Micropolar continuum mechanics of fractal media

International Journal of Engineering Science

Volumn 49, Issue 12, 2011, Pages 1302-1310

  Li, Jun ^a   Ostoja Starzewski, Martin ^a  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

Author keywords

Anisotropy; Dimensional regularization; Fractal; Fractional integrals; Micropolar continuum; Product measure; Reciprocal; Uniqueness theorem; Variational theorems

Indexed keywords

DIMENSIONAL REGULARIZATION; FRACTIONAL INTEGRALS; MICROPOLAR CONTINUUM; PRODUCT MEASURES; RECIPROCAL; UNIQUENESS THEOREM; VARIATIONAL THEOREMS;

ANISOTROPY; CONTINUUM MECHANICS; ELASTICITY; PARTIAL DIFFERENTIAL EQUATIONS; PARTIAL DISCHARGES;

FRACTAL DIMENSION;

EID: 80053983330     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2011.03.010     Document Type: Article

References (30)

1. M.V. Berry Diffractals Journal of Physics A: Mathematical and General 12 6 1979 781 797
2. A. Carpinteri, B. Chiaia, and P. Cornetti A disordered micro structure material model based on fractal geometry and fractional calculus Zeitschrift für Angewandte Mathematik und Mechanik 84 2004 128 135
3. A. Carpinteri, and N. Pugno Are scaling laws on strength of solids related to mechanics or to geometry? Nature Materials 4 2005 421 423 (Pubitemid 40774042)
4. E. Cosserat, and F. Cosserat Théorie des corps déformables 1909 Hermann et Fils Paris
5. Demmie, P., & Ostoja-Starzewski, M. (in press). Waves in fractal media. Journal of Elasticity (D.E. Carlson special issue), doi:10.1007/s10659- 011-9333-6.
6. A.V. Dyskin Continuum fractal mechanics of the Earth's crust Pure and Applied Geophysics 161 2004 1979 1989 (Pubitemid 39174545)
7. A.C. Eringen Microcontinuum field theories I: Foundations and solids 1999 Springer Berlin
8. J. Feder Fractals (physics of solids and liquids) 1988 Springer Berlin
9. D. Iesan, and L. Nappa Extremum principles and existence results in micromorphic elasticity International Journal of Engineering Science 39 2001 2051 2070 (Pubitemid 32720006)
10. Joumaa, H., & Ostoja-Starzewski, M. (in press). On the wave propagation in isotropic fractal media. Zeitschrift für angewandte Mathematik und Physik.
11. a Applied Mathematics Letters 18 2005 739 748 (Pubitemid 40612588)
12. G. Jumarie Table of some basic fractional calculus formulae derived from a modified Riemann - Liouville derivative for non-differentiable functions Applied Mathematics Letters 22 3 2008 378 385
13. J. Kigami Analysis on fractals 2001 Cambridge University Press Cambridge
14. Li, J., & Ostoja-Starzewski, M. (2009). Fractal solids, product measures and fractional wave equations. In Proc. R. Soc. A (Vol. 465, pp. 2521-2536). doi:10.1098/rspa.2009.0101; Errata (2010), doi:10.1098/rspa.2010. 0491.
15. Li, J., & Ostoja-Starzewski, M. (2010). Fractal solids, product measures and continuum mechanics. In Maugin, G. A., & Metrikine, A. V. (Eds.), Chapter 33 in mechanics of generalized continua: One hundred years after the Cosserats, Springer (pp. 315-323).
16. L. Limat Micropolar elastic percolation: The superelastic problem Physical Review B 38 10 1988 7219 7222
17. B.B. Mandelbrot The fractal geometry of nature 1982 Freeman New York
18. K.B. Oldham, and J. Spanier The fractional calculus 1974 Academic Press San Diego
19. M. Ostoja-Starzewski Towards thermomechanics of fractal media Zeitschrift für angewandte Mathematik und Physik 58 2007 1085 1096
20. M. Ostoja-Starzewski Towards thermoelasticity of fractal media Journal of Thermal Stresses 30 2007 889 896 (Pubitemid 47230554)
21. M. Ostoja-Starzewski On turbulence in fractal porous media Zeitschrift für angewandte Mathematik und Physik 59 6 2008 1111 1117
22. M. Ostoja-Starzewski Continuum mechanics models of fractal porous media: Integral relations and extremum principles Journal of Mechanics Materials and Structures 4 5 2009 901 912
23. M. Ostoja-Starzewski Extremum and variational principles for elastic and inelastic media with fractal geometries Acta Mechanica 205 2009 161 170
24. M. Ostoja-Starzewski, and J. Li Fractal materials, beams, and fracture mechanics Zeitschrift für angewandte Mathematik und Physik 60 2009 1194 1205
25. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional integrals and derivatives: Theory and applications 1993 Gordon & Breach New York
26. R.S. Strichartz Differential equations on fractals: A tutorial 2006 Princeton University Press Princeton
27. V.E. Tarasov Continuous medium model for fractal media Physics Letters A 336 2005 167 174 (Pubitemid 40215401)
28. V.E. Tarasov Fractional hydrodynamic equations for fractal media Annals of Physics 318 2 2005 286 307 (Pubitemid 40864807)
29. V.E. Tarasov Wave equation for fractal solid string Modern Physics Letters B 19 2005 721 728 (Pubitemid 41175839)
30. R. Temam, and A. Miranville Mathematical modeling in continuum mechanics 2005 Cambridge University Press Cambridge