 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
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| D. V. Babich, "On the Local Buckling of Compressed Shells of Revolution Due to Micro-Fracture in the Material," Mech. Solids. 38 (5), 106-112 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
5 |
Pages |
106-112 |
| Title |
On the Local Buckling of Compressed Shells of Revolution Due to Micro-Fracture in the Material |
| Author(s) |
D. V. Babich (Kiev) |
| Abstract |
Inhomogeneity of strength characteristics of structural elements causes accumulation of micro-defects like plane cracks or pores in many materials [1-3]. Such structural changes of a material are responsible for the nonlinearity of the strain diagram.
One of the methods for joint description of deformation and damage has been proposed in [4], where fractured micro-volumes are modeled by structural micro-elements in the form of micro-pores.
Below, we propose a continuous model of deformation of elastic-brittle materials with accumulation of damage in the form of micro-cracks randomly distributed over the deformed body. The model was constructed with the assumption that in the process of deformation the micro-cracks neither grow nor interact with each other. The model proposed here is used to study local buckling of convex shells of revolution. There are two types of buckling connected with the nonlinearity of the state equations that accounts for the accumulation of plane micro-cracks (a similar situation arises in the investigations of buckling beyond the elastic limit). These are the buckling under continuous loading (the absence of unloading regions) and the buckling under constant loading (the presence of regions of unloading and additional loading). In the unloading regions the crack concentration does not change, and therefore, deformation obeys the linear law. During the additional loading, the material undergoes nonlinear deformation due to an increase in crack concentration. Such a specific feature of deformation of the shell under constant loading, the reduced modulus load exceeds the tangential modulus load. To simplify the statement of the problem and increase the accuracy of the solution of the buckling problem, we use the concept of continuous loading. |
| References |
| 1. | L.N. Germanovich and A. V. Dyskin,
"A model of fracture of brittle material with cracks under uniaxial loading,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 118-131, 1988. |
| 2. | A. Dragan and Z. Mruz,
"A continuous model of plastic-brittle behavior of rock and concrete," in
G. S. Shapiro (Editor), Mechanics of Solids. Trends of Development [in Russian],
pp. 163-188, Mir, Moscow, 1983. |
| 3. | V. P. Tamuzh and V. S. Kuksenko,
Micro-mechanics of Polymer Fracture [in Russian], Zinatne, Riga, 1978. |
| 4. | L. P. Khoroshun,
"Fundamentals of micro-mechanics of damage. I. Short-term damage,"
Prikl. Mekh., Vol. 34, No. 10, pp. 120-127, 1998. |
| 5. | E. I. Grigolyuk, "Plastic buckling of shells of revolution,"
Izv. AN SSSR. OTN, No. 2, pp. 130-132, 1958. |
| 6. | D. V. Babich, "Approximate account for the material damage equilibrium problems for elastic shells," Probl. Prochn., No. 3, pp. 20-30, 1996. |
| 7. | D. V. Babich, "An investigation of the stability of composite shells with cracked material components," Prikl. Mekh., Vol. 35, No. 11, pp. 46-54, 1999. |
| 8. | R. L. Salganik, "Mechanics of bodies with a large number of cracks,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 4, pp. 149-158, 1973. |
| 9. | V. V. Bolotin, Prediction of Service Life for Machines and Structures [in Russian],
Mashinostroenie, Moscow, 1984. |
| 10. | G. Kramer, Mathematical Methods of Statistics [Russian translation], Mir, Moscow, 1976. |
| 11. | Yu. N. Rabotnov, "Local stability of shells,"
Doklady AN SSSR, Vol. 52, No. 2, pp. 111-112, 1946. |
|
| Received |
18 January 2001 |
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