The characteristic special feature of deformation behavior of modern laminated composite materials and structural elements fabricated from these materials, at current levels of loading and operating conditions is the occurrence of the purely three-dimensional stress-deformed state. In this process some specific mechanical phenomena and effects may occur, which is impossible to describe within the framework of applied or approximate approaches existing currently in deformable solid body mechanics. The structure of massive laminated materials may be included in this class of phenomena when the critical parameters of the problem depend only on the ratio between mechanical and geometrical characteristics of single layers and are independent of the dimensions and the form of the total laminated body as a whole. Since this phenomenon may be the beginning of the process of fracture of these materials, and the loss of the load-carrying capacity of structure elements fabricated from them, we consider below, in three-dimensional formulation, the problem of the surface and internal instability in laminated composite materials under compressive surface loads. The classification of the existing types of stability problems is presented for laminated materials and approaches for their solution presented in the literature. On the basis of three-dimensional linearized stability theory, within the framework of the piecewise-homogeneous media model, the general formulation of the most characteristic classes of stability problems of laminated materials is given in Lagrangian coordinates at small and finite, homogeneous and inhomogeneous precritical deformation. Analytic and variational methods of investigation of formulated problems are given with application to various models of laminated bodies models, in accordance with accepted stability criteria. The accuracy of these models is evaluated, based on the example of the solution of certain model problems; the range of application is given for existing applied and approximate approaches to the analysis of formulated problems. Results of solution of specific problems are given; specific mechanical effects, characteristic for the phenomenon considered, are found. Recommendations are formulated for engineering design and computational methods. New promising areas of research are pointed out for the problem of laminated composite materials stability.

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