Steel Fibre Reinforced Concrete Simulation with the SPH Method

Abstract

Steel fibre reinforced concrete (SFRC) is very popular in many branches of civil engineering. Thanks to its increased ductility, it is able to resist various types of loading. When designing a structure, the mechanical behaviour of SFRC can be described by currently available material models (with equivalent material for example) and therefore no problems arise with numerical simulations. But in many scenarios, e.g. high speed loading, it would be a mistake to use such an equivalent material. Physical modelling of the steel fibres used in concrete is usually problematic, though. It is necessary to consider the fact that mesh-based methods are very unsuitable for high-speed simulations with regard to the issues that occur due to the effect of excessive mesh deformation. So-called meshfree methods are much more suitable for this purpose. The Smoothed Particle Hydrodynamics (SPH) method is currently the best choice, thanks to its advantages. However, a numerical defect known as tensile instability may appear when the SPH method is used. It causes the development of numerical (false) cracks, making simulations of ductile types of failure significantly more difficult to perform. The contribution therefore deals with the description of a procedure for avoiding this defect and successfully simulating the behaviour of SFRC with the SPH method. The essence of the problem lies in the choice of coordinates and the description of the integration domain derived from them – spatial (Eulerian kernel) or material coordinates (Lagrangian kernel). The contribution describes the behaviour of both formulations. Conclusions are drawn from the fundamental tasks, and the contribution additionally demonstrates the functionality of SFRC simulations. The random generation of steel fibres and their inclusion in simulations are also discussed. The functionality of the method is supported by the results of pressure test simulations which compare various levels of fibre reinforcement of SFRC specimens.Steel fibre reinforced concrete (SFRC) is very popular in many branches of civil engineering. Thanks to its increased ductility, it is able to resist various types of loading. When designing a structure, the mechanical behaviour of SFRC can be described by currently available material models (with equivalent material for example) and therefore no problems arise with numerical simulations. But in many scenarios, e.g. high speed loading, it would be a mistake to use such an equivalent material. Physical modelling of the steel fibres used in concrete is usually problematic, though. It is necessary to consider the fact that mesh-based methods are very unsuitable for high-speed simulations with regard to the issues that occur due to the effect of excessive mesh deformation. So-called meshfree methods are much more suitable for this purpose. The Smoothed Particle Hydrodynamics (SPH) method is currently the best choice, thanks to its advantages. However, a numerical defect known as tensile instability may appear when the SPH method is used. It causes the development of numerical (false) cracks, making simulations of ductile types of failure significantly more difficult to perform. The contribution therefore deals with the description of a procedure for avoiding this defect and successfully simulating the behaviour of SFRC with the SPH method. The essence of the problem lies in the choice of coordinates and the description of the integration domain derived from them – spatial (Eulerian kernel) or material coordinates (Lagrangian kernel). The contribution describes the behaviour of both formulations. Conclusions are drawn from the fundamental tasks, and the contribution additionally demonstrates the functionality of SFRC simulations. The random generation of steel fibres and their inclusion in simulations are also discussed. The functionality of the method is supported by the results of pressure test simulations which compare various levels of fibre reinforcement of SFRC specimens.