Nonfailure operating time of ideal elastoplastic structures under close-to-ultimate loads: Nonfailure operating time...: Y. S. Neustadt, V. A. Grachev.

During long-term operation of elastic–plastic systems, inelastic deformations inevitably appear in the structure, leading to a decrease in the ultimate load that a building can resist. The question is how to estimate the remaining failure-free operating time of the structure if the operating strength parameters and the future load history are known. The theory of ideal elastoplasticity with a fixed yield surface cannot be applied to solve this problem. The current literature considers two approaches. The first involves models where a solid is defined by stresses and microstresses linked to deformations via constitutive equations. The second approach (isochronous plasticity) introduces the stress–deformation equation in a more complex integro-differential form than the elastic medium does. Although numerous problems have been studied via these models, a common mathematical theory has not been developed owing to the resulting nonlinear equations. This study offers a solution to the problem in a generalized framework based on variational principles and the assumption of defect accumulation. The concept of the damage accumulation tensor is introduced within the Schleicher–Nadai model depending on plastic deformation. This tensor is assumed to be determined by mechanical testing of the structural material. If the bearing safety factor against plastic failure exceeds unity at a certain time, then generalized solutions to the reviewed problem exist. In conclusion, the issues arising from the accepted problem setting that require further study are identified. [ABSTRACT FROM AUTHOR]