Methodology of studying non-planar films and membranes of complex structure
Among the thin-walled structural elements combining lightness and high strength, film and membrane elements are used most widely. Smart coatings with a complex structure are being actively developed nowadays. Proceeding from their functional duty, it is advisable to produce non-planar forms - shell films, membranes and coatings - which can have a complex structure specified by the designer or acquired in the process of manufacture and operation. Study of the mechanical properties of the shell films and membranes with a complex structure using standard uniaxial method of testing appeared ineffective. Complex structures with macro-heterogeneity should not be studied by indentation methods, capable of determining the material properties in the vicinity of the point in question. We developed an experimental-theoretical method for determination of the mechanical characteristics of non-planar films or membrane compositions of complex structure. At the stage of experiment, the stiffness of a non-planar sample (e.g., spherical, cylindrical or toroidal shape) fixed along the contour and loaded with by a unilateral surface pressure is estimated. Then, using the ratios derived from the nonlinear theory of shells, the integral mechanical characteristics of the shell sample material are determined: the reduced modulus of elasticity (elastic strain) or reduced conditional modulus of elasticity (plastic strain), deformation curves, etc. The relations for thin spherical membranes for the case of large displacements and deformations, as well as relations for thin cylindrical membranes of variable radius are considered. Results of the case study of rubber spherical membrane with holes and defect-free catenoidal shell are presented to illustrate the developed methodology.