Modelization and identification of medical compression stocking: Part 2 – 3D interface pressure modelization

The goal of this article is to propose a practical and scientific model to complete the state of the art in the techniques of determining the pressure exerted by the medical compression stocking on the limbs. The proposed 3D model is developed to explain the mechanics of materials and in particular the compression phenomenon by the medical compression stocking on complex surfaces. This research includes three main parts: The first part presents the research field and assesses the dependence of the constraint between the crushing stress and local geometry of the medical compression stocking bottom. Meanwhile, a pragmatic strategy is provided to simplify the model substantially, based on the assumption that the medical compression stocking structure is subject to small movements induced by muscular contractions. The second part focuses on solving the exact 3D model as a generalization of Laplace's laws by dividing the complicated model into several simple sub-models, making it easier to reveal the non-trivial relations connecting the crushing stress, the local radius of curvature of the bottom, the membrane forces and the material constituting the bottom. Considering the fact that the bottom has extremely low thickness, the third part further provides the asymptotic model to obtain the limiting behavior of the 3D model, which shows that the bottom resists essentially by its tangential rigidity. Meanwhile, the influences of the radii ratio of curvature on the crushing stress are discussed and highlighted. The simulation results are also verified by the finite element method, aiming to optimize the design of medical compression stockings and increase their therapeutic effect.