Development of new mathematical models and their comparison with existing models for the prediction of compression pressure using the cut-strip method

Abstract

Compression socks are a highly acclaimed textile garment for pressure exertion on the lower part of the leg (ankle). This part of the research explains the theoretical investigation of compression pressure by the modelization technique that helped to develop two new mathematical models by incorporating a few missing parameters for the measurement of compression pressure (kPa) and compared with existing models simultaneously. These new parameters including deformed width ( wf), true stress ( σT), logarithmic strain ( εT), true modulus (ET), and engineering stress ( σE)/strain ( εE)/modulus (EE) were incorporated and compared with Hook’s law ( k = fx) used for elastic materials at the ankle position. Various brands of compression socks composed of similar fibrous combinations as well as the knit type were purchased. Initially they were hand-washed, put on the leg for marking, a square was marked, circular cut-strips were detached from the ankle portion of the compression socks, and they were then cut to a linear shape for all 13 sock samples. For this, all linear cut-strips were installed on a Testometric tensile testing machine and were extended to a fixed elongation of 65% of gauge length five times simultaneously, and were then extracted for different extension (mm) values considering the requisite practical elongation values (circumferential difference between leg and socks at the ankle portion). The models developed were compared with Hook’s law and Laplace’s law. The developed models were compared with compression pressure values measured using existing models statistically.

Enhancing Biosignal Quality in Electrocardiogram Monitoring Garments: Validation of a Simulation-Based Contact Pressure Model

“…Siddique’s model is defined as: P 0.25em = 0.25em 2 π E E A 0 ε E C W f where E E represents the engineering elastic modulus (N/mm 2 ), A 0 is the cross-sectional area (mm 2 ) defined as the product of strip width and thickness, ε E is the engineering strain, C is the circumference (mm), and W f is the deformed width of the strip (mm) …”

“…Moreover, the thicker filament may result in larger interfilament spaces, increasing surface roughness, facilitating a more efficient load transfer to the contact surface. 24 The plaited knits developed in this study are suitable for Compression Classification Levels (CCL) I to III 8 and wearable applications, as shown in Figure 5b. For medical purposes, individuals with varying degrees of vascular conditions or lymphedema can benefit from CCL-grade samples, which help reduce the risk of deep vein thrombosis (DVT).…”

“…The loadextension data from the third cycle were converted into a stress− strain curve for analysis. 8 Engineering stress (σ) was theoretically calculated by dividing the force exerted (in Newtons) by the crosssectional area of the specimen (in square meters), and engineering strain (%) was determined by dividing the change in length (in mm) by the specimen's original length. Three analytical approaches were used to comprehensively evaluate the fabric's elastic modulus, dividing elastic regions I, II, and III in Figure 2.…”

“…Models. We utilized two theoretical models (Siddique et al 8 and Teyeme et al 12 ) due to their demonstrated accuracy. The elastic modulus was obtained from three different elastic regions and cyclic tests, as described in Figure 2, and applied to both models.…”

“…Laplace's law relates pressure, tension, and the radius of circular body surfaces with modifications incorporating textileinherent properties like elastic modulus and Poisson's ratio to predict garment pressure. Notably, Siddique et al 8 introduced the EYM model, which expands upon Laplace's law by considering the deformed width of the fabric, thereby enhancing the model's precision and applicability to medical compressional stocking design. Their model has demonstrated greater precision compared to several mathematical models, including those of Leung et al, 9 Dubuis et al, 10 and Macintyre et al 11 While these models offer precision, they rely on uniaxial tensile tests, which present practical challenges.…”