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 (w_f), true stress (σ_T), logarithmic strain (ε_T), true modulus (E_T), and engineering stress (σ_E)/strain (ε_E)/modulus (E_E) 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.