Zusammenfassung
The present work addresses the modeling of the mechanical behavior of heterogeneous materials that are composed of solid particles on the microscopic or a coarser scale. To reproduce phenomena emerging on this scale, the heterogeneous material constitution out of particles is described in an explicit way. For this purpose a discrete element method is used, which models materials by separated, interacting particles. The introduced method employs rigid polygonal particles, a soft modeling of the particle interactions by contact and adhering bond as well as an explicit solution method in time. The aim of this work is, on the one hand, to enhance the models for the interaction between the particles. Since the numerical expense of the method is often high, the models shall depict the important mechanical characteristics of the interactions having acceptable numerical costs. On the other hand, the capability of the developed method is to be analyzed.
For the contact of the particles an elastic normal force model is adopted to represent the repulsive force. It is supplemented by a viscous model. In tangential direction sticking as well as sliding is described by an elasto-plastic contact model. Additionally, sticking and sliding due to friction between a particle and a plane background is modeled by a new, also elasto-plastic contact model. For the adhering bond between the particles an elasto-damage beam model is presented, which is able to reproduce different types of bond failure having acceptable numerical costs. This beam model is extended by a power-law model for the rate-dependent strength so that an increase of the bond strength can be depicted for an increase of the strain rate.
In order to analyze the capability of the developed method in a direct way, conceptual experiments are carried out. Those are, firstly, compression experiments on a granular model material. Using the contact models, characteristic phenomena like shear bands can be described in the simulations. Secondly, compression experiments on a model material out of glued particles are performed. It is demonstrated in the simulations that essential properties of the failure behavior can be represented using the beam model for the adhering bond. Finally, the method is used to simulate concrete. Typical properties of the concrete failure like the localization of the deformation and the failure pattern can be reproduced qualitatively. Using the model for the rate-dependent beam strength, an increase of the specimen strength can be shown for an increase of the loading velocity.
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