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A model of material of complex crystalline structure consisting of two lattices coupled by nonlinear interaction forces that ensure several stable equilibrium configurations is considered. The continuum model is compared with the discrete model whose analysis reveals the effect, which has been observed in high-speed deformation experiments, of decrease in the initial pulse under nonstationary actions.

Loss of stability under uniaxial tension in an infinite plate with a circular inclusion made of another material is analyzed. The influence exerted by the elastic modulus of the inclusion on the critical load is examined. The minimum eigenvalue corresponding to the first critical load is found by applying the variational principle. The computations are performed in Maple and are compared with results obtained with the finite element method in ANSYS 13.1. The computations show that the instability modes are different when the inclusion is softer than the plate and when the inclusion is stiffer than the plate. As the Young’s modulus of the inclusion approaches that of the plate, the critical load increases substantially. When these moduli coincide, stability loss is not possible.

In the process of deformation of such multilayer structures, significant stresses can arise on the foundation-coating interface because of the difference in their physical and mechanical properties, which can result in fracture or coating separation. The action of static or impact loads on damage onset and development in the adhesive layer in such multilayer structures has been investigated almost completely, but similar processes in the case of suddenly applied vibration loads have not been studied to a large extent. The latter draw attention because of the fact that even small variable actions can localize vibrations near the imperfections (inclusions, defects, etc.) and can be accompanied with an increase in the damage of the adhesion layer, which results in partial separation of the film. In the present paper, the possibility of vibration localization in damaged regions and the influence of the localization on the damage development till the film separation are studied. The first of the possible scenarios of the damage region behavior is its monotone increase. The second scenario of damage behavior is its constant stepwise growth. In this case, damage increases on some time intervals and is constant between the intervals. Under the conditions obtained in the paper, this second scenario can be transformed into the first one. The third scenario is that damage does not increase. This scenario can be realized under sufficiently large vibration load frequencies. Some conditions under which damage behavior is determined by the localized oscillating part of the solution are derived.

In modern constructions, thin-layer coats are often used as protecting or strengthening elements. Deformations of such constructions may cause significant stresses on the interface between the base and the coat because of the difference in their physical-mechanical properties, which leads to the destruction or detachment of the cover. Of special interest is strength analysis under dynamical or vibrational impacts because of the possibility of localizing oscillations in a neighborhood of the initial inhomogeneities (such as inclusions, defects, construction elements, etc.).

We suggest a two-component model of a material experiencing structural transformations and use it to study how dynamic and evolution processes affect these transformations. We note that an essential role is played by internal interactions caused by internal forces arising between the components as well as by exchange processes describing variations in the composition of both components. We illustrate the model by specific examples.