Predicting the Failure of Viscoelastic-Plastic Structures During Long-Term Operation

Abstract

This article evaluates the service life of a viscoelastic-plastic structure before potential failure during long-term operation under a given variable quasi-static load. Failures are predicted after a significant period of trouble-free service, when the material experiences relatively high stresses and strains. The material is subject to the Nadai–Schleicher yield condition, where constant structural tensors are replaced by damage accumulation tensors that are smooth functions of inelastic strains (plasticity and creep). A mechanical model for strength analysis is formulated within the framework of continuum mechanics under the following assumptions: viscous performance (creep) conditions are considered steady-state, the plastic part of the strain tensor is normal to the loading surface, and the elastic part of the strain follows Hooke's law. The mathematical problem is initially formulated in the space of bounded deformations studied by the Lions school. This space naturally integrates into the space of generalized Sobolev functions. Using methods of variational inequalities, we can prove the existence of generalized solutions to the problem. During the proof, we can determine the time at which the viscoelastoplastic structure fails. At this point in time, the factor of safety against plastic failure (unbounded flow) becomes less than one. Importantly, the proposed calculation algorithm can be implemented numerically.