Browsing by Author "Dettmar, Joachim Peter"

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Static and dynamic homogenization analyses of discrete granular and atomistic structures on different time and length scales
(2006) Dettmar, Joachim Peter; Miehe, Christian (Prof. Dr.-Ing.)
This work deals with scale bridging methods for discrete microscopic granular and nanoscopic atomistic aggregates of particles between different length and time scales. The bridging between the scales is achieved by direct homogenization of micro- and nanoscopic physical quantities. In the first part of the work, static homogenization techniques for granular materials are developed where a distinct definition of a granular microstructure serves as the starting point for the development of homogenization definitions. Three new boundary constraints are consistently derived from classical continuous definitions and implemented in a strain-driven environment. The finite-sized character of the particles is accounted for in the formulation. With regard to stiffness, it is shown that the periodic surface constraints are bounded by the linear deformation- and uniform traction constraints. Additionally, true dual-scale analyses of granular structures at large strains are performed. The continuum approach on the coarse scale employs the finite element method which serves as a numerical tool without any constitutive assumptions as the physical input is solely governed by the granular microstructures. The second part of the work covers dynamic homogenization techniques in connection with the classical molecular dynamics method for atomistic simulations. A uniform traction constraint is developed and it is shown that this formulation is the only suitable choice as it allows for a computational modeling of defects and cracks in a nanosystem. The constraint is implemented in a deformation-controlled environment allowing for computational treatments in coarse scale continuum methods. The dynamic homogenization incorporates the kinetics of all atoms in the aggregate. Several numerical examples in all sections of the thesis round off the discussion of the static and dynamic homogenization techniques for discrete structures.