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Within the framework of a one-temperature model of thermoelasticity, an analysis of the effect of electron localization processes on the thermoelastic response of conductors under pulsed-laser action is conducted. It is shown that electron localization can lead to considerable tightening of the deformation processes in conductors as compared with processes that develop in accordance with a typical thermoelastic mechanism.

The problem of a heating source acting on a certain part of a beam surface and moving along it with given speed $${v}$$ is solved. It is shown that the most significant role in formation of the beam deflection under loading by a compression force is played by concentrated moments occurring at the moving boundary of the heating source. It is noted that for a source speed less than some critical value, the beam deflection is essentially nonmonotonic. In this case, the largest beam bending deflection occurs when the source speed reaches a value corresponding to the Euler critical force.

The deformation and fracture of graphene sheets containing 555–777 defects have been investigated by molecular dynamics simulations. Each such defect is a divacancy forming a localized configuration of three pentagonal and three septangular cells of carbon atoms in a hexagonal graphene lattice. An emphasis is made on the influence of 555–777 defects in graphene on its mechanical characteristics (stress–strain curve, uniaxial tensile strength, and maximum elastic strain).

The deformation and fracture processes in graphene nanoribbons containing linear quadrupoles of disclinations are investigated by the method of molecular dynamics. Special attention is given to estimating the effect of the curvature formed by disclinations and free boundaries in graphene nanoribbons with linear quadrupoles of disclinations on their mechanical characteristics (the stress–strain curve, the strength at the single-axis tension, and the degree of plastic deformation).

The influence of localization of vibrations on film exfoliation from an elastic basis is investigated. A model is suggested that makes it possible to find an approximate analytical solution and to analyze the conditions of increasing and decreasing exfoliation.