摘 要:探索生物力學(xué)實(shí)驗(yàn)數(shù)據(jù)加載到滑板模型的有效途徑,計(jì)算足部結(jié)構(gòu)的力學(xué)響應(yīng)。使用CT與3D掃描儀獲取足、滑板鞋和滑板數(shù)據(jù)并建立有限元模型,使用壓力平板與壓力鞋墊在自然站立狀態(tài)時(shí)驗(yàn)證模型的有效性。所建立模型包括足骨(包括跗骨、跖骨、趾骨以及脛骨腓骨遠(yuǎn)端)、軟組織、滑板鞋面、滑板鞋底、板面、連接橋、輪子以及地面,共408043個(gè)節(jié)點(diǎn),260400個(gè)網(wǎng)格單元,網(wǎng)格質(zhì)量為0.79。足底壓力峰值實(shí)測(cè)為80kPa,仿真所得為82.2kPa,誤差為2.75%。實(shí)測(cè)板底后輪處最大壓力為2.314MPa,前輪處最大壓力為1.427MPa,仿真所得后輪處應(yīng)力峰值為2.392MPa,前輪處的應(yīng)力峰值為1.479MPa,誤差分別為3.37%與3.64%。本研究構(gòu)建的滑板鞋-板-足耦合模型具有較好的幾何和力學(xué)相似性,經(jīng)驗(yàn)證有效可靠。
關(guān)鍵詞:滑板運(yùn)動(dòng);滑板鞋;有限元;多體耦合;生物力學(xué)
中圖分類號(hào):G804.64" 文獻(xiàn)標(biāo)志碼:A
文章編號(hào):1000-4939(2025)01-0236-
07
Construction and verification of foot-shoe-board finite element model in skateboard
WU Yusen,WANG Haichun,ZHU Xiaolan
(Sport Science School,Beijing Sport University,100084 Beijing,China)
Abstract:This study explored an effective way to load biomechanical data into the model,simulate the moment of skateboard,and calculate the mechanical characteristics of foot structures.A male skateboarder was recruited to select a shoe and skateboard.CT and 3D scan were used to obtain the feet of healthy skateboarder,skateboard shoes and skateboard model,and use Ansys 2020 for modeling and calculations.Sensor Medica pressure plate and Pedar pressure insole were used to obtain the mechanical characteristics of the skateboard and foot when the subjects stood on the skateboard to verify the model. The model consisted of foot bones (including tarsal,metatarsal,phalangeal,and distal tibial fibula),soft tissue,skateboard shoes upper and outsole,board,bridges,wheels and ground.There were 408043 nodes and 260400 mesh cells,and the mesh element quality was 0.79.The measured peak foot pressure was 80kPa,and the calculated peak foot stress was 82.2kPa,with an error percentage of 2.75%.The measured peak pressure of the skateboard plate is 2.314MPa at the rear wheel,the front wheel is 1.427MPa,the simulated stress peak at the rear wheel is 2.392MPa,the front wheel is 1.479MPa,the error percentage is 3.37% and 3.64%.The constructed skateboard shoe-board-foot model has good geometric and mechanical similarity, proving it is effective and reliable.
Key words:skateboarding;skateboard shoe;finite element;multibody coupling;biomechanics
滑板運(yùn)動(dòng)是在不同地形、地面及特定設(shè)施上完成各種復(fù)雜的滑行、跳躍、旋轉(zhuǎn)、翻騰等高難度動(dòng)作的技巧型板類運(yùn)動(dòng)項(xiàng)目[1]。豚跳(ollie)作為滑板運(yùn)動(dòng)的基礎(chǔ)動(dòng)作,是國(guó)內(nèi)外研究的主要技術(shù)動(dòng)作[2-3],包括準(zhǔn)備、起跳上升、下落和著地緩沖4個(gè)階段?;中枰谶\(yùn)動(dòng)狀態(tài)下的滑板板面上完成上述4個(gè)動(dòng)作,人體足部與滑板鞋、滑板鞋與滑板板面以及滑板與地面之間,分別受到摩擦力、重力與反作用力的作用[4-5]。有數(shù)據(jù)表明,滑板運(yùn)動(dòng)員從22.9cm高度落到滑板,足踝部在著地瞬間受力為4.61倍人體自身體重[6],下肢損傷在滑板運(yùn)動(dòng)中較為常見[7]。
運(yùn)動(dòng)鞋作為必要的運(yùn)動(dòng)裝備,在人體運(yùn)動(dòng),尤其是極限運(yùn)動(dòng)中起到非常重要的支撐穩(wěn)固、緩沖震蕩和吸收能量的作用[8-9]。科學(xué)的運(yùn)動(dòng)鞋結(jié)構(gòu)可以影響下肢髖、膝、踝關(guān)節(jié)參數(shù)[10],不同的中底厚度和硬度可以影響踝關(guān)節(jié)穩(wěn)定性和緩沖時(shí)間[11],具有緩震功能的鞋墊可以提高壓力疼痛的閾值,降低足部損傷風(fēng)險(xiǎn)[12]。有限元法廣泛應(yīng)用在跑鞋[13]、冰球鞋[14]、羽毛球鞋[15]、高跟鞋[16]等領(lǐng)域的研究。建立人體足部-運(yùn)動(dòng)鞋計(jì)算機(jī)模型,仿真模擬并計(jì)算得到站立[17]、行走[18]、跑步[13]等運(yùn)動(dòng)狀態(tài)下人體各結(jié)構(gòu)的力學(xué)數(shù)據(jù),通過(guò)對(duì)中底與鞋墊材料、鞋跟高度、足弓支撐傾斜角度等參數(shù)的變化進(jìn)行優(yōu)化設(shè)計(jì)[19],提升鞋類產(chǎn)品的功能性。
目前,對(duì)于滑板運(yùn)動(dòng)和滑板裝備的研究主要集中在人體運(yùn)動(dòng)學(xué)參數(shù)分析與研究方法的探索等方面。本研究擬建立符合中國(guó)人體結(jié)構(gòu)特征的滑板鞋-板-足有限元耦合模型,將運(yùn)動(dòng)生物力學(xué)實(shí)驗(yàn)數(shù)據(jù)加載到計(jì)算機(jī)模型中,實(shí)現(xiàn)對(duì)滑板運(yùn)動(dòng)各特征時(shí)刻動(dòng)作的模擬。以人體足部結(jié)構(gòu)力學(xué)響應(yīng)作為仿真計(jì)算指標(biāo)和評(píng)測(cè)指標(biāo),將滑板運(yùn)動(dòng)與滑板鞋性能研究緊密結(jié)合在一起,為后續(xù)開展滑板動(dòng)作技術(shù)分析、人體足部運(yùn)動(dòng)損傷預(yù)警以及滑板鞋設(shè)計(jì)研發(fā)等提供數(shù)據(jù)支持。
1 材料與方法
1.1 研究對(duì)象
模型基于 1 名男性大學(xué)生(年齡24歲,身高178cm,體質(zhì)量71kg,鞋碼為42,無(wú)足部或下肢損傷,具有兩年以上的滑板運(yùn)動(dòng)經(jīng)歷),在測(cè)試前簽署《知情同意書》。掃描用板是一款8.0寸標(biāo)準(zhǔn)街式滑板,板面為Deathwish(美國(guó)),橋?yàn)閠heeve的鈦合金TIAX系列,輪子為Bones STF 99A V1。掃描用鞋是一款ES’(美國(guó))滑板鞋,鞋底為橡膠,鞋面為翻毛皮材料,鞋碼為42.5。該研究方案已通過(guò)北京體育大學(xué)運(yùn)動(dòng)科學(xué)實(shí)驗(yàn)倫理委員會(huì)的審批(編號(hào)為2023143H,日期為2023年4月28日)。
1.2 有限元模型的建立與耦合
使用計(jì)算機(jī)斷層掃描儀(西門子go.top 64排128層螺旋CT機(jī),德國(guó))獲取受試者穿鞋時(shí)右腳的影像數(shù)據(jù),掃描層厚1mm。使用三維激光掃描儀(Creaform 公司,加拿大)獲取滑板、橋、輪子的三維數(shù)據(jù),掃描分辨率為0.7mm。在Mimics 21.0(Materialise 公司,比利時(shí))中對(duì)足-滑板鞋模型進(jìn)行重建,使用圖像分割技術(shù)提取骨骼、軟組織與滑板鞋的優(yōu)化蒙版,骨骼根據(jù)閾值226~2657劃分,軟組織根據(jù)閾值-700~225劃分,鞋模型根據(jù)全覆蓋閾值蒙版減去骨骼與軟組織蒙版獲得。為便于網(wǎng)格劃分以及提高計(jì)算效率,對(duì)足部所有骨骼與關(guān)節(jié)進(jìn)行了融合簡(jiǎn)化操作[20]。對(duì)骨骼、軟組織、鞋進(jìn)行重建與平滑。在Geomagic Studio 2013 (Raindrop Geomagic公司,美國(guó))中完成滑板板面及輪子模型的重建,主要包括點(diǎn)云處理、三角網(wǎng)格面片修補(bǔ)、平滑與清除不必要的特征,最后擬合NURBS曲面生成實(shí)體模型。在ANSYS2020R2(ANSYS公司,美國(guó))軟件中完成足部骨骼、足部軟組織、鞋、滑板、輪子等結(jié)構(gòu)的耦合與接觸設(shè)置。使用Slice功能對(duì)滑板鞋進(jìn)行切割將其劃分為鞋面與鞋底,通過(guò)賦予鞋底和鞋面不同的材料進(jìn)行仿真計(jì)算??紤]到滑板鞋包裹性較好的問(wèn)題,運(yùn)用布爾運(yùn)算填充足部軟組織與滑板鞋空隙,作為鞋幫內(nèi)襯[21]。
1.3 網(wǎng)格劃分與接觸設(shè)置
利用 ANSYS 2020R2(ANSYS公司,美國(guó))軟件的網(wǎng)格劃分功能,將鞋-板-足模型的單元類型定義為Solid 187實(shí)體結(jié)構(gòu)單元[22],采用自動(dòng)劃分與人工控制網(wǎng)格大小與質(zhì)量相結(jié)合的方法,對(duì)模型使用四面體單元網(wǎng)格劃分(表1)。模型中所有接觸均為“面-面”接觸,其中軟組織、內(nèi)襯、鞋面、鞋底與板面之間設(shè)定為摩擦接觸,摩擦系數(shù)為0.6[23],其余零部件間的接觸均設(shè)定為綁定接觸[14],得到的模型如圖1所示。
1.4 定義模型材料參數(shù)
足、鞋和板各結(jié)構(gòu)的材料屬性參數(shù)(表2)均參考相關(guān)文獻(xiàn)[14,20,24-28]。考慮到模型的復(fù)雜性和模擬的收斂性能,設(shè)定足部各組織為各向同性、理想均質(zhì)的線彈性材料[29-30]。足部骨骼與軟組織材料參考文獻(xiàn)[20,28]設(shè)置,滑板結(jié)構(gòu)中板面為云杉木[27],橋與輪子為結(jié)構(gòu)鋼材料。
1.5 模型載荷與邊界條件
本研究選擇ANSYS Workbench軟件中靜態(tài)結(jié)構(gòu)力學(xué)來(lái)模擬受試者右足穿滑板鞋在滑板上自然平衡站立。雙足靜止站立時(shí)每只足大約承受體重一半的力[31],本實(shí)驗(yàn)?zāi)M地面反作用力為受試者體重的一半,即355N。平衡站立時(shí)小腿肌肉中僅小腿三頭肌有明顯肌電活動(dòng)[32],本次模擬僅考慮跟腱力對(duì)足部骨骼的作用,忽略其他肌肉力[33]。站立時(shí)跟腱力大約為足部承受載荷的50%[34],本實(shí)驗(yàn)?zāi)M跟腱力為 177.5N。
模型加載與邊界條件:在足跟處施加垂直向上的跟腱力(177.5N)。由于實(shí)際測(cè)量在站立過(guò)程中人-滑板-地面系統(tǒng)所發(fā)生的垂直向下的位移數(shù)據(jù)較為困難,本研究通過(guò)固定脛腓骨上表面,在地板添加向上的位移,模擬站立狀態(tài)下的整體系統(tǒng)的位移情況。采用重復(fù)調(diào)整地面向上位移量的方法來(lái)探索系統(tǒng)的整體位移情況,最終選擇在地板上添加1.4mm的垂直向上的位移,同時(shí)約束地面支撐板在大地坐標(biāo)系中x和y軸方向的位移,模擬受試者在滑板上靜止站立狀態(tài)(圖2)。
1.6 滑板鞋-板-足有限元模型的驗(yàn)證
在本研究中,通過(guò)對(duì)比自然站立狀態(tài)下仿真計(jì)算與實(shí)際測(cè)試得到的足底、板底壓力數(shù)據(jù),驗(yàn)證耦合模型的有效性(圖3)。應(yīng)用ANSYS Workbench 2020R2軟件計(jì)算獲得自然站立狀態(tài)下足底、板底的壓力分布云圖。使用Sensor Medica 足底壓力步態(tài)分析系統(tǒng)(Sensor Medica,意大利)獲取受試者穿著滑板鞋自然靜止站立在滑板上的板底壓力數(shù)據(jù),采樣頻率為100Hz,使用Pedar壓力感應(yīng)鞋墊測(cè)試系統(tǒng)(Pedar-X;Novel,Inc.,德國(guó))同步采集足底壓力峰值及分布數(shù)據(jù),采樣頻率為50Hz。
2 研究結(jié)果
2.1 鞋-板-足有限元模型建立結(jié)果
研究采用了一名具有滑板運(yùn)動(dòng)經(jīng)歷的男性大學(xué)生健康足部CT掃描數(shù)據(jù)、滑板三維掃描數(shù)據(jù)及有限元建模軟件成功建立了滑板鞋-板-足有限元模型,包括足骨(含跗骨、跖骨、趾骨以及脛骨腓骨遠(yuǎn)端)、足部軟組織、滑板鞋面、滑板鞋底、板面、連接橋、輪子以及地面支撐板。該模型完全依據(jù)建模對(duì)象的實(shí)際形態(tài)進(jìn)行耦合,共408043個(gè)節(jié)點(diǎn),260400個(gè)網(wǎng)格單元,網(wǎng)格質(zhì)量[35]為0.79。
2.2 足底壓力數(shù)據(jù)及驗(yàn)證
實(shí)際測(cè)量受試者穿著滑板鞋雙足站立在滑板上保持靜止時(shí)的足底壓力分布情況(圖4左),足底壓力峰值為80kPa,主要位于第一趾骨處。模擬計(jì)算所得同等條件下的足底應(yīng)力分布情況(圖4右),足底應(yīng)力峰值為82.2kPa,與實(shí)測(cè)值相比誤差為2.75%。
2.3 板底壓力數(shù)據(jù)及驗(yàn)證
實(shí)驗(yàn)測(cè)得板底壓力分布主要位于后輪處(圖5左),后輪處壓力峰值為2.314MPa,前輪處壓力峰值為1.427MPa。模擬計(jì)算所得板底應(yīng)力分布主要位于后輪處(圖5右),后輪處應(yīng)力峰值為2.392MPa,與實(shí)測(cè)值相比誤差為3.37%,前輪處的應(yīng)力峰值為1.479MPa,與實(shí)測(cè)值相比誤差為3.64%。
3 討論與分析
有限元法作為一種數(shù)值模擬方法,可以解決傳統(tǒng)生物力學(xué)實(shí)驗(yàn)法中無(wú)法直接測(cè)的人體骨骼、韌帶等內(nèi)部結(jié)構(gòu)力學(xué)數(shù)據(jù)的問(wèn)題[36]。目前使用
MRI(magnetic resonance imaging)、CT(computed tomography)技術(shù)和CAD、Mimics等軟件獲取足部模型被認(rèn)為是一種可靠的三維建模方法[37-38]。雖然建立的有限元模型越趨近于真實(shí)狀態(tài)越好,但考慮到建模的可操作性和計(jì)算的效率,研究所建立的模型可以根據(jù)研究目的降低復(fù)雜程度,進(jìn)行一定的簡(jiǎn)化處理。例如對(duì)足部踝關(guān)節(jié)不穩(wěn)的研究,簡(jiǎn)化了足部其他結(jié)構(gòu),只建立了踝關(guān)節(jié)相關(guān)的關(guān)節(jié)面、韌帶等結(jié)構(gòu)[39]。
模型的有效性對(duì)于計(jì)算結(jié)果至關(guān)重要,模型驗(yàn)證常采用對(duì)比仿真數(shù)據(jù)與實(shí)測(cè)數(shù)據(jù)的誤差[40],模型誤差率小于10%,可視為模型有效[41]。與足部相關(guān)的研究一般采用足底壓力測(cè)試、足部幾何形態(tài)或尸體實(shí)驗(yàn)獲取足底壓力、地面反作用力、模擬應(yīng)變等指標(biāo)[41]。對(duì)足部的骨骼、軟骨、韌帶等復(fù)雜結(jié)構(gòu)進(jìn)行簡(jiǎn)化處理[20],對(duì)材料屬性的不準(zhǔn)確定義[17,41],均有可能產(chǎn)生誤差。本研究利用CT掃描與三維掃描技術(shù)獲得了滑板愛好者足、鞋與滑板的掃描數(shù)據(jù)進(jìn)行建模,足底和板底的誤差率均小于4%,模型有效可靠,可用于下一步研究。
在運(yùn)動(dòng)生物力學(xué)分析中,使用運(yùn)動(dòng)分析系統(tǒng)、三維測(cè)力臺(tái)以及表面肌電儀等設(shè)備可獲取人體運(yùn)動(dòng)過(guò)程中關(guān)節(jié)角度、地面反作用力、肌電等指標(biāo)數(shù)據(jù)[19,28,42]。將這些指標(biāo)與有限元模型相結(jié)合,實(shí)現(xiàn)對(duì)運(yùn)動(dòng)場(chǎng)景的高度模擬,計(jì)算得到運(yùn)動(dòng)過(guò)程中人體內(nèi)部骨骼、關(guān)節(jié)、韌帶等的力學(xué)特征[18,43]。通過(guò)對(duì)人體復(fù)雜解剖結(jié)構(gòu)的受力情況進(jìn)行定量分析[44],可以更加深入地開展動(dòng)作技術(shù)分析、運(yùn)動(dòng)損傷、運(yùn)動(dòng)裝備等領(lǐng)域的研究[15,24,41,45-46]。例如,將三維拍攝的冰球運(yùn)動(dòng)員的蹬冰角度,作為模型的加載條件,分析并預(yù)測(cè)蹬冰角度對(duì)足踝部的損傷風(fēng)險(xiǎn)[14];或者將實(shí)驗(yàn)獲得的足球射速和轉(zhuǎn)速等輸入有限元模型中,研究足與鞋對(duì)足球運(yùn)動(dòng)軌跡的影響[20]。
在運(yùn)動(dòng)鞋的研究中,建立“足-鞋-使用場(chǎng)景”的計(jì)算機(jī)模型,可以在專項(xiàng)運(yùn)動(dòng)條件下系統(tǒng)地研究人體運(yùn)動(dòng)表現(xiàn)問(wèn)題[41]、運(yùn)動(dòng)損傷機(jī)制問(wèn)題[47]、足部結(jié)構(gòu)的生物力學(xué)問(wèn)題、力學(xué)傳遞問(wèn)題、運(yùn)動(dòng)鞋材料和結(jié)構(gòu)設(shè)計(jì)的功效問(wèn)題等[48-49]。例如,在研究人體起跳后單腳或者雙腳落地動(dòng)作,傳統(tǒng)生物力學(xué)方法獲得的受試者在運(yùn)動(dòng)狀態(tài)下的膝關(guān)節(jié)角度、跖趾關(guān)節(jié)角度、峰值時(shí)刻垂直地面反作用力等數(shù)據(jù),可以用于分析和評(píng)測(cè)運(yùn)動(dòng)鞋裝備對(duì)跑步、打球等動(dòng)作過(guò)程中下肢的運(yùn)動(dòng)影響。同時(shí),地面反作用力等對(duì)足部作用造成損傷風(fēng)險(xiǎn)[24],則可以通過(guò)計(jì)算機(jī)模型仿真計(jì)算出運(yùn)動(dòng)過(guò)程中的足部各結(jié)構(gòu)的壓力分布情況來(lái)評(píng)測(cè)[19],具體到每一條筋膜、韌帶、足趾、關(guān)節(jié)或軟骨[26,50-51]。此外,改變鞋結(jié)構(gòu)[45]或者材料硬度[26]、厚度[42]等參數(shù),通過(guò)對(duì)比計(jì)算仿真獲得的人體結(jié)構(gòu),尤其是足踝部的應(yīng)力、應(yīng)變數(shù)據(jù),可以進(jìn)行運(yùn)動(dòng)鞋設(shè)計(jì)的定量評(píng)估以及結(jié)構(gòu)優(yōu)化[18]。
本研究在建模過(guò)程中,考慮到足-滑板鞋-滑板復(fù)雜的計(jì)算環(huán)境和計(jì)算效率,對(duì)模型進(jìn)行了簡(jiǎn)化處理,將足部骨骼和關(guān)節(jié)融合為一體,用來(lái)分析足底的壓力變化情況,后續(xù)可對(duì)骨骼、韌帶、軟骨等結(jié)構(gòu)區(qū)別細(xì)化,提高模型的還原度。在實(shí)際運(yùn)動(dòng)過(guò)程中,左右足分別承擔(dān)了不同的動(dòng)作任務(wù),本研究?jī)H將多數(shù)運(yùn)動(dòng)員的優(yōu)勢(shì)足(右足)作為研究對(duì)象,后續(xù)可考慮對(duì)雙足有限元模型進(jìn)行滑板動(dòng)作同步分析。未來(lái)可將滑板動(dòng)作的運(yùn)動(dòng)學(xué)與動(dòng)力學(xué)等特征加載至足-滑板鞋-滑板有限元模型中,開展動(dòng)態(tài)仿真研究,實(shí)現(xiàn)滑板技術(shù)動(dòng)作的動(dòng)態(tài)還原,深入分析滑板運(yùn)動(dòng)中足內(nèi)部結(jié)構(gòu)的受力特征,及優(yōu)化滑板鞋與鞋墊設(shè)計(jì)。
4 結(jié)束語(yǔ)
本研究構(gòu)建的滑板鞋-板-足耦合模型具有較好的幾何和力學(xué)相似性,經(jīng)驗(yàn)證有效可靠,可以為設(shè)計(jì)滑板鞋和研究滑板運(yùn)動(dòng)表現(xiàn)以及預(yù)防足部運(yùn)動(dòng)損傷等提供研究思路與數(shù)據(jù)支持。
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(編輯 李坤璐)