韓林原 練婉婷 楊允出
摘要:為了模擬壓力襪對不同圍度腳踝所施加的確切壓力分布,提出一種基于有限元軟件構建的腳踝-壓力襪仿真模型,模擬壓力襪在穿著時對不同圍度的人體腳踝施加的壓力值。通過三維人體掃描獲取腳踝初始形態(tài)尺寸,建立腳踝-壓力襪幾何模型。通過材料密度、彈性模量和泊松比建立Ⅰ級、Ⅱ級、Ⅲ級壓力襪及腳踝的材料模型。運用有限元軟件進行網格劃分,建立醫(yī)療襪與腿部接觸受力仿真模型。由仿真結果得到腳踝正前、后兩點模擬壓力值。結果表明:腳踝前部處所受壓力值始終大于后部;穿著不同等級壓力襪時,壓力隨壓力襪等級的增加而增加;穿著相同等級壓力襪時,腳踝所受的壓力值隨腳踝周長增長而增加,呈線性規(guī)律分布;經實測對比,實驗驗證所建立的有限元模型是合理且有效的。
關鍵詞:壓力襪;腳踝;壓力分布;有限元模型;壓力測試
中圖分類號:TS101.8
文獻標志碼:A
文章編號:1009-265X(2023)02-0055-08
下肢靜脈曲張是最常見的疾病之一[1]。據(jù)國內相關報道,中國下肢靜脈曲張的患者總數(shù)已超過1億,發(fā)病率約為15%[2]。據(jù)國外統(tǒng)計,下肢靜脈曲張在女性中更常見,且女性患靜脈潰瘍的概率約為男性的3倍[3]。因此,對靜脈疾病的綜合防治和臨床研究逐漸受到人們的關注和重視。壓力襪是目前針對下肢靜脈曲張應用比較廣泛的治療產品,其作用原理是采取漸進式分段設計,由腳踝處漸次向上遞減壓力,收縮小腿肌肉,阻止深靜脈擴張,促進血液回流心臟[4-5]。所采用的加壓技術包括氣囊式、彈力面料式、氣囊與彈力面料相結合、智能材料和結合智能終端等方法[6]。
目前服裝壓力的測量方法包括流體壓力法、改良流體法(氣壓式服裝壓力測量法)、傳感器法、Laplace定律法、有限元法和軟體假人法等[7],其中,有限元分析法被廣泛運用于服裝壓力分析。Sun等[8]利用靜態(tài)、動態(tài)有限元模型結合的方法,模擬了乳房的非線性特征和運動變形,測定乳房體超彈性材料系數(shù),用于分析穿著文胸后乳房的壓力分布;Lin等[9]建立男性腿部及緊身褲有限元模型,評估了腿部的接觸壓力;覃蕊等[10]模擬男短襪襪口對腿部施壓后壓力與位移的關系,分析了二維截面壓力與位移的關系;王永榮等[11]仿真模擬醫(yī)療襪穿著在人體腿部的動態(tài)過程,分析醫(yī)療襪應力分布和腿部接觸壓力分布;Wu等[12]通過彈性模量數(shù)值模型和壓力有限元模擬方法,根據(jù)織物的針織參數(shù)預測織物的拉伸性能,模擬大腿的緊密壓縮情況;孫亞博等[13]通過建立緯平針單位線圈和筒狀針織物模型,利用有限元軟件對單位線圈和筒狀針織物拉伸力學性能進行模擬分析,得到織物拉伸變形過程動畫和拉伸后應力分布云圖,用于更好地了解筒狀緯編針織物抵抗拉伸變形的能力。
目前,現(xiàn)有的壓力仿真模擬模型多為固定單一模型,無法根據(jù)測試者測試部位圍度精確變換粗細,不能便捷地根據(jù)腿部尺寸模擬不同圍度下的多組壓力值數(shù)據(jù)。本文通過構建腳踝與壓力襪的幾何模型,對模型進行網格劃分,利用有限元軟件進行仿真計算與分析,進而獲得人體穿著壓力襪時不同圍度腳踝所受的壓力分布,并通過壓力試驗對有限元計算的仿真結果進行驗證,本文運用的有限元技術可用于壓力襪個人定制,使每款測試產品施加壓力值符合人體舒適范圍。
1腳踝-壓力襪幾何模型建立
參照YY/T 0853-2011《醫(yī)用靜脈曲張壓縮襪》各部位壓力值測量要求,所需測量部位包括大腿根部、大腿中部、脛骨初隆處、小腿周長最大、跟腱與小腿肌轉變處以及踝部周長最細處,本研究選擇以左腿腳踝周長最細處為基礎建立仿真模型。當不同腳踝圍度的患者穿著壓力襪后,壓力襪緊密包裹住腳踝,人體所受到的壓力也不同。根據(jù)標準中描述的壓力襪壓力測試要求,將測試模型設計為精確、可移動的腳踝模型:腳踝模型分為前后兩部分,通過前后模型沿相反方向分開,拉伸后腳踝周長發(fā)生變化,經過有限元模擬得到穿著不同壓力襪時各圍度腳踝正前、后兩處壓力值。這樣模型的設計具有可移動性、可改變的尺寸、容易穿戴等優(yōu)點,能夠真實模擬不同腳踝圍度大小。
1.1腳踝曲面模型建立
根據(jù)《醫(yī)用靜脈曲張壓縮襪》標準中腳踝規(guī)格的數(shù)據(jù)范圍(主要集中在18~30 cm),選取一位在標準范圍內腳踝圍度相對較小的青年女性作為模型掃描對象,以便于后續(xù)的研究中能夠對模型進行放大處理,其腿部具體尺寸如表1所示。通過[TC]2非接觸式三維人體掃描系統(tǒng)對該女性進行掃描,獲取人體的3D點云數(shù)據(jù)。使用Imageware軟件將多余的點云數(shù)據(jù)刪除或隱藏,只留下需分析的點云數(shù)據(jù),創(chuàng)建截面點云并對每個截面進行曲線擬合后,繪制截面曲線,通過對曲面放樣與優(yōu)化和光順處理等方式,去除表面尖銳部分,最終得到所需腳踝部位曲面模型,如圖1所示。
1.2腳踝-壓力襪3D幾何模型創(chuàng)建
將擬合好的曲面模型導入Solidworks軟件中,保留腳踝形態(tài)曲線,將腳踝最細處截面進行填充和加厚處理得到實體;為了后續(xù)模型圍度可調,通過主體分割工具將模型從中間分為腳踝前和腳踝后兩部分,得到所需腳踝處3D幾何模型;使用殼體工具創(chuàng)建人體穿著狀態(tài)下腳踝處的壓力襪幾何模型,殼體厚度即壓力襪的厚度,結果如圖2所示,腳踝-壓力襪3D幾何模型的建立為后續(xù)有限元模擬做準備。
2有限元模擬
本研究采用有限元分析法模擬計算腳踝前后處所受到的壓力值,在ANSYS Workbench 中,輸入材料性質,經過網格劃分,確定接觸方式和邊界條件后,軟件根據(jù)設定的程序說明進行計算,最后模擬相應的壓力值和壓力分布情況。
2.1材料定義
本實驗有限元模型主要由3個部分組成,即腳踝前、后模型和壓力襪模型,為了更好地提高仿真效果,趨近于真實情況,將腳踝和壓力襪視為各向同性線彈性體。在工程數(shù)據(jù)中根據(jù)具體情況設定材料參數(shù),將腳踝的材料參數(shù)設置為彈性模量0.177 MPa,泊松比0.4[12]。以某品牌M碼中筒壓力襪為原型,該壓力襪按照施加給腳踝處的壓力值分為Ⅰ、Ⅱ、Ⅲ3個等級,Ⅰ級壓力為2.0~2.8 kPa、Ⅱ級壓力為3.1~4.3 ?kPa、Ⅲ級壓力為4.5~6.1 ?kPa。參照FZ/T 70006—2004《針織物拉伸彈性回復率試驗方法》,采用Instron3367型萬能拉伸儀測試其力學性能。在大氣溫度為(20±2)℃、相對濕度為(65.0±3.0)%的環(huán)境下進行測試,得到腳踝部位壓力襪材料參數(shù),如表2所示。
2.2網格與接觸
在有限元的模擬計算中,為使模型的模擬結果更準確,應在不影響運算效率的情況下合理劃分網格。本文將模型劃分為四面體實體網格,網格單元最大尺寸為5 mm,結果如圖3所示。模型裝配后,設定壓力襪與腳踝的接觸面集合?;谡鎸崰顩r分析,將壓力襪的內表面被視為接觸面,腳踝外表面被視為目標面,壓力襪與腳踝外表面之間的接觸方式設定為有摩擦,摩擦系數(shù)為0.2[14];腳踝前、后模型之間由于分開,接觸方式設定為無摩擦。
2.3有限元邊界條件及求解
施加的力或約束被叫作載荷,載荷的定義方式影響了有限元計算結果的精度。為模擬不同腳踝圍度受試者穿著壓力襪時的狀態(tài),對腳踝前模型外表面施加固定約束,對腳踝后模型的外表面定義位移約束,坐標系Y軸正方向對應腳踝后側,負方向對應腳踝前側,X軸對應腳踝左右方向,Z軸對應腳踝的高度方向。腳踝后模型沿Y軸正方向發(fā)生一定位移,X、Z軸方向上不施加位移,如圖4所示。在模擬過程中,腳踝前模型根據(jù)邊界條件移動到指定位置上,包裹在外側的壓力襪拉伸從而產生壓力。
在本實驗中,研究對象腳踝初始維度為19 cm,將模型拉伸5次,拉伸距離依次增加,使腳踝模型周長遞增1 cm,表3為拉伸后腳踝模型數(shù)據(jù)值。腳踝前、后模型外側中間點為壓力測量位置,如圖5所示,標記為腳踝正前點A和腳踝正后點B,通過仿真模擬得到腳踝周長5次變化后分別穿著Ⅰ、Ⅱ、Ⅲ等級壓力襪的A、B兩點壓力值。通過上述邊界條件的設置,軟件將根據(jù)程序指令進行計算。通過上述邊界條件的設置,軟件將根據(jù)程序指令進行計算。在模擬過程中,需要實時檢查計算狀態(tài),如果計算未能收斂,可以及時進行調整。
3結果與分析
仿真結果分析模擬穿著3個等級壓力襪腳踝前
后測試點壓力值的實驗結果如圖6所示,由圖6可知,穿著不同等級壓力襪,腳踝前測試點A壓力值均比腳踝后測試點B大,這是由于兩者位置的曲率半徑不同所導致的,A點曲率半徑為79.88 mm,B點曲率半徑為31.78 mm。圖7展示了Imageware軟件得出所測腳踝截面的曲率半徑結果,由圖7可以得到實驗測量腳踝部分的曲率半徑變化趨勢。圖7中數(shù)據(jù)外圓表示點的角度位置,內圓表示點位置的曲率半徑值,中間的直線長度表示曲率大小,因此可以看出B點曲率小于A點曲率。根據(jù)拉普拉斯方程,人體表面所受的壓力與人體的曲率半徑成反比,因此B點壓力值小于A點。
穿著者的腳踝圍度是除人體曲率外影響腳踝周服裝壓力的重要因素。以Ⅱ級壓力襪為例,圖8可以看到腳踝模型沿Y軸上下拉伸5次后壓力分布云圖。以腳踝周長同為20 cm為例,由圖6得出的仿真結果數(shù)據(jù)可以看出得到,當腳踝周長為20 cm時,Ⅰ級壓力襪A點壓力值為3953.3 Pa,B點壓力值為4164.9 Pa,Ⅱ級壓力襪A點壓力值為5066.2 Pa,B點壓力值為5416.5 Pa,Ⅲ級壓力襪A點壓力值為6205.4 Pa,B點壓力值為6531.2 Pa;所以當壓力襪處于拉伸狀態(tài)時,腳踝所受壓力值隨壓力襪等級增加而逐漸增加;在壓力等級不變的情況下,腳踝周長與壓力值成正比,壓力襪壓力主要由線圈排列密度的變化而產生的,當組成線圈的紗線拉伸越長時,產生的壓力值越大,當?shù)竭_一定值后趨于平穩(wěn),所以腳踝周長較長的模型在穿著壓力襪時可以產生更高的壓力。
對每個壓力等級的A、B兩點壓力值分別進行線性擬合,圖9為壓力值線性擬合圖,由圖9可知,6條直線的擬合度R2均在0.99以上,擬合度較高,線性結果較為明顯,由此可得,Ⅰ、Ⅱ、Ⅲ級壓力襪的壓力值均隨腳踝的周長增加而逐步增加,并且壓力值與周長之間呈線性回歸關系。在治療過程中,需要根據(jù)患者的腿圍設計合適壓力值的壓力襪,針對同款壓力襪在設計不同周長圍度的壓力值時可根據(jù)周長與壓力的線性關系得出相應的壓力值。
4實驗驗證
采用Novelpliance-x-32壓力測試系統(tǒng),如表4所示,選擇腳踝周長與模型周長相對接近的5名測試者,編號為測試者1-5,選擇腳踝最細處正前側和正后側的2個測試點,編號為A(腳踝正前側)、B(腳踝正后側),5位測試者裸腿直立,在測試點處貼好壓力傳感器,測試者依次穿著3個等級醫(yī)療襪進行測試,待顯示器數(shù)值穩(wěn)定后記錄數(shù)據(jù)。每個壓力襪測試3次,結果取平均值。5名測試者均重復以上操作。對比3個等級醫(yī)療襪的A、B兩點壓力模擬值和實測值,結果如圖10所示。
通過真實測出的壓力值與模擬預測出的壓力值相比較可以得到,穿著不同等級壓力襪時,腳踝前后壓力仿真結果與真實值有一定差異,但誤差較小,整體分布均呈增長趨勢,表明基于有限元建模的計算預測壓力值方法有效。出現(xiàn)誤差的原因可能是:在仿真模擬方面,真實腳踝包括皮膚、骨骼、肌肉等較為復雜,而實驗中腳踝模型未細分結構,與真實的腳踝存在差異,彈性模量、密度等數(shù)據(jù)在各處有所不同,模擬時無法根據(jù)材質分布的變化而變換數(shù)據(jù)。在測量真實值過程中,壓力襪穿著過程面料拉伸不均勻會對壓力值產生影響;壓力襪穿脫一定次數(shù)后產生塑性變形會導致壓力衰減;腳踝表面被施加接觸壓力,內部組織發(fā)生相對位移,因此產生的壓力襪-腳踝的共偶變形也會使實測值與模擬值之間出現(xiàn)誤差[15]。
通過SPSS對數(shù)據(jù)進行分析兩組壓力模擬值與實測值的相關系數(shù),A、B兩點處相關系數(shù)如表5所示,3個壓力等級醫(yī)療襪的壓力模擬值與實測值的相關系數(shù)均在0.90~1.00,且P<0.05,可知壓力擬值與實測值具有較高的相似度,說明模型有效。
5結論
本文通過逆向工程技術建立所需壓力襪-腳踝幾何模型,根據(jù)壓力襪和腳踝的材料參數(shù),根據(jù)有限元仿真模擬分析3個壓力等級的壓力襪穿著在人體不同圍度腳踝的接觸壓力值及壓力分布云圖,通過分析結果可得到:
a)當壓力襪處于拉伸狀態(tài)時,腳踝所受壓力值隨壓力襪等級增加而遞增,相同圍度腳踝穿著任意等級壓力襪時,腳踝前側壓力均大于腳踝后測壓力。不同腳踝圍度穿著相同等級壓力襪時,腳踝所受的壓力值隨腳踝周長增加而增加且呈線性規(guī)律分布。
b)通過與人體穿著醫(yī)療襪時接觸壓力測試結果進行對比,驗證了模型有效,有助于根據(jù)患者腿圍設計出更加符合人體所需壓力值的壓力襪。
本文提出一種針對腳踝-壓力襪的有效建模方法,能夠通過有限元仿真模擬得到不同腳踝圍度的壓力分布。在實際應用中,為基于有限元建模研究的壓力襪方向研究提供了新思路。
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Finite element modeling of three dimensional contact pressure of ankle-compression stockings
HAN Linyuana, LIAN Wantinga, YANG Yunchub,c
(a.School of FashionDesign & Engineering; b.School of International Education; c.MOC Key Laboratory of Silk Culture
Heritage and Product Design Digital Technology, Zhejiang Sci-Tech University, Hangzhou 310018, China)
Abstract: Varicose veins of the lower extremities are a common and frequently-occurring disease in clinical practice. Lower extremity venous diseases affect 25%-40% of women and 10%-20% of men worldwide. With the improvement of medical theory and application technology, the treatment methods and techniques of lower extremity venous diseases have been continuously improved. Compression therapy has a long history in the treatment of varicose veins. Pressure socks are widely used in the treatment of varicose veins. The pressure socks are designed in a progressive segmented manner, and the pressure applied to the leg is gradually reduced from the ankle to the thigh. Due to the different shapes and sizes of human legs, the pressure distribution of different individuals is different. Therefore, it is particularly important to detect the pressure distribution of the actual human body wearing medical socks. At present, the finite element analysis method is widely used in pressure analysis. However, the existing pressure simulation models are mostly fixed single models, which cannot accurately change the thickness according to the circumference of the tester's test site, and cannot easily simulate multiple sets of pressure values under different circumferences according to the leg size.
In orderto simulate the exact pressure distribution exerted by compression stockings on ankles with different girths, an ankle-compression stocking simulation model based on finite element software was proposed to simulate the pressure exerted by compression stockings on human ankles with different girths. Firstly, the initial shape and size of ankle were obtained by three-dimensional human body scanning, and the geometric model of ankle-pressure sock was established. Then, the material density, elastic modulus and Poisson's ratio of fabrics at ankle were tested and calculated, and the material models of grade I, grade II and grade III compression stockings and ankle were established. On this basis, the finite element software was used to mesh and establish the contact force simulation model of medical socks and legs. From the simulation results, the simulated pressure values of the anterior and posterior two points of the ankle were obtained, and the contact pressure of the human body after wearing the pressure socks was tested. The results show that the pressure value of the anterior part of the ankle is always greater than that of the posterior part. When people wear different grades of compression stockings, the pressure increases with the increase of the grade of compression stockings. When people wear the same grade of compression stockings, the pressure value of the ankle increases with the increase of the circumference of the ankle, which is linearly distributed. The finite element model is reasonable and effective.
While establishing an effective finite element pressure simulation model, this study provides a new idea for the research of compression stockings from the perspective of the physical and mechanical properties of knitted fabrics.Giving play to the potential of finite element analysis technology in the gradient compression stockings research and application can greatly save product development time and reduce development costs. In practical applications, this study can be used for personal customization of pressure socks, so that the pressure value of each test product conforms to the comfort range of human body, and provides reference for the development and testing of pressure socks products and sportswear protection products, which is conducive to better measurement of clothing pressure.
Keywords: compression stockings; ankles; pressure distribution; finite element model; pressure test
收稿日期:20220531
網絡出版日期:20220914
基金項目:浙江省自然科學基金項目(LY17E06007);浙江理工大學基本科研項目(2020Q083)
作者簡介:韓林原(1998—),女,黑龍江牡丹江人,碩士研究生,主要從事數(shù)字化與功能性服裝方面的研究。
通信作者:楊允出,E-mail:gary0577@zstu.edu.cn