ANALYSIS OF IMPACT ON COMPOSITE STRUCTURES WITH THE METHOD OF DIMENSIONALITY REDUCTION

Valentin L. Popov

DOI Number
-
First page
39
Last page
46

Abstract


In the present paper, we discuss the impact of rigid profiles on continua with non-local criteria for plastic yield. For the important case of media whose hardness is inversely proportional to the indentation radius, we suggest a rigorous treatment based on the method of dimensionality reduction (MDR) and study the example of indentation by a conical profile.


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References


Popov L. E., Kobytev V. S., Kovalevskaya T. A., 1982, Concepts of strengthening and dynamic recovery in the theory of plastic deformation, Russian Physics Journal, 25, pp. 520-541.

Popov L. E., Slobodskoi M. I., Kolupaeva S. N., 2005, Simulation of single slip in FCC metals, Russian Physics Journal, 49, pp. 62-73.

L. E. Popov, Kolupaeva S.N., Vihor N.A., Puspesheva S.I., 2000, Dislocation dynamics of elementary crystallographic shear, Computational materials science, 19(1), pp. 267-274.

Griffith A.A., 1921, The phenomena of rupture and flow in solids, Philos. Trans. R. Soc. Lond. Ser. A, 221, pp.163–198.

Prandtl L., 1933, Ein Gedankenmodell für den Zerreißvorgang spröder Körper, ZAMM, J. Appl. Math. Mech., 13, pp. 129–133.

Rice J.R., 1968, A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks, Journal of Applied Mechanics, 35, pp. 379–386.

Aifantis E.C., 1999, Strain gradient interpretation of size effects, Int. J. Fracture, 95, pp. 299–314.

Nix W.D., Gao H., 1998, Indentation size effects in crystalline materials: a law for strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 46(3), pp. 411-425.

Gao H., Huang Y., Nix W.D., Hutchinson J.W., 1999, Mechanism-based strain gradient plasticity—I. Theory, Journal of the Mechanics and Physics of Solids, 47(6), pp.239-1263.

Popov V.L., 1992, Gauge theory of plastically incompressible medium without dissipation. 1. Dispersion relations and propagation of perturbations without dissipation, International Journal of Engineering Science, 30, pp. 329-334.

Wrucke A.J., Han C.-S., Majumdar P., 2013, Indentation size effects of multiple orders of magnitude in Polydimethylsiloxane, J. Appl. Polym. Sci., 128, pp. 258–264.

Budakian R., Putterman S.J., 2002, Time scales for cold welding and the origins of stick-slip friction, Phys. Rev. B, 65, pp. 235429.

Corcoran S.G., Colton J., 1997, Anomalous plastic deformation at surfaces: nanoindentation of gold single crystals, Phys. Rev. B, 55 pp. R16057.

Hess M., 2012, On the reduction method of dimensionality: The exact mapping of axisymmetric contact problems with and without adhesion, Phys. Mesomech., 15(5-6), pp. 264-269.

Popov V.L., Hess M., 2013, Methode der Dimensionsreduktion in Kontaktmechanik und Reibung – Eine Berechnungsmethode im Mikro- und Makrobereich, Springer-Verlag.

Popov V.L, 2013, Method of reduction of dimensionality in contact and friction mechanics: A linkage between micro and macro scales, Friction, 1(1), pp. 41-62.

Popov V.L., Hess M., 2014, Method of dimensionality reduction in contact mechanics and friction, Springer.

Popov V.L., 2010, Contact Mechanics and Friction. Physical Principles and Applications, Springer-Verlag, 362 pp.

Kleis I., Kulu P., 2008, Solid Particle Erosion, Occurence, prediction and control, Springer, 206 pp.

Popov V.L., Psakhie S.G., 2007, Numerical simulation methods in tribology, Tribology International, 40, pp. 916–923.

Hess M. and Popov V.L., 2013, Wärmeleitung und Wärmeerzeugung, In: Popov, V.L. and Hess, M.. Methode der Dimensionsreduktion, Springer, pp. 115-131.

Hess M. and Popov V.L., 2013, Exakte Lösungen in drei Dimensionen für den Normalkontakt rotationssymmetrischer Körper, In: Popov V.L. and Hess M., Methode der Dimensionsreduktion, Springer, pp. 227-239.

Hess M. and Popov V.L., 2013, Exakte Lösungen in drei Dimensionen für den Tangentialkontakt rotationssymmetrischer Körper, In: Popov V.L. and Hess M. (Eds.), Methode der Dimensionsreduktion, Springer, pp. 227-239.


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ISSN: 2335-0164 (Online)

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