The maximum friction law postulates that the friction stress is equal to the maximum possible shear stress admissible by the constitutive equations. The boundary value problems including the maximum friction stress as a boundary condition reveal special mathematical features which are of interest in the development of theories and models, numerical simulation and engineering applications. The present paper shortly reviews the singularity in velocity fields that can occur in the vicinity of maximum friction surfaces. A large class of rigid plastic (in a broad sense that the elastic portion of the strain rate tensor is neglected) is considered. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

References

[1] V. V. Sokolovskii, Prikl. Matem. Mech. (PMM). 20, 328-334 (1956) [in Russian].
Google Scholar
[2] S. Alexandrov, O. Richmond, Int J. Non-Linear Mech. 36, 1-11 (2001).
10.1016/S0020-7462(99)00075-X
Web of Science® Google Scholar
[3] J. W. Graggs, Quart. J. Mech. Appl. Math. 7, 35-39 (1954).
10.1093/qjmam/7.1.35
Web of Science® Google Scholar
[4] A. G. Atkins, G. M. Rowe, W. Johnson, Int. J. Mech. Engng Educ. 10, 265-278 (1982).
Google Scholar
[5] J. Ostrowska-Maciejewska, D. Harris, Math. Proc. Camb. Phil. Soc. 108, 153-169 (1990).
10.1017/S0305004100069024
Web of Science® Google Scholar
[6] S. Alexandrov, Trans. ASME J. Appl. Mech. 70, 212-219 (2003).
10.1115/1.1532319
Web of Science® Google Scholar
[7] S. Alexandrov, E. Lyamina, Doklady-Physics 47, 308-311 (2002).
10.1134/1.1477887
CAS Web of Science® Google Scholar
[8] S. Alexandrov, J. Appl. Mech. Techn. Physics 46, 766-771 (2005).
10.1007/s10808-005-0133-2
Google Scholar
[9] S. Alexandrov, D. Harris, Int. J. Mech. Sci. 48, 750-762 (2006).
10.1016/j.ijmecsci.2006.01.009
Web of Science® Google Scholar
[10] S. Alexandrov, E. Lyamina, J. Appl. Mech. Techn. Physics 46, 883-890 (2005).
10.1007/s10808-005-0148-8
Google Scholar
[11] S. Alexandrov, N. Alexandrova, Meccanica 35, 393-398 (2000).
10.1023/A:1010374313491
Web of Science® Google Scholar
[12] J. G. Sevillano, P. van Houtte, E. Aernoudt, Progress Mater. Sci. 25, 69-112 (1981).
10.1016/0079-6425(80)90001-8
Web of Science® Google Scholar
[13] S. Alexandrov, N. Alexandrova, Mech. Time-Dependent Mater. 4, 99-104 (2000).
10.1023/A:1009851621518
Web of Science® Google Scholar
[14] O. M. Smirnov, Metal forming in superplasticity, (Mashinostroenie, Moscow, 1979) [in Russian].
Google Scholar
[15] H. Zhu, Y. D. Kim, D. De. Kee, J. Non-Newtonian Fluid Mech., 129, 177-181 (2005).
10.1016/j.jnnfm.2005.06.001
CAS Web of Science® Google Scholar
[16] I. F. Collins, S. A. Meguid, Trans. ASME J. Appl. Mech., 44, 271-278 (1977).
10.1115/1.3424037
Web of Science® Google Scholar
[17] A. N. Bramley, J. Mater. Process. Technol., 116, 62-66 (2001).
10.1016/S0924-0136(01)00849-4
Web of Science® Google Scholar
[18] N. Rebelo, S. Kobayashi, Int. J. Mech. Sci., 22, 707-718 (1980).
10.1016/0020-7403(80)90073-9
Web of Science® Google Scholar
[19] S. Alexandrov, O. Richmond, Int. J. Solids Struct., 37, 669-686 (2000).
10.1016/S0020-7683(99)00023-2
Web of Science® Google Scholar
[20] T. Aukrust, S. LaZghab, Int. J. Plasticity, 16, 59-71 (2000).
10.1016/S0749-6419(99)00047-9
CAS Web of Science® Google Scholar
[21] M. F. Kanninen, C. H. Popelar, Advanced fracture mechanics, (Oxford University Press, New York, 1985).
Google Scholar
[22] S. Alexandrov, In: Physical Aspects of Fracture, edited by E. Bouchaud et.al. (Kluwer, Dordrecht, 2001) p.179.
Google Scholar
[23] S. Alexandrov, R. V. Goldshtein, E. A. Lyamina, Doklady-Physics, 48, 131-133 (2003).
10.1134/1.1565618
CAS Web of Science® Google Scholar
[24] S. Alexandrov, E. Lyamina, J. Technol. Plasticity, 30, 53-59 (2005).
Google Scholar