The aim of this work is to investigate the fully nonlinear dynamics of mixed convection in porous media heated non-uniformly from below and through which an axial flow is maintained. Depending on the choice of the imposed inhomogeneous temperature profile, two cases prove to be of interest: the base flow displays an absolute instability region either detached from the inlet or attached to it. Results from a combined direct numerical simulations and linear stability approach have revealed that in the first case, the nonlinear solution is a steep nonlinear global mode, with a sharp stationary front located at a marginally absolutely unstable station. In the second configuration, the scaling laws for the establishment of a nonlinear global mode quenched by the inlet are found to agree perfectly with the theory. It is also found that in both configurations, the global frequency of synchronized oscillations corresponds to the local absolute frequency determined by linear criterion, even far from the threshold of global instability

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In this paper, a new experimental technique for measuring Stress Intensity Factor (SIF) and T-stress under mode I loading is developed. The expressions of the normal and tangential strains close to the crack tip are given using the first five terms of the generalized Westergaard formulation. In order to accurately determine the SIF and T-stress, the method exploits the optimal positioning of a rectangular strain gage rosette near a crack tip in mode I. Thus, errors due to the higher order terms of the asymptotic expansion are eliminated. Finally, a comparison of the analytical results with a finite element calculations, for different specimen dimensions, is carried out.

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