Dr.-Ing. Felix Ockelmann
Discrete Element Method in modelling heterogeneous materials
The discrete element method is part of the particle methods and is based on Newton's laws of motion. The method is widely used for modelling heterogeneous materials and granular matter. Calculating the sum of all forces acting on a particle, Newton's second law of motion can be solved for the acceleration of the particle. Explicit time integration schemes are used to solve the initial value problem for the equation of motion and describe the motion of the particles.
Forces acting on a particle result from gravitational effects, contacts with oder particles and boundary conditions. Different contact models can be taken into account when evaluating the interactions of particles with boundaries or each other. The contact model parameter can be fit to the macroscopic properties of the material. An approach to fit the macroscopic parameter to the model parameter is to identify the specific stored strain energy in an chosen unit cell and compare it to the continuum. This method allows a scale transition from a macroscopic continuum approach to an discontinuous approach on the micro scale.
The contact parameter are able to model the macroscopic deformation behavior of the material. In addition it is possible to formulate a local fracture or failure criterion for each contact. The discrete formulation allows the modelling from the crack initiation until to total failure of the structure. The limitation of the local strains is an example for a suitable failure criterion.
The detection of possible collisions with search algorithms is an important part of the software realisation and is able to reduce the computational cost of simulations with many particles significantly. The computation time can be reduced furthermore by parallelizing the evaluation of the contacts.
Publications within the framework of the RTG:
Doctoral thesis:
F. Ockelmann. Modellierung und numerische Analyse von Beton sowie faserverstärktem Ultrahochleistungsbeton mit der Diskrete Elemente Methode.
Publications in peer-reviewed scientific journals:
F. Ockelmann and D. Dinkler. A discrete element model for the investigation of the geometrically nonlinear behaviour of solids. Computational Particle Mechanics, 2017.
Conference contribution with publication in conference proceedings:
F. Ockelmann and D. Dinkler, A three-dimensional discrete element model for heterogeneous solids under mechanical loading. Proceedings in Applied Mathematics and Mechanics (PAMM), 16(1): 227-228, 2016.