Modelling and simulation of constitutive inelastic effects in composite cables by means of Prandtl-Ishlinskii operators

Abstract

This thesis develops a mathematical framework for modelling the inelastic bending behaviour of composite electric cables within the theory of Cosserat rods. Motivated by industrial cable simulation, the cable is treated as a homogenised slender structure whose constitutive response exhibits rate-independent hysteresis. Prandtl-Ishlinskii hysteresis operators are used to describe the curvature-moment relation, allowing inelastic memory effects to be captured in a mathematically compact way. The operators are formulated in vector form, discretised, and interpreted in terms of classical elastoplastic concepts and homogenised spiral strand mechanics. The resulting constitutive model is integrated into a two-dimensional Cosserat rod formulation and validated through benchmark bending simulations. The approach provides a rigorous yet practical link between applied analysis, numerical simulation, and engineering applications, enabling predictive modelling of flexible composite structures.