Discrete element representation of continua: Proof of concept and determination of the material parameters
A common approach for the modelling of metal or microfibre reinforced materials is to see these materials as a continuum on the macro scale. A major drawback is that an equation based on the continuum theory is unable to predict the various complicated microscopic effects, even though those effects have a strong influence on the macroscopic behaviour, e.g. on fracture, fatigue and life time. A large number of attempts has been made to correct the shortcomings of the continuum-based theories. One interesting alternative to common approaches for the numerical modelling of discontinuous materials is the Discrete Element Method (DEM).
Within the DEM, the individual particles are modelled as stiff (or rigid) bodies which interact via contact forces. This simplification has the advantage of the complicated microscopic behaviour being represented by a simple system of linear equations based on a relatively small number of parameters. This paper describes the requirement for new computational methods for the modelling of fracture mechanics. First of all a proof of the described method will be shown. Then two examples are presented in order to verify the Discrete Element Method. Furthermore it will be shown how the corresponding material parameters are gained and implemented and how the boundary conditions have to be modelled in order to achieve exact results for the stress and strain fields of 2D shells.
Keywords: Continuum mechanics, Lattice model, Discrete Element Method, Framework method, Spring network models, Fracture, Material parameter, Airy stress function