No abstract

Solid particle erosion is one of the main damage mechanisms in high-pressure compressors of jet engines. The significant shape change of the compressor blades leads to performance degradation over lifetime. To enhance predictive capabilities of erosive wear measurements under conditions, related to high pressure compressors, were performed. Even if there is no general model to describe erosive wear, it is understood that the transfer of kinetic energy from the impacting particle into the material is a central aspect in modelling erosion. In order to predict erosive wear of general geometries, SCHRADE ET AL. [9] developed a numerical model, based mainly on experimentally determined erosion rates. The shortcoming of such modelling approaches is the limited applicability in situations deferring to the measurement conditions. In the following, we will describe a physically based damage model, closing the gap between measurement and calculating shape changes of general specimens. Based on the phase-field approach for predicting crack evolution presented by MIEHE ET AL. [6], an overall energy balance of the considered specimen is constructed. A dissipative portion describes the influence of propagating damage, while special boundary conditions provides information about the energy transfer between impinging particles and specimen.

The hypercircle theorem leads to a posteriori error estimates for the three-field variational formulation of the Biot problem involving displacements, total pressure and fluid pressure. Based thereon, adaptive strategies can be constructed. In particular, the error estimator is derived on the basis of H(div)-conforming reconstructions of stress and flux approximations while the symmetry of the reconstructed stress is allowed to be satisfied only weakly. The reconstructions can therefore be performed locally on a set of vertex patches. The local nature of the reconstruction leads to two different possible adaptive strategies. In this paper, we review these two different adaptive strategies for the Biot problem. Numerical experiments underline the differences between the two strategies.