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The features of thin-film membranes, which are formed above round holes in silicon substrates using the Bosch-process are considered. The membrane has a complex shape due to the presence of the stress state of the initial films. The analysis of the dependence of the membrane deflection w on the supplied overpressure P is used to calculate the mechanical characteristics of the membranes. In this case, it is necessary to determine directly on the membrane its diameter, the thickness of the constituent layers, the change in the topography of the membrane surface over its entire area as the overpressure increases. Determination of the membrane diameter and the thicknesses of the constituent layers is shown by the example of p-Si*/SiNx/SiO2 and SiNx/SiO2/SiNx/SiO2 membranes. We used spectral ellipsometry, energy-dispersive X-ray spectroscopy, optical profilometry, optical microscopy. The influence of the peculiarities of the fixing conditions on the stress-strain state of membranes is shown, and the assessment is carried out by means of numerical modeling. A technique has been developed for measuring and calculating the mechanical characteristics of membranes that have an initial deflection. The calculation result is shown on the example of a membrane with an initial deflection of 2 μm --- SiNx/SiO2/SiNx/SiO2 and a membrane with an initial deflection of 30 μm --- Al/SiO2/Al. Keywords: stress, bulging method, films, thin-layer coating, film thickness, membrane, pressure blister test, residual stress, microelectromechanical systems, MEMS, silicon substrate, large deformations, strain, deflections, circular membrane, bulge testing.

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In the paper the relationship between pure geometrical concepts of the theory of affine connections, physical concepts related with non-linear theory of distributed defects and concepts of non-linear continuum mechanics for bodies with variable material composition is discussed. Distinguishing feature of the bodies with variable material composition is that their global reference shapes can not be embedded into Euclidean space and have to be represented as smooth manifolds with specific (material) connection and metric. The method for their synthesis based on the modeling of additive process are proposed. It involves specific boundary problem referred to as evolutionary problem. The statement of such problem as well as illustrative exact solutions for it are obtained. Because non-Euclidean connection is rarely used in continuum mechanics, it is illustrated from the perspective of differential geometry as well as from the point of view, adopted in the theory of finite incompatible deformations. In order to compare formal structures defined within the models of solids with variable material composition with their counterpart in non-linear theory of distributed defects, a brief sketch for latter is given. The examples for cylindrical and spherical non-linear problems are presented. The correspondences between geometrical structures that defines material connection, fields of related defect densities and evolutionary problems for bodies with variable material composition are shown.