Fast mesoscopic simulation of grain growth and macroscopic modeling

The Orientated Tessellation Updating Method (OTUM) is a fast mesoscopic model of grain growth that has been published recently for a single phased metal without diffusion or segregation of alloying elements. It is based on tessellation techniques and simple linear algebra. On this basis, some ideas to develop an upscaling strategy are broached in this work. The aim is to develop a macroscopic model of grain growth whose state variables contain for each material point the statistical descriptors of the microstructure (e.g., disorientation, grain size and shape distributions). The approach consists in reducing the amount of data needed in the mesoscopic model. Indeed, state variables of the mesoscopic model lies in a high-dimensional space (several hundreds of dimensions) although state variables of the corresponding macroscopic model should ideally be in a low-dimensional space (e.g., less than 10 dimensions). The strategy is to determine macroscopic free energy and dissipation potentials on the basis of a large number of computations at the mesoscopic scale (i.e., polycrystal). In addition, the mesoscopic model is perfectly deterministic. However, as a macroscopic state may corresponds to a large number of different mesoscopic states an epistemic randomness arises at the macroscopic scale.