Selforganized Mesh Generation For The Simulation of Potential Based Forming Processes

The main goal of this dissertation is the development of procedures, that allow the simulation of any desired potential based forming. The initial states consist of mechanical material systems.

Forces, that are in accordance with the negative gradients of the applied potentials, cause selforganized deformations of the material systems. Within this research some simulation procedures shall be developed that discretize the material system first. Similar to Finite-Element-Methods meshes must be generated. But in order to model selforganizing processes theses meshes themselves should have process conformed topologies. In cases of 2D-surfaces in 3D-space hexagonal or graphene meshes are provided. Additionally, in cases of 3D-bodies diamond lattice structures are proposed. Their generation should start similar to a nucleation and should continue with a selforganized growth as a consequence of a given mathematical rule.

The availability of these tools allows the prediction of final geometries of sintered structures even in the presence of volume shrinkage. Furthermore any desired intermediate state geometries can be calculated with very few efforts. Very specific curvatures are anticipated: minimal surfaces and triple periodic surfaces with constant mean curvature.