Issue 24

S. Psakhie et alii, Frattura ed Integrità Strutturale, 24 (2013) 26-59; DOI: 10.3221/IGF-ESIS.24.04

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[38] M.P. Wnuk, A. Yavari, Engineering Fracture Mechanics 75 (2008) 1127. [39] M.P. Wnuk, A. Yavari, Engineering Fracture Mechanics 76 (2009) 548. [40] M. Elices, G.V. Guinea, J. Gomez, J. Planas, Engineering Fracture Mechanics, 69 (2002) 137. [41] N. Chawla, K.K. Chawla, Metal matrix composites, Springer, New York, (2006). [42] S. Suresh, A. Mortensen, A. Needleman, Fundamentals of metal-matrix composites, Butterworth-Heinemann, Stoneham, MA, (1993). [43] K.U. Kainer, In: K.U. Kainer (Ed.), Metal Matrix Composites. Custom-made materials for Automotive and Aerospace Engineering, Wiley-VCH Verlag, Weinheim, (2006). [44] A. Pramanik, L.C. Zhang, J.A. Arsecularante, International Journal of Machine Tools and Manufacture, 46 (2006) 1795. [45] V.E. Ovcharenko, Baohai Yu, S.G. Psahie, Journal of Materials Science and Technology, 21 (2005) 427. [46] Baohai Yu, V.E. Ovcharenko, S.G. Psakhie, O.V. Lapshin, Journal of Materials Science and Technology, 22 (2006) 511. [47] P.A. Vityaz, L.I. Grechikhin, Physical Mesomechanics, 7 (5-6) (2004) 51. [48] A. Ayyar, N. Chawla, Composites Science and Technology, 66 (2006) 1980. [49] S.N. Kulkov, Physical Mesomechanics, 9 (1-2) (2006) 73. [50] W.F. Caley, B. Paton, D.P. Bishop, G.J. Kipouros, Journal of Materials Science, 38 (2003) 1755. [51] K.N. Tran, Y. Ding, J.A. Gear, ANZIAM Journal, 51 (2010) C16. [52] Yu.V. Sokolkin, V.E. Vil’deman, A.V. Zaitsev, I.N. Rochev, Mechanics of Composite Materials, 34 (1998) 171. [53] T. Christman, A. Needleman, S. Nutt, S. Suresh, Materials Science and Engineering A, 107 (1989) 49. [54] L. Mishnaevsky, M. Dong, S. Honle, S. Schmauder, Computational Materials Science, 16 (1999) 133. [55] N. Chawla, K.K. Chawla, Journal of Materials Science, 41 (2006) 913. [56] W. Österle, A.I. Dmitriev, Wear, 271(9-10) (2011) 2198. [57] A.I. Dmitriev, W. Österle, H. Kloss, Nanosystems: Physics, Chemistry, Mathematics, 2(2) (2011) 58. [58] S.G. Psakhie, V.L. Popov, E.V. Shilko, A.Yu. Smolin, A.I. Dmitriev, Physical Mesomechanics, 12(5-6) (2009) 221. [59] S.G. Psakhie, D.D. Moiseyenko, A.Yu. Smolin, E.V. Shilko, A.I. Dmitriev, S.Yu. Korostelev, E.M. Tatarintsev, Computational Materials Science, 16 (1999) 333. [60] Ig.S. Konovalenko, A.Yu. Smolin, S.Yu. Korostelev, S.G. Psakhie, Technical Physics, 54(5) (2009) 758. [61] S.G. Psakhie, V.V. Ruzhich, E.V. Shilko, V.L. Popov, S.V. Astafurov, Tribology International, 40(6) (2007) 995. [62] S.V. Astafurov, E.V. Shilko, S.G. Psakhie, Physical Mesomechanics, 13(3-4) (2010) 164. A PPENDIX A et’s assume that under consideration of isotropic linearly elastic medium the expressions for specific forces of normal (central) and shear (tangential) response of discrete element i to mechanical action by neighbouring element j are defined on the basis of reformulation of Hooke’s law for diagonal and off-diagonal components of stress tensor (19): L





G

2

 

i 

ij 



1  

G

2

i

    

K

 

i

mean

i j

(A1)

i

ij 



G

2

 

i i j

Explanation of meaning of variables in (A1) can be found in Sections 2-4 ( Main parameters of interaction of discrete elements - Discrete element interaction for modeling consolidated elastic-plastic medium ). The proposed expressions (A1) are correct as they provide fulfillment of Hooke’s law (19) for average stress and strain tensors in the volume of discrete element i . Actually, substitution of relations (A1) in the expression (16  ) for  =  = x leads to the following relationship:

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