1 Introduction to the Combined Finite- Discrete Element Method Máté Hazay Budapest University of Technology and Economics, Hungary Ante Munjiza Queen Mary University of London, England ABSTRACT This chapter presents a general overview of the combined finite-discrete element method (FEM/DEM) which is considered as a state-of-the-art technique for the mechanical analysis of masonry structures. In a FEM/DEM simulation each discrete element representing a stone block is discretised into finite elements in order to describe the deformability of the blocks. This chapter deals with the main steps of the FEM/DEM including contact detection, contact interaction, fracture and fragmentation algorithms, calculation of deformations and the time integration of the equation of motion. The FEM/DEM is advantageously used to simulate transition from continua to discontinua processes which may lead to the collapse of the structure. Some examples for practical applications found in the literature are mentioned. Keywords: Contact detection, Contact interaction, Potential force concept, Green-St. Venant tensor, Fracture, Fragmentation, Central difference method, Parallelization, Ante Munjiza, Y3D INTRODUCTION The two basic types of mechanical models are the classical models of continuum mechanics and the models of discrete elements. The finite element method (FEM) is the most widely used technique to model continuum mechanical problems. On the other hand, the discrete element method (DEM) is able to describe discontinuum-based phenomena including the motion and interaction of individual particles. However in certain situations the two different phenomena arise at the same time, thus the development of a coupled numerical tool was required. Therefore, in the early 1990s the two above mentioned methods have been combined and the resulting method was termed the combined finite- discrete element method (FEM/DEM). A typical combined finite-discrete element simulation comprises large number – thousands or even millions – of particles which are represented by a single discrete element. In FEM/DEM each discrete element is discretized into finite elements in order to describe the deformations of the blocks. Furthermore, the classical steps of discrete element method, including contact detection, contact interaction and time integration are applied to follow the motion and interaction of the individual particles. This method was implemented mainly to simulate so-called transition from continua to discontinua problems, including failure, fracture and fragmentation processes. Thus, detailed structural collapse simulations can be performed with the help of the FEM/DEM. These simulations can play a vital role in the design of structures against hazardous loading conditions. In this case the load bearing capacity of the structure can be determined, and the progressive collapse modes can be identified as well. Some examples for modelling transition from continua to discontinua problems can be found in (Munjiza, 2004, pp. 30-32).
Introduction to the Combined FiniteDiscrete Element Method
Jun 15, 2023
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