A membrane equivalent method to reproduce the macroscopic mechanical responses of steel wire-ring nets under rockfall impact

Abstract

Steel wire-ring nets, which have complex nonlinear mechanical behaviour, are widely used in rockfall protection engineering. At present, the circular beam model with a discrete contact boundary is the most accurate method to simulate steel wire-ring nets’ mechanical responses, but its computational efficiency is low. This paper hereby proposes a membrane equivalence-based continuum simulation method: the membrane equivalent method (MEM)11MEM: abbreviation of the membrane equivalent method proposed in this paper to reproduce the macroscopic mechanical behaviour of steel wire-ring nets.. This study’s aim is to greatly improve the computational efficiency of numerical models through the MEM without compromising computational accuracy in macroscopic mechanical behaviour, compared to the circular beam model. According to the out-of-plane loading experimental results of the net panel and membrane analytical model of orthogonal tension belts, an exponential hardening constitutive model of the equivalent membrane was derived. The MEM’s material parameters were corrected in numerical models for a less than 10% error between the simulated and experimental results. Under the rigid boundary condition, the net panel impact simulation results established by the MEM agreed with extant literature’s experimental results, the peak acceleration error was 4.3%, and the rebound characteristic of the net was reproduced. Under the flexible boundary condition, the MEM’s obtained maximum impact displacement and impact force errors were 10.3% and 7.7%, respectively, compared to 3000 kJ full-scale impact experimental results. The MEM’s computational efficiency can be increased almost tenfold compared to that of the circular beam model.