The purpose of this paper is to develop a method to model entire structures on a large scale, at the same time taking into account localized non-linear phenomena of the discrete microstructure of cohesive-frictional materials.
Finite element (FEM) based continuum methods are generally considered appropriate as long as solutions are smooth. However, when discontinuities like cracks and fragmentation appear and evolve, application of models that take into account (evolving) microstructures may be advantageous. One popular model to simulate behavior of cohesive-frictional materials is the discrete element method (DEM). However, even if the microscale is close to the macroscale, DEMs are computationally expensive and can only be applied to relatively small specimen sizes and time intervals. Hence, a method is desirable that combines efficiency of FEM with accuracy of DEM by adaptively switching from the continuous to the discrete model where necessary.
An existing method which allows smooth transition between discrete and continuous models is the quasicontinuum method, developed in the field of atomistic simulations. It is taken as a starting point and its concepts are extended to applications in structural mechanics in this paper. The kinematics in the method presented herein is obtained from FEM whereas DEM yields the constitutive behavior. With respect to the constitutive law, three levels of resolution – continuous, intermediate and discrete – are introduced.
The overall concept combines model adaptation with adaptive mesh refinement with the aim to obtain a most efficient and accurate solution.
The present study is supported by the German research foundation (DFG) within the Cluster of Excellence in Simulation Technology. This support is gratefully acknowledged.
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