Mathematical modeling of extension of an inhomogeneous elastic cloth

Abstract

We propose mathematical models for a knitted fabric in tension that can be used to calculate the strain of the cloth thread from the properties of the cloth and the loads applied to the cloth. Under simplifying assumptions, the problem is reduced to consideration of an elementary cell of the cloth that contains a thread loop. The loop is first modeled by a thread oval with point forces and then by a plate with a hole under distributed loads. In strength analysis, this allows one to use methods of elasticity theory. A number of hypotheses are used to establish the relation between the stress state of the thread oval and the corresponding state of the plate, which makes it possible to model the mechanical behavior of a thread in the material in a variety of forms. The theoretical relationships obtained are compared to the experimental data available in the literature.