Computational homogenisation of thermomechanical problems

Abstract

The thesis at hand deals with the modelling of heat input and mass deposition during thermal spraying and especially with the capturing of the effective material behaviour of microstructures under consideration of inelasticity in the framework of thermo-mechanical continua. The heat input during thermal spraying is modelled by means of convective heat transfer as well as radiation in the framework of a non-linear rigid heat conductor which is implemented into a finite element programme. This model is subsequently extended in order to capture mass deposition via hot particles by a novel thermodynamically consistent ansatz. As this work proceeds, the main emphasis of this thesis is on the development of a thermo-mechanically coupled two-scale finite element programme. Here, the effective material behaviour of underlying microstructures is directly used in the solution of boundary value problems at the upper scale of application by means of numerical homogenisation. The implementation is carried out in the framework of small as well as finite deformations. In both cases, a thermo-viscoplastic material model is applied in order to exemplarily represent non-linear inelastic material behaviour. Furthermore, novel boundary conditions are elaborated for the solution of thermo-mechanically coupled boundary values problems at the scale of the underlying microstructure. The capabilities of the developed finite element frameworks as well as of the novel methods included therein are shown by means of descriptive numerical simulations.