It is a well-known fact that the first 70-80% of the lifetime of a material or a component subjected to real operation conditions occurs in a damage or crack initiation phase, where damage or cracks are on microstructural scale and damage progression is influenced by the materials local microstructure. Hence, to correctly assess the lifetime of materials or components it is very important to take the influence of the materials microstructure into account. However, to address the influence of the local microstructure on the macroscopic behaviour of the material and component for example homogenization and multiscale methods are needed, which are quite numerically demanding. This mini-symposium is focused on the numerical assessment of the lifetime of materials during this early damage or crack initiation phase, where damage progression is dominated by the materials microstructure. In addition, in real applications materials and components operate under multi-physical conditions, i.e. the material is exposed to elevated temperatures and/or a hostile environment causing degradation for example due to: - Fatigue loads particularly in the low-cycle fatigue regime causing cyclic plastification - Corrosion, for example due to corrosive combustion products such as sulfur dioxide, carbon monoxide, nitrogen oxide and water vapour. Here, the impact of the increased water vapour content of synthetically and environmentally friendly produced sustainable fuels is of particular interest - Hydrogen embrittlement and hydrogen assisted cracking of materials in hydrogen environments. Here, the impact of hydrogen on the materials in fuel cells, storage tanks or in hydrogen combustion engines is a particular focus - Fretting wear due micro-sliding in contact areas Particularly under low-cycle fatigue loads damage occurs at the surface of the component, which strongly interacts with other degradation mechanisms acting on the surface. Hence, for this mini-symposium presentations and contributions focusing on the interactions between the aforementioned damage mechanisms are of particular interest. While the mini-symposium is focusing on the development of numerical methods to address the problem areas described above, examples, where a validation of the numerical methods using experimental data was demonstrated shall also be included.