The mechanical stability of the surface is discussed in this master thesis. The theoretical part is divided into two sections: in the first, surface buckling due to volumetric tissue growth is analyzed, and the second deals with stresses and strains in the two-layer system, which consists of a thin film lying on a thicker substrate. The system is loaded in three different ways: over the entire domain, through a film due to its growth, and by pre-stretching the substrate. Systems with different stiffness ratios between the film and the substrate, beta. A general set of 8 governing equations for the instability of two-layer systems is derived and further reduced depending on the case under consideration. As a result, a relationship for the critical deformation as a function of the stiffness ratio and the normalized wavelength is obtained. We also perform numerical simulations in Abaqus and find that the results are quite consistent with the analytical results for beta=100 and 10, while the deviations become very large at lower ratios. For planar cases we also perform a static structural analysis. Based on the data obtained, we show where the system buckles. The numerical simulations also predict wrinkling in several directions, which are not predicted analytically. Finally, we also analyze some of the eigenmodes and find that in some cases they are very close to each other in terms of critical load.
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