Presentations

Damage predictability of visco-elasto-plastic structures under long-term operation

Grachev V.A., Neustadt Y.S.

Samara State Technical University, Department of Civil Engineering, Subdepartment of Metal and Wooden Structures Russia, 443001, Samara, St. Molodogvardeyskaya 194, Phone: +7(846)339-14-94, E-mail: neustadt99@mail.ru

The purpose of this study is to estimate the time of failure-free operation of visco-elasto-plastic structures until the moment of their possible collapse during extensive operation under a variable quasistatic load. The damage is predicted after a long service life of a building when its material has relatively high stresses and deformations. The properties of the material are described with the equations of the ideal elasto-plastic bodies in combination with creeping [1,2]. The yield criterion is taken in the Nadai-Schleicher form where constant tensors of the structure are replaced with damage accumulation tensors that are differentiable functions of non-elastic deformations (plasticity and creeping) [3,4]. The model of the strength analysis within the mechanics of solids is based on the following main assumptions: the creep regime is considered to be steady, the plastic part of the strain tensor is normal to the loading surface while the elastic part of the deformations follows Hooke’s law. Mathematically, the problem is initially defined within the space of bounded deformations introduced by Lions and his successors. The generalized solutions to the problem of damage predictability are studied in the space of distributions using variational inequalities. In this setting the existence of the solutions is managed to be proved. During the proof, the time when the visco-elasto-plastic structure collapses is determined. At that moment the safety factor against plastic failure (free flow) becomes small than one. The proposed calculation algorithm can be numerically implemented [5].

References.

1. Kachanov L.M. Fundamentals of damage mechanics. — M.: Nauka, 1974.

2. Rabotnov Y.N. Creeping of structural elements. Ed. 3.— М.: URSS, 2019.

3. Novozhilov V.V., Kadashevich Y. I. Microstresses in structural materials. — L.: Mashinostroenie, Lenindrad division. 1990.

4. Neustadt Y.S., Grachev V.A. Nonfailure operating time of ideal elastoplastic structures under close-to-ultimate loads. Z. Angew. Math. Phys.—2025. –Vol. 76, — 35 https://doi.org/10/1007/s00033-024-02410-9

5. Langtangen H.P., Mardal K.A.: Introduction to Numerical Methods for Variational Problems. Springer, New York. 2019

• abstract in Russian (PDF)