脂肪组织压缩实验中摩擦系数对力学响应的影响
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摘要
目的针对当前摩擦力对脂肪组织无约束压缩实验结果影响的不确定性,研究压缩实验中合适的摩擦系数设置及适用于模拟脂肪组织生物力学响应的材料本构模型。方法构建低应变率(0. 2 s-1)和中应变率(20 s-1)下的脂肪组织有限元模型,分别应用LS-DYNA中常用于模拟脂肪组织的线性黏弹性材料本构、Mooney-Rivlin超弹性材料本构、Ogden超弹性材料本构、软组织材料本构,在不同摩擦系数下进行无约束压缩实验,分析不同摩擦系数及本构模型对接触力大小的影响。结果 4种材料本构模型在低、中应变率下,输出的接触力均与摩擦系数呈正相关,有摩擦时的接触力比无摩擦时的接触力大50%左右。中应变率下脂肪组织的力学响应对摩擦系数的灵敏度比低应变率下的更高,且不同材料本构模型输出的接触力差异显著。结论在脂肪组织无约束压缩实验中,静摩擦系数取0. 1,动摩擦系数取0. 05是合理的,在低、中应变率下Ogden超弹性材料本构能够良好地反映脂肪组织的生物力学响应。
Objective In view of the uncertainty of the effect of friction on the experimental results of unconstrained compression of adipose tissue,the appropriate friction coefficient setting in compression experiments and the material constitutive model for simulating the biomechanical response of adipose tissue are studied. Methods The finite element( FE) models of adipose tissue used for low strain rate( 0. 2 s-1) and medium strain rate( 20 s-1) were developed. The unconstrained compression tests of adipose tissue under different friction coefficient were simulated by LS-DYNA code using the developed FE models with different constitutive models,such as linear viscoelastic material constitutive model of adipose tissue,the Mooney-Rivlin hyperelastic material constitutive model,Ogden hyperelastic constitutive materials,soft tissue material constitutive model. The influence of different friction coefficients and constitutive models on the contact force was analyzed. Results Under the low and medium strain rate,the contact force with four kinds of material constitutive models obtained from the simulations was positively correlated with the friction coefficient,and the contact force with friction was more than 50% higher than that without friction. The mechanical response of adipose tissue under medium strain rate was more sensitive to friction coefficient than that under low strain rate. Furthermore,the contact force of the constitutive models of different materials was significantly different. Conclusions For the unconstrained compression test of adipose tissue,the static friction coefficient of 0. 1 and the kinetic friction coefficient of 0. 05 are reasonable in the simulation. Under low and medium strain rate,Ogden hyperelastic constitutive models can well reflect the biomechanical response of adipose tissue.
Objective In view of the uncertainty of the effect of friction on the experimental results of unconstrained compression of adipose tissue,the appropriate friction coefficient setting in compression experiments and the material constitutive model for simulating the biomechanical response of adipose tissue are studied. Methods The finite element( FE) models of adipose tissue used for low strain rate( 0. 2 s-1) and medium strain rate( 20 s-1) were developed. The unconstrained compression tests of adipose tissue under different friction coefficient were simulated by LS-DYNA code using the developed FE models with different constitutive models,such as linear viscoelastic material constitutive model of adipose tissue,the Mooney-Rivlin hyperelastic material constitutive model,Ogden hyperelastic constitutive materials,soft tissue material constitutive model. The influence of different friction coefficients and constitutive models on the contact force was analyzed. Results Under the low and medium strain rate,the contact force with four kinds of material constitutive models obtained from the simulations was positively correlated with the friction coefficient,and the contact force with friction was more than 50% higher than that without friction. The mechanical response of adipose tissue under medium strain rate was more sensitive to friction coefficient than that under low strain rate. Furthermore,the contact force of the constitutive models of different materials was significantly different. Conclusions For the unconstrained compression test of adipose tissue,the static friction coefficient of 0. 1 and the kinetic friction coefficient of 0. 05 are reasonable in the simulation. Under low and medium strain rate,Ogden hyperelastic constitutive models can well reflect the biomechanical response of adipose tissue.
引文
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[2] Gefen A,Dilmoney B. Mechanics of the normal woman’s breast[J]. Technology and Health Care,2007,15(4):259-271.
[3] Qiu S,Zhao X,Chen J, et al. Characterizing viscoelastic properties of breast cancer tissue in a mouse model using indentation[J]. Journal of Biomechanics,2018,69:81-89.
[4] Gefen A,Megido-Ravid M,Itzchak Y. In vivo biomechanical behavior of the human heel pad during the stance phase of gait[J]. Journal of Biomechanics,2001,34(12):1661-1665.
[5] Weaver JB,Doyley M,Cheung Y,et al. Imaging the shear modulus of the heel fat pads[J]. Clinical Biomechanics,2005,20(3):312-319.
[6] Suzuki R,Ito K,Lee T,et al. In-vivo viscous properties of the heel pad by stress-relaxation experiment based on a spherical indentation[J]. Medical Engineering and Physics,2017,50:83-88.
[7] Ahanchian N,Nester CJ,Howard D,et al. Estimating the material properties of heel pad sub-layers using inverse finite element analysis[J]. Medical Engineering and Physics,2017,40:11-19.
[8] Grigoriadis G,Newell N,Carpanen D,et al. Material properties of the heel fat pad across strain rates[J]. Journal of the Mechanical Behavior of Biomedical Materials,2017,65:398-407.
[9] Samani A,Zubovits J,Plewes D. Elastic moduli of normal and pathological human breast tissues:an inversion-technique-based investigation of 169 samples[J]. Physics in Medicine and Biology,2007,52(6):1565-1576.
[10] Samani A,Plewes D. A method to measure the hyperelastic parameters of ex vivo breast tissue samples[J]. Physics in Medicine and Biology,2004,49(18):4395-4405.
[11] Miller-Young JE,Duncan NA,Baroud G. Material properties of the human calcaneal fat pad in compression:experiment and theory[J]. Journal of Biomechanics,2002,35(12):1523-1531.
[12] Erdemir A,Viveiros ML,Ulbrecht JS,et al. An inverse finiteelement model of heel-pad indentation[J]. Journal of Biomechanics,2006,39(7):1279-1286.
[13] Wearing SC,Smeathers JE,Yates B,et al. Bulk compressive properties of the heel fat pad during walking:a pilot investigation in plantar heel pain[J]. Clinical Biomechanics,2009,24(4):397-402.
[14] Spilker RL,Suh JK,Mow VC. Effects of friction on the unconfined compressive response of articular cartilage:a finite element analysis[J]. Journal of Biomechanical Engineering,1990,112(2):138-146.
[15] Armstrong CG,Lai WM,Mow VC. An analysis of the unconfined compression of articular cartilage[J]. Journal of Biomechanical Engineering,1984,106(2):165-173.
[16] Brown TD,Singerman RJ. Experimental determination of the linear biphasic constitutive coefficients of human fetal proximal femoral chondroepiphysis[J]. Journal of Biomechanics,1986,19(6):474.
[17] Wu JZ,Dong RG,Schopper AW. Analysis of effects of friction on the deformation behavior of soft tissues in unconfined compression tests[J]. Journal of Biomechanics,2004,37(1):147-155.
[18] Comley K,Fleck N. The compressive response of porcine adipose tissue from low to high strain rate[J]. International Journal of Impact Engineering,2012,46:1-10.
[19] Comley K,Fleck NA. The toughness of adipose tissue:measurements and physical basis[J]. Journal of Biomechanics,2010,43(9):1823-1826.
[20] Saraf H,Ramesh KT,Lennon AM,et al. Mechanical properties of soft human tissues under dynamic loading[J]. Journal of Biomechanics,2007,40(9):1960-1967.
[21] Engelbrektsson K. Evaluation of material models in LS-DYNA for impact simulation of white adipose tissue[D]. Goteborg,Sweden:Chalmers University of Technology,2011.
[22] Martin AD,Daniel MZ,Drinkwater DT,et al. Adipose tissue density,estimated adipose lipid fraction and whole body adiposity in male cadavers[J]. International Journal of Obesity and Related Metabolic Disorders:Journal of the International Association for the Study of Obesity,1994,18(2):79-83.
[23] Yamada H. Strength of biological materials[M]. Baltimore:Williams&Wilkins,1970.
[24] Comley K,Fleck NA. The high strain rate response of adipose tissue[C]//IUTAM Symposium on Mechanical Properties of Cellular Materials. LMT-Cachan,Cachan,France:Springer Netherlands,2009:27-33.
[25] Wu JZ,Cutlip RG,Andrew ME,et al. Simultaneous determination of the Nonlinear-elastic properties of skin and subcutaneous tissue in unconfined compression tests[J]. Skin Research and Technology,2007,13(1):34-42.
[26] Mihai LA,Chin LK,Janmey PA,et al. A comparison of hyperelastic constitutive models applicable to brain and fat tissues[J]. Journal of the Royal Society Interface,2015,12(110):486.
[27] Calvo-Gallego JL,Domínguez J,Cía TG,et al. Comparison of different constitutive models to characterize the viscoelastic properties of human abdominal adipose tissue. A pilot study[J].Journal of the Mechanical Behavior of Biomedical Materials,2018,80:293-302.
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