
14	赵佳仪，门永锋. 聚烯烃弹性体的拉伸形变机理研究进展［J］. 中国科学：化学， 2018， 48（8）： 894⁃901.
	ZHAO J Y， MEN Y F. Progress in understanding of deformation mechanism of polyolefin elastomers during tensile stretching［J］. Scientia Sinica（Chimica）， 2018， 48（8）： 894⁃901.
15	Choi Myung Chan， Jung Ji⁃Yeon， Chang Young⁃Wook. Shape memory thermoplastic elastomer from maleated polyolefin elastomer and nylon 12 blends［J］. Polymer Bulletin， 2014， 71（3）： 625⁃635.
16	Min⁃Su Heo， Kim Tae⁃Hoon， Chang Young⁃Wook， et al. Near⁃infrared light⁃responsive shape memory polymer fabricated from reactive melt blending of semicrystalline maleated polyolefin elastomer and polyaniline［J］. Polymers， 2021， 13（22）： 3984.
17	Bae Tae Soo，Ko Cheol Woong. Biomechanical effect of changes in bed positions and different types of mattresses in preventing decubitus ulcer［J］. Tissue Engineering and Regenerative Medicine， 2014， 11（1）： 93⁃98.
18	Edlich Richard F， Winters Kathryne L， Woodard Charles R， et al. Pressure ulcer prevention［J］. Journal of Long⁃term Effects of Medical Implants， 2004， 14（4）： 285⁃304.
19	De Vocht James W， Wilder David G， Bandstra Eric R， et al. Biomechanical evaluation of four different mattresses［J］. Applied Ergonomics， 2006， 37（3）： 297⁃304.
20	张宏玉，申黎明，房娇娇，等. TPEE空气纤维与普通海绵组合对床垫综合刚度的影响［J］. 家具， 2022， 43（2）： 8⁃12， 18.
	ZHANG H Y， SHEN L M， FANG J J， et al. The influence of combination of TPEE air fiber and common sponge on the comprehensive stiffness of mattress［J］. Furniture， 2022， 43（2）： 8⁃12， 18.
21	Cantournet S， Desmorat R， Besson J. Mullins effect and cyclic stress softening of filled elastomers by internal sliding and friction thermodynamics model［J］. International Journal of Solids and Structures， 2009， 46（11）： 2 255⁃2 264.
22	胡圣飞，陈祥星，李慧，等. 聚丙烯/木粉发泡材料的准静态压缩特性［J］. 高分子材料科学与工程， 2012， 28（11）： 55⁃58.
	HU S F， CHEN X X， LI H， et al. Quasi static compression characteristic of PP/wood flour foams［J］. Polymer Materials Science & Engineering， 2012， 28（11）： 55⁃58.
23	Casati F M， Herrington R M， Broos R， et al. Tailoring the performance of molded flexible polyurethane foams for car seats［J］. Journal of Cellular Plastics， 1998， 34（5）： 430⁃466.
24	Shen Wenqi， Vértiz Alicia M. Redefining seat comfort［J］. Sae Transactions， 1997， 106： 1 066⁃1 073.
25	Wong D W C， Wang Y， Lin J， et al. Sleeping mattress determinants and evaluation： a biomechanical review and critique［J］. PeerJ， 2019：7.
26	Du Zhaoqun， Wu Yuanxin， Li Ming， et al. Analysis of structure of warp⁃knitted spacer fabric on pressure indices［J］. Fibers and Polymers， 2015， 16（11）： 2 491⁃2 496.
27	张涵茵，王柳，王玉龙. EPO材料缓冲性能的探究［J］. 包装工程， 2019， 40（21）： 99⁃104.
	ZHANG H Y， WANG L， WANG Y L. Cushioning performance of EPO materials［J］. Packaging Engineering， 2019， 40（21）： 99⁃104.
28	Qu Mingyue， Xia Fenglin， Fang Fangfang， et al. Influence of spacer filament fineness on indentation characterizations of warp⁃knitted spacer fabrics for mattresses［J］. Journal of Engineered Fibers and Fabrics， 2022， 17： 1⁃10.
29	林玲，周雁红，张新昌. “齿形”结构EPS材料的等效厚度及静态缓冲性能研究［J］. 塑料工业， 2019， 47（11）： 87⁃91.
	LIN L， ZHOU Y H， ZHANG X C. Study on the equivalent thickness and static buffering performance of “tooth⁃shape” structure EPS foam［J］. China Plastics Industry， 2019， 47（11）： 87⁃91.
30	Junho Moon，Sinha Tridib Kumar，Kwak Sung Bok， et al. Study on seating comfort of polyurethane multilayer seat cushions［J］. International Journal of Automotive Technology， 2020， 21（5）： 1 089⁃1 095.
31	Kreter P E. Polyurethane foam physical properties as a function of foam density［J］. Journal of Cellular Plastics， 1985， 21（5）： 306⁃310.
32	Liu Yanping， Hu Hong. An experimental study of compression behavior of warp⁃knitted spacer fabric［J］. Journal of Engineered Fibers and Fabrics， 2014， 9（2）： 61⁃69.
33	Chaves Eduardo W V. Notes on continuum mechanics［M］： Springer Science & Business Media， 2013：423⁃462.
34	Peng Xiangfeng， Han Lei， Li Luxian. A consistently compressible model for the vulcanized rubber based on the Penn's experimental data［J］. Polymer Engineering and Science， 2021， 61（9）： 2 287⁃2 294.
35	Ehret A E， Stracuzzi A. Variations on Ogden’s model： close and distant relatives［J］. Philosophical Transactions of the Royal Society A： Mathematical， Physical and Engineering Sciences， 2022， 380：2234.
36	Zhou Wei， Wang Chengwen， Fan Peng， et al. The sealing effect improvement prediction of flat rubber ring in roller bit based on yeoh_revised model［J］. Materials， 2022， 15（16）： 5529.
37	Szabolcs Berezvai， Attila Kossa. Closed⁃form solution of the Ogden⁃Hill’s compressible hyperelastic model for ramp loading［J］. Mechanics of Time⁃dependent Materials， 2017， 21（2）： 263⁃286.
38	胡小玲，刘秀，李明，等. 炭黑填充橡胶超弹性本构模型的选取策略［J］. 工程力学， 2014， 31（5）： 34⁃42， 48.
	HU X L， LIU X， LI M， et al. Selection strategies of hyperelastic constitutive models for carbon black filled rubber［J］. Engineering Mechanics， 2014， 31（5）： 34⁃42， 48.
39	李雪冰，危银涛. 一种改进的Yeoh超弹性材料本构模型［J］. 工程力学， 2016， 33（12）： 38⁃43.
	LI X B， WEI Y T. An improved Yeoh constitutive model for hyperelastic material［J］. Engineering Mechanics， 2016， 33（12）： 38⁃43.
40	Melly Stephen Kirwa， Liu Liwu， Liu Yanju， et al. Modified Yeoh model with improved equibiaxial loading predictions［J］. Acta Mechanica， 2022， 233（2）： 437⁃453.
41	王鹭，付宾，杨晓翔. 炭黑填充天然橡胶Mullins效应的仿真与计算分析［J］. 计算力学学报， 2017， 34（3）： 372⁃378.
	WANG L， FU B， YANG X X. Numerical simulation and analysis of carbon⁃reinforced rubber's Mullins effect［J］. Chinese Journal of Computational Mechanics， 2017， 34（3）： 372⁃378.
42	Fan⁃Zhe Low，Chua Matthew Chin⁃Heng， Pan⁃Yin Lim， et al. Effects of mattress material on body pressure profiles in different sleeping postures［J］. Journal of Chiropractic Medicine， 2017， 16（1）： 1⁃9.

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