On crack propagation in thermo-elastic media with inhomogeneities by Sergei Serkov (U. of U. Math) JTB 120 3:20 PM Monday March 30th, 1998 Abstract We consider a crack in an infinite thermo-elastic medium with inhomogeneities. The inhomogeneities are represented in the form of inclusions or cavities of arbitrary shape. They are located far away from the crack line. Thus the presence of a small parameter allows one to apply asymptotic methods. The solution of the inverse problem - determination of the crack trajectory - is analysed. The crack trajectory is determined in terms of Polya-Szego (``polarization'') matrices, which specify the energy change associated with a defect. Knowledge of the Polya-Szego matrices for the different defects allows one to analyse the crack behaviour and to determine situations when the crack deflection is maximal (or minimal). For an inclusion with a debonding-type interface, conditions when the shield effect occurs are found. A number of examples are given where the crack trajectories are calculated explicitly. Comparison with experimental data is discussed.