Anita Ilska, Krzysztof Kowalski, Magdalena Kłonowska, *Tomasz Marek Kowalski Department of Knitting Technology *Computer Engineering Department Lodz University of Technology ul. Żeromskiego 116, 90-924 Łódź, Poland E-mail: [email protected] Influence of Stress and Relaxation Characteristics of Knitted Fabrics on the Unit Pressure of Compression Garments Supporting External Treatment Abstract The paper presents an analysis of the influence of the mechanical properties’ heterogeneity of knitted fabrics and the method of determining their characteristics of stress and relaxation (deformation) on the value of unit pressure of compression garments. Changes in the value of force as a function of relative elongation were described by experimental dependencies for stress and relaxation phases for the 6th hysteresis loop, taking into account the confidence intervals. Model calculations were performed for a wide range of body circumferences G1 = 5 - 110 cm and for two values of unit pressure: 20 and 30 hPa using Laplace’s law and experimental functions determined which describe the relationship between force and relative elongation of a knitted fabric. The research indicates one of the reasons for changes in the unit pressure in the compression garments designed. Key words: medtextiles, unit pressure, Laplace law, mechanical parameters, knitted fabrics, body circumferences. n Introduction An effective method supporting the process of external treatment is the compression therapy used, among others, in the treatment of post-burn scars, lymphoedema, varicose veins, and after plastic surgery operations. An important parameter of compression garments supporting the process of external treatment is the unit pressure exerted on the protected (covered) body parts. The range of values of this parameter, depending on the type of therapy, is determined from a medical point of view and should be obeyed [1 - 6]. Works on the modelling of unit pressure [6 - 9] are based on a model of the human body in which the circumferences are treated as circles (Figure 1). Changes in the value of unit pressure depending on the circumferences, with a variable radius of curvature of the human body circumferences, is shown in [10]. [7] presents the results of modelling the unit pressure with the finite element method for the case of a cylinder and Circumference CircumferenceG1 G1 An important step in the procedure of designing compression garments is the method of determining the mechanical characteristics of a knitted fabric in the form of the relationship between the force and relative elongation. The aim of the study was to determine the influence of the characteristics of stress and relaxation (deformation) of a compression knitted fabric on the changes in values of the unit pressure exerted on the cylindrical model of a body for a wide range of body circumferences taking into consideration the confidence intervals determined for the dependencies mentioned above. The aim of the study also includes the development of a new procedure for determining the stress-relaxation (deformation) characteristics of a knitted fabric,which takes into account the results of tests on the basis of a partition into sub-ranges of deformations, instead of a single range thereof. Peripheral force in band F cone. In these works, the linear mechanical characteristic of knitted fabric of a constant value of stretching rigidity was assumed for modelling. F S Band width Figure 1. Cylindrical model of a body part covered with a compression band (tourniquet) [7]. (1) where: P - unit pressure in, hPa, F - peripheral force of a knitted band of width s, in cN, G1 - circumference of a body part, in cm, s - width of a knitted band, in cm. Report of threading: I full – poliuretane yarn II full, empty – poliamide multifilament III full, empty – poliamide multifilament Recording of model links: I 11/ 00// II 34/ 32/34/ 43/ 45/43// III 32/ 34/ 32/ 23/ 21/ 23/ Poliamide multifilament Poliuretane yarn Basis for modelling compression knitted fabrics The basis for modelling and designing compression garments is Laplace’s law (1), which describes the relationship between the unit pressure exerted on a cylindrical body model of circumference G1 and the peripheral force F in a knitted band of width s (Figure 1). Ilska A, Kowalski K, Kłonowska M, Kowalski TM. Influence of Stress and Relaxation Characteristics of Knitted Fabrics on the Unit Pressure of Compression Garments Supporting External Treatment. FIBRES & TEXTILES in Eastern Europe 2014; 22, 4(106): 87-92. Figure 2. Report of threading with a recording of model links and a stitch of highly elastic knitted fabric with elastomeric threads. 87 relaxation phases decrease with the number of hysteresis loops performed. The largest differences occur between the 1st and 2nd loop, while those between the 4th and 5th loop are insignificantly small, as shown in Figure 3, which presents five examples of hysteresis loops. 30 25 Force, N 20 15 10 5 0 0 20 40 60 80 100 120 Absolute elongation Δl, mm 1 loop 2 loop 3 loop 4 loop 5 loop Figure 3. Exemplary graph of force as a function of absolute elongation in hysteresis loops in the stress and relaxation cycle. Research conditions: width of sample s 5 cm, length of sample 10 cm, and rate of deformation 5 mm/min. In order to determine the dimensions of a compression garment in a free state with the value of unit pressure assumed, it is necessary to know the mechanical characteristics of the knitted fabric in the form of an experimental relationship between the force and relative elongation. Research subject and methodology Compression garments used in postburn therapies are often made from plain stitch warp-knitted fabric with elastomeric threads, whose stitch is presented in Figure 2. It is a three-guide knitted fabric composed of a binding stitch made of textured polyamide mul- (C1) I II (C) (h) Figure 4. Three-element Zener model: I Hooke’s segment, II Maxwell’s segment, C, C1 – elasticity constants, η - dynamic viscosity 88 tifilament with a linear density of 78 dtex (76%) and vertical weft threads made of polyurethane yarn with a linear density of 480 dtex (24%). The parameters describing the yarn are the following: course density Pr = 120, wale density Pk = 140 and surface mass G = 234 g/m2. Compression garments used in e.g. post-burn therapies are practically worn 23 hours a day over a period of several months. In order to maintain the unit pressure desired at a specific range of values determined from a medical point of view, the product should have characteristics of the body seeking to be perfectly elastic, which involves obtaining a minimum hysteresis loop during stretching and relaxation. The research on a knitted fabric was conducted by increasing the range of elongation of 0.25 of the relative elongation ε in five separate cycles of stretching and relaxation. In total, 25 rectangular samples were used in the tests, 5 for each range of stretching. The knitted samples were stretched and relaxed at a rate of 5 mm/min using a tensile testing machine by Hounsfield. The relationship between the force F and relative elongation was determined on the basis of experimental results obtained from the 6th hysteresis loop for the stretching and relaxation phases. The assumption of six hysteresis loops is associated with the mechanical conditioning of a knitted fabric. Differences between the values of forces for the stress and Differences in the values of forces between the phases of stress and relaxation of a knitted fabric can be interpreted qualitatively from the behaviour of the three-element standard Zener model [11] (Figure 4), because knitted fabrics with elastomeric threads are subject to the laws for viscoelastic materials. The relationship between the relative elongation ε, the value of tensile force F, the working time t of this force and rheological parameters c, c1 & η in the Zener model is described by the following differential Equation 2: F+ dF η dF t C1 ddt = C ε + (C + C1) η dε (2) c1 dt dt Assuming that the rate of increase of relative deformations is constant dε/dt = const and the initial force during stretching is F0 = 0, Equation 2 takes the Equation 3 for this case: -t C − ⋅tC 11 dε F1 = C ⋅ ε + η ⋅ dt 1 − e η dt (3) In both the stress and relaxation phases, the Maxwell term in the standard model is responsible for the relaxation process. Table 1. Results of statistical analysis. Stress phase Fng; R = 0.9992; F = 686.81; p < 0.00009 Regression coefficient value t statistics Significance level p bo 0 b1 905.9 8.248 0.003732 b2 -943.9 -3.696 0.034373 b3 473.0 3.360 0.043721 Fns; R = 0.9959; F = 616.914; p < 0.00001 bo 0 b1 433.6 b2 0 b3 24.838 1.97E-06 0 Relaxation phase Fod; R = 0.9993; F = 1131.8; p < 0.00005 bo 0 b1 336.4 18.518 0.000344 b2 -141.6 -7.377 0.005151 b3 0 Fos; R = 0.9996; F = 2181.3; p < 0.00002 bo 0 b1 366.7 18.51758 0.000344 b2 -161.6 -7.37678 0.005151 b3 0 FIBRES & TEXTILES in Eastern Europe 2014, Vol. 22, 4(106) η From the considerations presented above, a thesis can be advanced that introducing mechanical characteristics of a knitted fabric in the form of the relationship between the force and relative elongation for the stress phase into the procedure of designing compression garments causes the lowering of values of the unit pressure in relation to the value intended. For this reason a comparative analysis of changes in the value of the unit pressure will be carried out on the basis of relations between the force and elongation of knitted fabrics for stress and relaxation phases used in the procedure of designing compression garments. In order to determine a general characteristic of knitted fabrics an analysis of regression was used. As an independent variable the relative elongation of the knitted fabrics was assumed within the range of 0 - 1.25 for the stress phase, and from 1 to 0 for the relaxation phase, in separate cycles of stretching with measuring points every 0.25. For each of the values of elongation five measurements of the force were carried out. From the point of view of assessing the usefulness of the products, important are not only the average characteristics of forces, but also boundary conditions. For this reason, two characteristics of forces were taken into account as a dependent variable - the mean value and its upper estimation for the stress phase, and a FIBRES & TEXTILES in Eastern Europe 2014, Vol. 22, 4(106) Fng 500 400 300 200 100 (4) From the analysis of the equation it results that the peripheral forces in the knitted fabric will aim to be equal to C∙ε as the expression exp (-t C1/η) for t → ∞ takes the value of 0. The relaxation of forces occurs as a result of adopting the deformations of a spring with rigidity C1 by a viscous term (attenuator). Fns 600 0 0 0,2 0,4 0,6 0,8 1 1,2 1,4 Relative elongation εe Figure 5. Values of average Fns and upper estimation Fng of confidence intervals for the relaxation phase as a function of the relative elongation ε for the 6th hysteresis loop; width of knitted band s = 1 cm. 600 Fos Fod 500 400 Force F, cN F1 = C ⋅ ε + C1 ⋅ e − t ⋅C1 700 Force F, cN From the interpretation of the expression exp (-t C1/η), which describes the process of relaxation of forces, it results that these forces depend inversely exponentially on their time of action. Transferring these model interpretations to the behaviour of compression garments during use, it should be noted that during several months of usage it refers to the classical process of relaxation. Assuming the conditions of relaxation, i.e. ε = const, dε/dt = 0, we obtain Equation 4, describing the relaxation process of forces according to the three-element Zener model. 300 200 100 0 0 0,2 0,4 0,6 0,8 1 1,2 1,4 Relative elongation e Figure 6. Values of average Fos and lower estimation Fod of confidence intervals for relaxation phases as a function of the relative elongation ε for the 6th hysteresis loop; width of knitted band s = 1 cm. lower estimation for the relaxation phase, taken as the boundary of the 95% confidence interval for the value of the force expected. t1−α / 2 S Fnng (5) g = Fnsns + n −1 Food d = Fosos − t1−α / 2 S n −1 (6) where: Fns - average value of force in stress phase, Fos - average value of force in relaxation phase, Fng - upper estimation of force for stress phase, Fod - lower estimation of force for relaxation phase, S - standard deviation from the sample, n - number of measurements (n = 5), t1+a/2 - quantile of Student’s t-distribution of n - 1 degrees of freedom. In order to determine the curves of stress and relaxation the method of backward stepwise regression was used assuming that the regression model for values Fns, Fos Fng, and Fod with respect to ε is the polynomial of the degree 3 maximum. F = b0 + b1 ⋅ ε + b2 ⋅ ε 2 + b3 ⋅ ε 3 (7) 89 700 600 Fns Fns = 433.6 . ε (9) 200 100 0 0 (10) Fos = 366.7 . ε - 161.6 . ε2 (11) The equations determined (8 – 11) refer to the band width of knitted fabric s = 1 cm. Despite the lack of significance of regression coefficients b0, b2 and b3 of the regression model for value Fns, a polynomial of degree three was used in further calculations (12) because within the range of values of relative elongation ε = 0.2 - 0.5 in the stress zone there is a considerable difference between the experimental values and those calculated according to the linear function (Figure 5). Fns = 768.9 . ε - 682.9 . ε2 + + 327.4 . ε3 (12) R2=0.9939 Influence of characteristics of stress and relaxation (deformations) of knitted fabrics on changes in the unit pressure Changes in the unit pressure in relation to the intended values of 20 and 30 hPa 90 0,2 0,4 0,6 0,8 Relative elongation ee 1 1,2 1,4 Figure 7. Values and models of force observed in the knitted fabric as a function of the relative elongation in the stress and relaxation phase for average values and the upper & lower estimation of forces, respectively; width of knitted band s = 1 cm. 26 23 20 17 14 n For the relaxation phase: Fod = 336.4 . ε - 141.6 . ε2 Fod 300 P, hPa (8) Fos 400 On the basis of the results presented in Table 1, the following models of the pressing force as a function of the relative elongation were obtained: n For the stress phase: Fng = 905.9 . ε - 943.9 . ε2 + + 473.0 . ε3 Fng 500 Force F, cN Table 1 presents the values of regression coefficients. The values of coefficients equal to 0 were taken for cases where, on the basis of the test of significance for a given regression coefficient, there was no reason to reject the hypothesis that it is equal to zero. For the models obtained the values of multiple regression coefficient R, the results of the regression significance test (F statistics and level of significance p), and the results of tests of the regression coefficient’s significance (t statistics and significance level of p) were presented. Only the significant regression coefficients are taken into account in the models adopted. In all cases, due to the insignificance of the absolute term (no evidence to reject the hypothesis that b0 = 0), it was necessary to determine a regression model without the absolute term. 11 8 5 15 25 35 Pmax - stress 45 55 65 P = 20 hPa 75 85 95 Pmin - relaxation 105 G1, cm Figure 8. Changes in the values of unit pressure as a function of circumference G1 as a result of changes in forces from the upper and lower estimation of confidence intervals for the stress and relaxation phases, respectively, in relation to the intended value of pressure Pint = 20 hPa. were determined according to the following procedure: Calculation procedure Step I: for successive values of circumference G1 within the range of 5 - 110 cm and those of unit pressure P = 20 and 30 hPa, values of the relative elongation ε were defined from Equation 13, which was obtained by introducing an experimental function (12) into Equation 1. The calculations were performed using Excel tools. P= = 2p(768.9 . ε - 682.9 . ε2 + 327.4 . ε3) G1s (13) Step II: Next for successive values of circumference G1 within the range of 5 - 110 cm, the values of unit pressure were determined by introducing values of the relative elongation ε obtained from the first step into dependence (14), which was obtained by introducing experimental dependence (8) into Equation 1. The course of these functions is illustrated by the curves situated above the straight lines of intended values of unit pressure P = 20 and 30 hPa (Figure 7 and 8), illustrating the maximum values of unit pressure for the upper estimation of ranges for the stress phase. P= = 2p(905.9 . ε - 943.9 . ε2 + 473.0 . ε3) G1s (14) FIBRES & TEXTILES in Eastern Europe 2014, Vol. 22, 4(106) (16) 37 34 where: Pcal – value calculated, Pint – assumed values of 20 and 30 hPa. 31 P, hPa 28 25 22 19 16 13 10 5 15 25 35 P max - stress 45 55 P=30 hPa 65 75 85 95 Pmin - relaxation 105 G1, cm Figure 9. Changes in the values of unit pressure as a function of circumference G1 as a result of changes in forces from the upper and lower estimation of confidence intervals for the stress and relaxation phases, respectively, in relation to the intended value of unit pressure Pint = 30 hPa. 20 percentage difference ∆P, % 10 0 -10 5 20 35 50 65 80 95 circumference G1,cm 110 -20 -30 -40 -50 -60 -70 series 1 series 2 series 3 series 4 Figure 10. Percentage differences ΔP between the intended values of unit pressure Pint =20 and 30 hPa, and the boundary values of Pcal calculated for the stress (series 1 and 3) and relaxation phases (series 2 and 4) resulting from the upper and lower estimation of the confidence intervals. Then, introducing dependence (10) into Equation 1, we obtain the minimum values of unit pressure resulting from the lower estimation of the confidence interval for the relaxation phase, which was calculated from Equation 15. P= 2p(336.4 . ε - 141.6 . ε2 ) G1s (15) The course of these functions is illustrated by the curves in Figures 7 and 8, situated below the straight lines of the intended value of unit pressure P = 20 and 30 hPa. These curves show the minimum values of unit pressure for the lower estiFIBRES & TEXTILES in Eastern Europe 2014, Vol. 22, 4(106) mations of the force from the confidence interval for the relaxation phase. The results presented in Figures 8 and 9 show significant changes in the values of unit pressure under the influence of possible, statistically documented, changes in the values of peripheral forces in the knitted fabric for equal values of relative elongation. The percentage differences between the intended value of unit pressure Pint = 20 and 30 hPa presented in Figure 10, and the values calculated using Equations 1, 14 and 15) are the generalisation of the results presented in Figures 8 and 9. The percentage differences were calculated according to the following Equation: A qualitative explanation of the significant decrease in the value of unit pressure (approximately -50%) in relation to the average maximum values obtained for the stress phase can be documented on the basis of the relaxation process analysed above and, at the same time, by not considering in the procedure of designing compression garments the relationship between the force and relative elongation for the relaxation phase of a knitted fabric. Values of unit pressure increased in relation to the assumed values of 20 and 30 hPa from about 6% to 17%, resulting from the upper estimation of the values of forces from the confidence intervals for the stress phase. Figure 9 shows that the percentage difference ∆P arising from the changes in peripheral forces for this phase decreases with an increase in the value of circumference G1. From the considerations given above it results that the procedure currently valid for determining the mechanical characteristics of a knitted fabric for the stress phase - according to Standard [6] - leads to lowering the value of the unit pressure, as it only partially takes into account the relaxation process occurring during the use of garments, which in many therapies are worn practically 23 hours a day over a period of several months. The results obtained correspond to experimental results of the unit pressure of sock tops, for which after 12 hours of usage a decrease in pressure exceeding 50% of the initial pressure was noted [13]. The results presented enable us to clearly state that one of the main causes of lowering the value of the unit pressure in relation to the intended value is the procedure limited to determining the characteristics of stress - deformation. n Conclusions 1.The research conducted shows that the procedure currently valid for determining mechanical characteristics in the form of the relation between the force and relative elongation of a knitted fabric limited to the stress phase leads to a significant lowering of values of the unit pressure, because it does not take into account the relaxation processes occurring during 91 the usage of garments which in many therapies are worn practically 23 hours a day over a period of several months. 2. Percentage differences in unit pressure in relation to the intended value of pressure determined on the basis of the relaxation phase are about 50% lower due to the visco-elastic properties, mechanical heterogeneity of the knitted fabric tested and the method used for determining its mechanical characteristics. 3. The research performed indicates one of the reasons for changes in the unit pressure of compression garments, which is primarily related to adopting in the design process the characteristic of a knitted fabric in the form of a force and relative deformation in the stress phase. 1. Nyka W, Tomczak H. Rehabilitacja chorych z oparzeniami termicznymi. Rehabilitacja Medyczna 2003; 7, 4. 2. Garrison SJ. Podstawy rehabilitacji i medycyny fizykalnej. Ed. Wydawnictwo Lekarskie PZWL, Warszawa, 1997. 3. Adamczyk W, Magierski M. Treatment of hypertrophic scars with pressing method (in Polish). Roczniki Oparzeń 1996-97; 7/8: 219-222. 4. Mikołajczyk A, Sośniak K, Fryc D, Miś K. Dermatologia Kliniczna i Zabiegowa 1999; 1, 2: 74-76. 5. Fritz K, Gahlen I, Itschert G. Gesunde Venen – Gesunde Beine. Rowohlt Taschenbuch Verlag GmbH, Reinbek bei Hamburg, 1996. 6. CEN/TR 15831:2009. Method for Testing Compression in Medical Hosiery. 7. Mirjalili SA, Mansour R, Soltanzadeh Z. Fibres & Textiles in Eastern Europe 2008; 3, 68: 69-73. 8. Maklewska E, Nawrocki A, Ledwoń J, Kowalski K. Fibres & Textiles in Eastern Europe 2006; 14, 5: 111-113. 9. Nawrocki A, Kowalski K, Maklewska E. Modelling and instrument evaluation of compression exerted by textile garments used in a treatment and rehabilitaion of post-burn scars. Research Project 4T08 E 05425, Łódź, 2000. 10. Kowalski K, Mielicka E, Kowalski TM. Fibres & Textiles in Eastern Europe 2012; 20, 6A, 95: 98- 102. 11. Bland DR. The theory of linear viscoelasticity. Pergamon Press, 1960. 12. Krysicki W, et al. Rachunek prawdopodobieństwa i statystyka matematyczna w zadaniach, część I, II (in Polish). Ed. Wydawnictwo Naukowe PWN, Warszawa, 2004. 13. Dan R, Dan M-H, Fan X-R, Chen D-S, Shi Z, Zhang M. Fibres & Textiles in Eastern Europe 2013; 21, 4, 100: 112-117. 92 Conference & Exhibition ‘PROGRESS 14’ INNOVATIONS & COMPETITIVENESS 23-25 September 2014 r., Hotel Andel’s, Łódź, Poland Topics: n Main factors which create the development of the world’s papermak- ing industry: globalization, protection of the environment, informative technologies, the increasing use of waste-paper n Actual state of art and tendencies of technologies development for manufacturing the fibrous pulp, paper and board References Received 19.12.2013 18th International Papermaking n Raw materials and auxiliary products for the production of fibrous pulp and paper – wood and non-wood raw materials, waste-paper, fillers, pigments, paper sizes and other products n Machines, devices and equipment n New technologies and equipment for the manufacturing of packaging from corrugated board n Quality of paper and paper products n Energy problems Exhibition and poster session Simultaneously with the two-day conference activity a poster session presenting research works will be held, as well as a technical exhibition of the manufacturers and suppliers, who will present machines, equipment, control and measuring devices, informative systems, as well as raw materials and auxiliary agents. For more information please contact: Association of Polish Papermakers Plac Komuny Paryskiej 5a, skr. poczt. 200, 90-007 Łódź, Poland, Tel. (42) 6300117, Fax (42) 6324365, E-mail: [email protected] Reviewed 14.04.2014 FIBRES & TEXTILES in Eastern Europe 2014, Vol. 22, 4(106)

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