An isotropic dynamically consistent gradient elasticity model derived from a 2D lattice

References

• Gazis , DC , Herman , R and Wallis , RF . 1960 . Phys. Rev. , 119 : 533
   Web of Science ®Google Scholar
• Viktorov , IA . 1967 . Rayleigh and Lamb waves , New York : Plenum Press .
   Google Scholar
• Krause , M , Barmann , M Frielinghaus , R . 1997 . NDT E Int. , 30 : 195
   Web of Science ®Google Scholar
• Mindlin , RD . 1964 . Arch. Ration. Mech. Anal. , 16 : 51
   Web of Science ®Google Scholar
• Green , AE and Rivlin , RS . 1964 . Arch. Ration. Mech. Anal. , 17 : 113
   Web of Science ®Google Scholar
• Mindlin , RD and Tiersten , HF . 1962 . Arch. Ration. Mech. Anal. , 11 : 415
   Web of Science ®Google Scholar
• Weitsman , Y . 1965 . J. Appl. Mech.-Trans. ASME , 32 : 424
   Google Scholar
• Weitsman , Y . 1967 . Q. J. Mech. Appl. Math. , 25 : 213
   Google Scholar
• Bogy , DB and Sternberg , E . 1967 . Int. J. Solids Struct. , 3 : 757
   Google Scholar
• Bogy , DB and Sternberg , E . 1967 . Int. J. Solids Struct. , 4 : 159
   Google Scholar
• Papamichos , E , Vardoulakis , I and Mühlhaus , H-B . 1990 . Int. J. Numer. Anal. Methods Geomech. , 14 : 473
   Web of Science ®Google Scholar
• Aifantis , EC . 1992 . Int. J. Eng. Sci. , 30 : 1279
   Web of Science ®Google Scholar
• Mühlhaus , H-B . 1993 . “ Comprehensive Rock Engineering; Principles, Practice and Projects ” . In Analysis and Design Methods , Edited by: Hudson , JA . Vol 2 , Oxford : Pergamon .
   Google Scholar
• Anderson , WB and Lakes , RS . 1994 . J. Mater. Sci. , 29 : 6413
   Web of Science ®Google Scholar
• Fleck , NA , Muller , GM Ashbya , MF . 1994 . Acta Metall. Sin. , 42 : 475
   Google Scholar
• Vardoulakis , I and Sulem , J . 1995 . Bifurcation Analysis in Geomechanics , London : Blackie .
   Google Scholar
• Wei , Y and Hutchinson , JW . 1997 . J. Mech. Phys. Solids , 45 : 1253
   Web of Science ®Google Scholar
• Chen , JY , Huang , Y and Ortiz , M . 1998 . J. Mech. Phys. Solids , 46 : 789
   Web of Science ®Google Scholar
• Lubarda , VA and Markenscoff , X . 2000 . J. Mech. Phys. Solids , 48 : 553
   Web of Science ®Google Scholar
• Bardet , JP and Vardoulakis , I . 2001 . Int. J. Solids Struct. , 38 : 353
   Web of Science ®Google Scholar
• Mühlhaus , H-B and Pasternak , E . 2002 . Int. J. Fract. , 113 : L21
   Google Scholar
• Pasternak , E . 2002 . Generalised homogenisation procedures for granular and layered materials , PhD Thesis The University of Western Australia .
   Google Scholar
• Pasternak , E , Mühlhaus , H-B and Dyskin , AV . 2004 . Pure Appl. Geophys. , 161 : 2309
   Web of Science ®Google Scholar
• Pasternak , E , Mühlhaus , H-B and Dyskin , AV . 2002 . IUTAM Symposium on Analytical and Computational Fracture Mechanics of Non-homogeneous Materials , Edited by: Karihaloo , B . Dordrecht : Kluwer Academic Publishers .
   Google Scholar
• Pasternak , E and Mühlhaus , H-B . 2005 . J. Eng. Math. , 52 : 199
   Web of Science ®Google Scholar
• Aifantis , EC . 1984 . J. Eng. Mater. Technol.-Trans. ASME , 106 : 326
   Web of Science ®Google Scholar
• Aifantis , EC . 1987 . Int. J. Plast. , 3 : 211
   Web of Science ®Google Scholar
• Schreyer , HL and Chen , Z . 1986 . J. Appl. Mech.-Trans. ASME , 53 : 791
   Web of Science ®Google Scholar
• Lasry , D and Belytschko , T . 1988 . Int. J. Solids Struct. , 24 : 581
   Google Scholar
• Mühlhaus , H-B and Aifantis , EC . 1991 . Int. J. Solids Struct. , 28 : 845
   Web of Science ®Google Scholar
• de Borst , R and Mühlhaus , H-B . 1992 . Int. J. Numer. Methods Eng. , 35 : 521
   Web of Science ®Google Scholar
• Sluys , LJ . 1992 . Wave propagation, localisation and dispersion in softening solids , PhD Thesis Delft University of Technology .
   Google Scholar
• Pamin , J . 1992 . Gradient-dependent plasticity in numerical simulation of localization phenomena PhD Thesis, Delft University of Technology
   Google Scholar
• Triantafyllidis , N and Aifantis , EC . 1986 . J. Elast. , 16 : 225
   Web of Science ®Google Scholar
• Peerlings , RHJ , de Borst , R , Brekelmans , WAM and de Vree , JHP . 1996 . Int. J. Numer. Methods Eng. , 39 : 3391
   Web of Science ®Google Scholar
• Altan , BS and Aifantis , EC . 1997 . J. of the Mech. Behav. Mater. , 8 : 231
   Google Scholar
• Zhu , HT , Zbib , HM and Aifantis , EC . 1997 . Acta Mech. , 121 : 165
   Web of Science ®Google Scholar
• Fleck , NA and Hutchinson , JW . 2001 . J. Mech. Phys. Solids , 49 : 2245
   Web of Science ®Google Scholar
• Askes , H and Sluys , LJ . 2002 . Eur. J. Mech. A-Solids , 21 : 379
   Google Scholar
• Askes , H and Sluys , LJ . 2003 . Arch. Appl. Mech. , 73 : 448
   Google Scholar
• Palmov , VA . 1964 . Pmm-J. Appl. Math. Mech. , 28 : 496
   Google Scholar
• Suhubi , ES and Eringen , AC . 1964 . Int. J. Eng. Sci. , 2 : 389
   Google Scholar
• Erofeyev , VI . 2003 . Wave Processes in Solids with Microstructure , Singapore : World Scientific .
   Google Scholar
• Vardoulakis , I and Aifantis , EC . 1994 . Mech. Mater. , 18 : 151
   Web of Science ®Google Scholar
• Rubin , MB , Rosenau , P and Gottlieb , O . 1995 . J. Appl. Phys. , 77 : 4054
   Web of Science ®Google Scholar
• Mühlhaus , H-B and Oka , F . 1996 . Int. J. Solids Struct. , 33 : 2841
   Web of Science ®Google Scholar
• Georgiadis , HG , Vardoulakis , I and Lykortafitis , G . 2000 . Wave Motion , 31 : 333
   Web of Science ®Google Scholar
• Chen , W and Fish , J . 2001 . J. Appl. Mech.-Trans. ASME , 68 : 153
   Web of Science ®Google Scholar
• Suiker , ASJ , de Borst , R and Chang , CS . 2001 . Acta Mech. , 149 : 161
   Web of Science ®Google Scholar
• Suiker , ASJ , de Borst , R and Chang , CS . 2001 . Acta Mech. , 149 : 181
   Web of Science ®Google Scholar
• Suiker , ASJ , Metrikine , AV and de Borst , R . 2001 . Int. J. Solids Struct. , 38 : 1563
   Web of Science ®Google Scholar
• Fish , J , Chen , W and Nagai , G . 2002 . Int. J. Numer. Methods Eng. , 54 : 331
   Web of Science ®Google Scholar
• Fish , J , Chen , W and Nagai , G . 2002 . Int. J. Numer. Methods Eng. , 54 : 347
   Web of Science ®Google Scholar
• Andrianov , IV . 2002 . Pmm-J. Appl. Math. Mech. , 66 : 261
   Google Scholar
• Wang , Z-P and Sun , CT . 2002 . Wave Motion , 36 : 473
   Web of Science ®Google Scholar
• Metrikine , AV and Askes , H . 2002 . Eur. J. Mech. A-Solids , 21 : 555
   Web of Science ®Google Scholar
• Askes , H and Metrikine , AV . 2002 . Eur. J. Mech. A-Solids , 21 : 573
   Web of Science ®Google Scholar
• Georgiadis , HG and Velgaki , EG . 2003 . Int. J. Solids Struct. , 40 : 2501
   Web of Science ®Google Scholar
• Andrianov , IV , Awrejcewicz , J and Barantsev , RC . 2003 . Appl. Mech. Rev. -Trans. ASME , 56 : 87
   Google Scholar
• Askes , H and Metrikine , AV . 2005 . Int. J. Solids Struct. , 42 : 187
   Web of Science ®Google Scholar
• Kunin , IA . 1982 . Elastic Media with Microstructure 1. One-dimensional models , Berlin, Heidelberg, New York : Springer-Verlag .
   Google Scholar
• Goldstein , H . 1964 . Classical Mechanics , Reading : Addison-Wesly .
   Google Scholar
• Lurie , AI . 2002 . Analytical Mechanics , Berlin : Springer .
   Google Scholar
• Washizu , K . 1975 . Variational Methods in Elasticity and Plasticity , Oxford : Pergamon .
   Google Scholar