VARIATIONAL PRINCIPLE FOR DESCRIBING LIMITING LOADING PROCESSES.

The functional relationship between the damage and stress tensors, postulated by Il'yushin's theory of long-term strength, provides the basis for developing strength theories that evaluate the degree of danger of the most general forms of loading. The limit of applicability of this theory can be expanded somewhat by assuming that there exists a simultaneous functional relationship between the damage tensor and the stress and strain tensors, whose components are nonperiodic functions of time, and also by constructing one of the versions of strength theory for loads that are described by functions of bounded variation. The theory presented in the article employs linear integral operators in Hilbert space and variational calculus to describe limiting processes of damage accumulation in solids under the action of mechanical loading. This approach is consistent with the thermodynamics of closed equilibrium systems.