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## Presentations

### Predictability of damage for ideal elastoplastic systems under continuous load

Grachev V.A., Nayshtut Yu.S.

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

Structural data of typical steel specimens cut from the operated structures can vary de-pending on the time of testing: as a rule, the strength of the specimens reduces after a long operation. The problem is to estimate how much longer the structure can operate fail-safe if we know its strength properties under operation and further history of the system loading. It is impossible to solve this problem using the theory of ideal elasto-plasticity with the fixed yield surface. The yield surface is waived in two ways. In the first case scenario we review models [1], where the solid is described with stresses and microstresses associated with deformations by constitutive equations. The second model (isochronous plasticity) postulates the “stress–deformation” equations in a more complex integro-differential form [2]. It is possible to maintain the ideal elasto-plastic model but change the yield surface under irreversible defor-mations [3, 4]. Multiple specific problems have been solved within the above models; howev-er, a comprehensive mathematical theory has not been developed because of the non-linear resulting equations. In this paper the problem is solved in the finite-dimensional timed ap-proximation based on the variational setting and the assumption of defect accumulation [5, 6]. If the load-bearing safety factor is more than one at the initial instant, the solutions can be found until the bearing capacity is completely lost.

Литература.

1. Novozhilov V.V., Kadashevich Yu.I. Microstress in structural materials, — L.: Mashino-stroyenie, Leningrad division, 1990. 224 pages.

2. Valanis K.C. Fundamental consequences of a new intrinsic time measure. Plasticity as a limit of the endochronic theory // Archives of Mechanics, 32, 1980. p. 171–191.

3. Murakami S. Continuum Damage Mechanics // A Continuum Mechanics Approach to the Analysis of Damage and Fracture, Springer: Verlag, 2012. p. 3–13.

4. Kachanov L.M. Fundamentals of fracture mechanics, — M.: Nauka, 1974. 311 pages.

5. Panagiotopulos P. Inequalities in mechanics and their applications. – М.: Mir, 1989. 494 pages.

6. Nayshtut Yu.S. Generalized solutions in the flow theory for elasto-plastic solids // Mechanics of solids, No. 6, 1993. p. 74–78.

#### Presentation

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