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Volumn 59, Issue 1-6, 2006, Pages 283-304

Scaling laws and multiscale approach in the mechanics of heterogeneous and disordered materials

Author keywords

[No Author keywords available]

Indexed keywords

BUILDING MATERIALS; CONCRETE CONSTRUCTION; CRACK INITIATION; MATHEMATICAL MODELS; TENSILE STRENGTH;

EID: 33846365256     PISSN: 00036900     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2204076     Document Type: Review
Times cited : (49)

References (153)
  • 1
    • 33645916042 scopus 로고
    • Renormalization Group and Critical Phenomena
    • Wilson, K. G., 1971, "Renormalization Group and Critical Phenomena," Phys. Rev. B, 4 pp. 3174-3205.
    • (1971) Phys. Rev. B , vol.4 , pp. 3174-3205
    • Wilson, K.G.1
  • 4
    • 0024944108 scopus 로고
    • Decrease of Apparent Tensile and Bending Strength With Specimen Size: Two Different Explanations Based on Fracture Mechanics
    • Carpinteri, A., 1989, "Decrease of Apparent Tensile and Bending Strength With Specimen Size: Two Different Explanations Based on Fracture Mechanics," Int. J. Solids Struct., 25, pp. 407-429.
    • (1989) Int. J. Solids Struct , vol.25 , pp. 407-429
    • Carpinteri, A.1
  • 5
    • 0003586464 scopus 로고
    • Plenum, New York
    • Feder, J., 1988, Fractals, Plenum, New York.
    • (1988) Fractals
    • Feder, J.1
  • 8
    • 6244232696 scopus 로고
    • Fractal Character of Fractal Surfaces of Metals
    • Mandelbrot, B. B., Passoja, D. E., and Paullay, A. J., 1984, "Fractal Character of Fractal Surfaces of Metals," Nature (London), 308, pp. 721-722.
    • (1984) Nature (London) , vol.308 , pp. 721-722
    • Mandelbrot, B.B.1    Passoja, D.E.2    Paullay, A.J.3
  • 9
    • 33745578188 scopus 로고
    • Fractal Characterization of Fracture Surfaces in Concrete
    • Saouma, V. E., Barton, C. C., and Gamaleldin, N. A., 1990, "Fractal Characterization of Fracture Surfaces in Concrete," Eng. Fract. Mech., 35, pp. 47-53.
    • (1990) Eng. Fract. Mech , vol.35 , pp. 47-53
    • Saouma, V.E.1    Barton, C.C.2    Gamaleldin, N.A.3
  • 10
    • 0028468278 scopus 로고
    • Fractal Nature of Material Microstructure and Size Effects on Apparent Mechanical Properties
    • Carpinteri, A., 1994, "Fractal Nature of Material Microstructure and Size Effects on Apparent Mechanical Properties," Mech. Mater., 18, pp. 89-101.
    • (1994) Mech. Mater , vol.18 , pp. 89-101
    • Carpinteri, A.1
  • 11
    • 0028374089 scopus 로고
    • Scaling Laws and Renormalization Groups for Strength and Toughness of Disordered Materials
    • Carpinteri, A., 1994, "Scaling Laws and Renormalization Groups for Strength and Toughness of Disordered Materials," Int. J. Solids Struct., 31, pp. 291-302.
    • (1994) Int. J. Solids Struct , vol.31 , pp. 291-302
    • Carpinteri, A.1
  • 12
    • 0028669676 scopus 로고
    • Size Effects on Tensile Fracture Properties: A Unified Explanation Based on Disorder and Fractality of Concrete Microstructure
    • Carpinteri, A., and Ferro, G., 1994, "Size Effects on Tensile Fracture Properties: A Unified Explanation Based on Disorder and Fractality of Concrete Microstructure," Mater. Struct., 28, pp. 563-571.
    • (1994) Mater. Struct , vol.28 , pp. 563-571
    • Carpinteri, A.1    Ferro, G.2
  • 13
    • 0028466767 scopus 로고
    • Scaling Law for Strength and Toughness of Disordered Materials: A Unified Theory Based on Fractal Geometry
    • Carpinteri, A., Ferrara, G., and Imperato, L., 1994, "Scaling Law for Strength and Toughness of Disordered Materials: A Unified Theory Based on Fractal Geometry," Eng. Fract. Mech., 48, pp. 673-689.
    • (1994) Eng. Fract. Mech , vol.48 , pp. 673-689
    • Carpinteri, A.1    Ferrara, G.2    Imperato, L.3
  • 14
    • 0029386770 scopus 로고
    • Multifractal Natural of Concrete Fracturc Surface and Size Effects on Nominal Fracture Energy
    • Carpinteri, A., and Chiaia, B., 1995, "Multifractal Natural of Concrete Fracturc Surface and Size Effects on Nominal Fracture Energy." Mater. Struct., 28, pp. 435-443.
    • (1995) Mater. Struct , vol.28 , pp. 435-443
    • Carpinteri, A.1    Chiaia, B.2
  • 15
    • 33846393105 scopus 로고    scopus 로고
    • Carpinteri, A., Chiaia, B., and Maradei, F., 1995, Experimental Determination of the Fractal Dimension of Disordered Fracture Surfaces, in Advanced Technology for Design and Fabrication of Composite Materials and Structures, A. Carpinteri G. C. Sin, and G. Surface, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 269-292.
    • Carpinteri, A., Chiaia, B., and Maradei, F., 1995, "Experimental Determination of the Fractal Dimension of Disordered Fracture Surfaces," in Advanced Technology for Design and Fabrication of Composite Materials and Structures, A. Carpinteri G. C. Sin, and G. Surface, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 269-292.
  • 16
    • 0000357002 scopus 로고
    • The Phenomena of Rupture and Flow in Solids
    • Griffith, A. A., 1921, "The Phenomena of Rupture and Flow in Solids," Philos. Trans. R. Soc. London, Ser. A, A221, pp. 163-198.
    • (1921) Philos. Trans. R. Soc. London, Ser. A , vol.A221 , pp. 163-198
    • Griffith, A.A.1
  • 17
    • 0015490231 scopus 로고
    • The j-Integral as a Fracture Criterion
    • Begley, J. A., and Landes, I. D., 1972, "The j-Integral as a Fracture Criterion," ASTM Spec. Tech. Publ., 514, pp. 1-23.
    • (1972) ASTM Spec. Tech. Publ , vol.514 , pp. 1-23
    • Begley, J.A.1    Landes, I.D.2
  • 18
    • 33745792664 scopus 로고
    • Model Experiments and the Form of Empirical Equations
    • Buckingham, E., 1915, "Model Experiments and the Form of Empirical Equations," ASME Trans. J. Appl. Mech., 37, pp. 263-296.
    • (1915) ASME Trans. J. Appl. Mech , vol.37 , pp. 263-296
    • Buckingham, E.1
  • 19
    • 0019918473 scopus 로고
    • Notch Sensitivity in Fracture Testing of Aggregative Materials
    • Carpinteri, A., 1982, "Notch Sensitivity in Fracture Testing of Aggregative Materials," Eng. Fract. Mech., 16, pp. 467-481.
    • (1982) Eng. Fract. Mech , vol.16 , pp. 467-481
    • Carpinteri, A.1
  • 20
    • 0019561632 scopus 로고
    • Static and Energetic Fracture Parameters for Rocks and Concretes
    • Carpinteri, A., 1981, "Static and Energetic Fracture Parameters for Rocks and Concretes," Mater. Struct., 14, pp. 151-162.
    • (1981) Mater. Struct , vol.14 , pp. 151-162
    • Carpinteri, A.1
  • 22
    • 0024689885 scopus 로고
    • Size Effects on Strength, Toughness and Ductility
    • Carpinteri, A., 1989, "Size Effects on Strength, Toughness and Ductility," J. Eng. Mech., 115, pp. 1375-1392.
    • (1989) J. Eng. Mech , vol.115 , pp. 1375-1392
    • Carpinteri, A.1
  • 23
    • 0024883904 scopus 로고
    • Cusp Catastrophe Interpretation of Fracture Instability
    • Carpinteri, A., 1989, "Cusp Catastrophe Interpretation of Fracture Instability," J. Mech. Phys. Solids, 37, pp. 567-582.
    • (1989) J. Mech. Phys. Solids , vol.37 , pp. 567-582
    • Carpinteri, A.1
  • 25
    • 33846384897 scopus 로고    scopus 로고
    • Standards method of test for plane strain fracture toughness of metallic materials, Technical Report No. E399-74, A.S.T.M.
    • Standards method of test for plane strain fracture toughness of metallic materials, Technical Report No. E399-74, A.S.T.M.
  • 26
    • 67650813253 scopus 로고
    • Size Effect in Fracture Toughness Testing: A Dimensional Analysis Approach
    • G. C. Sih and M. Mirabile, eds, Rome, Italy, Sijthoff and Noordhoff, pp
    • Carpinteri, A., 1980, "Size Effect in Fracture Toughness Testing: A Dimensional Analysis Approach," in G. C. Sih and M. Mirabile, eds., Conference on Analytical and Experimental Fracture Mechanics, Rome, Italy, Sijthoff and Noordhoff, pp. 785-797.
    • (1980) Conference on Analytical and Experimental Fracture Mechanics , pp. 785-797
    • Carpinteri, A.1
  • 27
    • 0020114843 scopus 로고
    • Application of Fracture Mechanics to Concrete Structures
    • Carpinteri, A., 1982, "Application of Fracture Mechanics to Concrete Structures," J. Eng. Mech., 108, pp. 833-848.
    • (1982) J. Eng. Mech , vol.108 , pp. 833-848
    • Carpinteri, A.1
  • 29
    • 0009231269 scopus 로고
    • The Formation of Equilibrium Cracks During Brittle Fracture: General Ideas and Hypotheses
    • Barenblatt, G. I., 1959, "The Formation of Equilibrium Cracks During Brittle Fracture: General Ideas and Hypotheses," J. Appl. Math. Mech., 23, pp. 622-636.
    • (1959) J. Appl. Math. Mech , vol.23 , pp. 622-636
    • Barenblatt, G.I.1
  • 30
    • 77649193465 scopus 로고
    • The Mathematical Theory of Equilibrium Cracks in Brittle Fracture
    • Barenblatt, G. I., 1962, "The Mathematical Theory of Equilibrium Cracks in Brittle Fracture," Adv. Appl. Mech., 7, pp. 55-129.
    • (1962) Adv. Appl. Mech , vol.7 , pp. 55-129
    • Barenblatt, G.I.1
  • 31
    • 50549180512 scopus 로고
    • Yielding of Steel Sheets Containing Slits
    • Dugdale, D. S., 1960, "Yielding of Steel Sheets Containing Slits," J. Mech. Phys. Solids, 8, pp. 100-114.
    • (1960) J. Mech. Phys. Solids , vol.8 , pp. 100-114
    • Dugdale, D.S.1
  • 33
    • 84980287971 scopus 로고
    • A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
    • Rice, J. R., 1968, "A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks," J. Appl. Mech., 15, pp. 379-386.
    • (1968) J. Appl. Mech , vol.15 , pp. 379-386
    • Rice, J.R.1
  • 34
    • 0001526247 scopus 로고
    • A Comparison of the Fracture Criteria of Griffith and Barenblatt
    • Willis, J. R., 1967 "A Comparison of the Fracture Criteria of Griffith and Barenblatt," J. Mech. Phys. Solids, 15, pp. 151-162.
    • (1967) J. Mech. Phys. Solids , vol.15 , pp. 151-162
    • Willis, J.R.1
  • 35
    • 0016034446 scopus 로고
    • Quasistatic Extension of a Tensile Crack Contained in Viscoelastic-Plastic Solid
    • Wnuk, M. P., 1974, "Quasistatic Extension of a Tensile Crack Contained in Viscoelastic-Plastic Solid," J. Appl. Mech., 41, pp. 234-242.
    • (1974) J. Appl. Mech , vol.41 , pp. 234-242
    • Wnuk, M.P.1
  • 36
    • 0004725612 scopus 로고
    • Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements
    • Hillerborg, A., Modeer, M., and Petersson, P. E., 1976, "Analysis of Crack Formation and Crack Growth in Concrete by Means of Fracture Mechanics and Finite Elements," Cem. Concr. Res., 6, pp. 773-782.
    • (1976) Cem. Concr. Res , vol.6 , pp. 773-782
    • Hillerborg, A.1    Modeer, M.2    Petersson, P.E.3
  • 37
    • 0002083040 scopus 로고
    • Influence of Material Parameters and Geometry on Cohesive Crack Propagation
    • F. H. Wittmann, ed, Elsevier, pp
    • Carpinteri, A., Di Tommaso, A., and Fanelli, M., 1985, "Influence of Material Parameters and Geometry on Cohesive Crack Propagation," in Fracture Toughness and Fracture Energy of Concrete, F. H. Wittmann, ed., Elsevier, pp. 117-135.
    • (1985) Fracture Toughness and Fracture Energy of Concrete , pp. 117-135
    • Carpinteri, A.1    Di Tommaso, A.2    Fanelli, M.3
  • 38
    • 0003941527 scopus 로고
    • Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Materials
    • Report No. TVBM-1006, Division of Building Materials, Lund Institute of Technology, Denmark
    • Petersson, P. E., 1981, "Crack Growth and Development of Fracture Zones in Plain Concrete and Similar Materials," Report No. TVBM-1006, Division of Building Materials, Lund Institute of Technology, Denmark.
    • (1981)
    • Petersson, P.E.1
  • 39
    • 0020840790 scopus 로고
    • Prediction of Nonlinear Fracture Process Zone in Concrete
    • Wecharatana, M., and Shah, S. P., 1983, "Prediction of Nonlinear Fracture Process Zone in Concrete," J. Eng. Mech., 109, pp. 1231-1246.
    • (1983) J. Eng. Mech , vol.109 , pp. 1231-1246
    • Wecharatana, M.1    Shah, S.P.2
  • 40
    • 0021644899 scopus 로고
    • Concrete Fracture via Stress-Strain Relations
    • Bažant, Z. P., and Oh, B. H., 1984, "Concrete Fracture via Stress-Strain Relations," J. Eng. Mech., 110, pp. 1015-1035.
    • (1984) J. Eng. Mech , vol.110 , pp. 1015-1035
    • Bažant, Z.P.1    Oh, B.H.2
  • 42
    • 0024862124 scopus 로고
    • Post-Peak and Post-Bifurcation Analysis on Cohesive Crack Propagation
    • Carpinteri, A., 1989, "Post-Peak and Post-Bifurcation Analysis on Cohesive Crack Propagation," Eng. Fract. Mech., 32, pp. 265-278.
    • (1989) Eng. Fract. Mech , vol.32 , pp. 265-278
    • Carpinteri, A.1
  • 43
    • 33846347860 scopus 로고    scopus 로고
    • Carpinteri, A., Colombo, G., and Giuseppetti, G., 1985, Accuracy of the Numerical Description of Cohesive Crack Propagation, in Fracture Toughness and Fracture Energy of Concrete, F. H. Wittmann. ed., Elsevier Science, pp. 189-195.
    • Carpinteri, A., Colombo, G., and Giuseppetti, G., 1985, "Accuracy of the Numerical Description of Cohesive Crack Propagation," in Fracture Toughness and Fracture Energy of Concrete, F. H. Wittmann. ed., Elsevier Science, pp. 189-195.
  • 44
    • 0037535321 scopus 로고
    • Experimental Evaluation of Concrete Fracture Energy Through a New Identification Method
    • F. H. Wittmann, ed, Elsevier Science, pp
    • Carpinteri, A., Di Tommaso, A., Ferrara, G., and Melchiorri, G., 1985, "Experimental Evaluation of Concrete Fracture Energy Through a New Identification Method," in Fracture Toughness and Fracture Energy of Concrete, F. H. Wittmann, ed., Elsevier Science, pp. 423-436.
    • (1985) Fracture Toughness and Fracture Energy of Concrete , pp. 423-436
    • Carpinteri, A.1    Di Tommaso, A.2    Ferrara, G.3    Melchiorri, G.4
  • 45
    • 33846337013 scopus 로고    scopus 로고
    • Carpinteri, A., and Valente, S., 1988, Numerical Modeling of Mixed-Mode Cohesive Crack Propagation, in International Conference on Computational Engineering Science, S. N. Atluri and G. Yagawa, eds., Springer Verlag, pp. 12 VI. 1-12. VI.26.
    • Carpinteri, A., and Valente, S., 1988, "Numerical Modeling of Mixed-Mode Cohesive Crack Propagation," in International Conference on Computational Engineering Science, S. N. Atluri and G. Yagawa, eds., Springer Verlag, pp. 12 VI. 1-12. VI.26.
  • 46
    • 0026927097 scopus 로고
    • Bifurcations and Instabilities in Fracture of Cohesive-Softening Structures: A Boundary Elements Analysis
    • Cen, Z., and Maier, G., 1992, "Bifurcations and Instabilities in Fracture of Cohesive-Softening Structures: A Boundary Elements Analysis," Fatigue Fract. Eng. Mater. Struct., 15, pp. 911-928.
    • (1992) Fatigue Fract. Eng. Mater. Struct , vol.15 , pp. 911-928
    • Cen, Z.1    Maier, G.2
  • 48
    • 0035930887 scopus 로고    scopus 로고
    • The Cohesive Zone Model: Advantages, Limitation, and Challenges
    • Elices, M., Guinea, G. V., Gomez, J., and Planas, J., 2002, "The Cohesive Zone Model: Advantages, Limitation, and Challenges," Eng. Fract. Mech., 69, pp. 137-163.
    • (2002) Eng. Fract. Mech , vol.69 , pp. 137-163
    • Elices, M.1    Guinea, G.V.2    Gomez, J.3    Planas, J.4
  • 49
    • 0033329770 scopus 로고    scopus 로고
    • Size Effect and Inverse Analysis in Concrete Fracture
    • Planas, J., Guinea, G. V., and Elices, M., 1999, "Size Effect and Inverse Analysis in Concrete Fracture," Int. I. Fract., 95, pp. 367-378.
    • (1999) Int. I. Fract , vol.95 , pp. 367-378
    • Planas, J.1    Guinea, G.V.2    Elices, M.3
  • 50
    • 0035930828 scopus 로고    scopus 로고
    • Concrete Fracture Model: Testing and Practice
    • Bazant, Z. P., 2002, "Concrete Fracture Model: Testing and Practice," Eng. Fract. Mech., 69, pp. 165-205.
    • (2002) Eng. Fract. Mech , vol.69 , pp. 165-205
    • Bazant, Z.P.1
  • 51
    • 84903424725 scopus 로고    scopus 로고
    • Fracture Assessment in Concrete Structures
    • R. A. Ainsworth and K. H. Schwalbe, eds, Amsterdam, Holland, Elsevier Applied Science
    • Carpinteri, A., and Ferro, G., 2003, "Fracture Assessment in Concrete Structures," in Comprehensive Structural Integrity, R. A. Ainsworth and K. H. Schwalbe, eds., Amsterdam, Holland, Elsevier Applied Science, Vol. 7, pp. 501-528.
    • (2003) Comprehensive Structural Integrity , vol.7 , pp. 501-528
    • Carpinteri, A.1    Ferro, G.2
  • 52
    • 0038211545 scopus 로고    scopus 로고
    • On the Cohesive Surface Methodology for Fracture of Brittle, Heterogeneous Solids,
    • Ph.D. thesis, Technical University of Delft, The Netherlands
    • Tijssens, M. G. A., 2000, "On the Cohesive Surface Methodology for Fracture of Brittle, Heterogeneous Solids," Ph.D. thesis, Technical University of Delft, The Netherlands.
    • (2000)
    • Tijssens, M.G.A.1
  • 53
  • 54
    • 0023410904 scopus 로고
    • A Continuum Model for Void Nucleation by Inclusion Debonding
    • Needleman, A., 1987, "A Continuum Model for Void Nucleation by Inclusion Debonding," J. Appl. Mech., 54, pp. 525-531.
    • (1987) J. Appl. Mech , vol.54 , pp. 525-531
    • Needleman, A.1
  • 55
    • 45149136479 scopus 로고
    • An Analysis of Tensile Decohesion Along an Interface
    • Needleman, A., 1990, "An Analysis of Tensile Decohesion Along an Interface," J. Mech. Phys. Solids, 38, pp. 289-324.
    • (1990) J. Mech. Phys. Solids , vol.38 , pp. 289-324
    • Needleman, A.1
  • 56
    • 44049109778 scopus 로고
    • The Relation Between Crack Growth Resistance and Fracture Process Parameters in Elastic-Plastic Solids
    • Tvergaard, V., and Hutchinson, J. W., 1992, "The Relation Between Crack Growth Resistance and Fracture Process Parameters in Elastic-Plastic Solids," J. Mech. Phys. Solids, 40, pp. 1377-1397.
    • (1992) J. Mech. Phys. Solids , vol.40 , pp. 1377-1397
    • Tvergaard, V.1    Hutchinson, J.W.2
  • 57
    • 0028400816 scopus 로고
    • Effect of T-Stress in Mode I Crack Growth Resistance in a Ductile Solid
    • Tvergaard, V, and Hutchinson, J. W., 1994, "Effect of T-Stress in Mode I Crack Growth Resistance in a Ductile Solid," Int. J. Solids Struct., 31, pp. 823-833.
    • (1994) Int. J. Solids Struct , vol.31 , pp. 823-833
    • Tvergaard, V.1    Hutchinson, J.W.2
  • 58
    • 21844524284 scopus 로고
    • Toughness of an Interface Along a Thin Ductile Layer Joining Elestic Solids
    • Tvergaard, V., and Hutchinson, J. W., 1994, "Toughness of an Interface Along a Thin Ductile Layer Joining Elestic Solids," Philos. Mag. A, 70, pp. 641-656.
    • (1994) Philos. Mag. A , vol.70 , pp. 641-656
    • Tvergaard, V.1    Hutchinson, J.W.2
  • 59
    • 0035500149 scopus 로고    scopus 로고
    • Resistance Curves for Mixed Mode Interface Crack Growth Between Dissimilar Elastic-Plastic Solids
    • Tvergaard, V, 2001, "Resistance Curves for Mixed Mode Interface Crack Growth Between Dissimilar Elastic-Plastic Solids," J. Mech. Phys. Solids, 49, pp. 2689-2703.
    • (2001) J. Mech. Phys. Solids , vol.49 , pp. 2689-2703
    • Tvergaard, V.1
  • 60
    • 0007219837 scopus 로고    scopus 로고
    • Numerical Investigation of Crack Growth Behaviour Using a Cohesive Zone Model,
    • Ph.D. thesis, University of Hamburg-Harburg, Geesthacht, Germany
    • Lin, G., 1998, "Numerical Investigation of Crack Growth Behaviour Using a Cohesive Zone Model," Ph.D. thesis, University of Hamburg-Harburg, Geesthacht, Germany.
    • (1998)
    • Lin, G.1
  • 61
    • 0000498220 scopus 로고    scopus 로고
    • Three-Dimensional Finite Element Simulation of Crack Extension in Aluminum Alloy 2024-FC
    • Lin, G., Cornec, A., and Schwalbe, K. H., 1998, "Three-Dimensional Finite Element Simulation of Crack Extension in Aluminum Alloy 2024-FC," Fatigue Fract. Eng. Mater. Struct., 21, pp. 1159-1173.
    • (1998) Fatigue Fract. Eng. Mater. Struct , vol.21 , pp. 1159-1173
    • Lin, G.1    Cornec, A.2    Schwalbe, K.H.3
  • 62
    • 0033458026 scopus 로고    scopus 로고
    • The Effect of Strength Mismatch on Mechanical Performance of Weld Joints
    • Lin, G., Meng, X. G., Cornec, A., and Schwalbe, K. H., 1999, "The Effect of Strength Mismatch on Mechanical Performance of Weld Joints," Int. J. Fract., 96, pp. 37-54.
    • (1999) Int. J. Fract , vol.96 , pp. 37-54
    • Lin, G.1    Meng, X.G.2    Cornec, A.3    Schwalbe, K.H.4
  • 63
    • 0028497372 scopus 로고
    • Numerical Simulations of Fast Crack Growth in Brittle Solids
    • Xu, X. P., and Needleman, A., 1994. "Numerical Simulations of Fast Crack Growth in Brittle Solids," J. Mech. Phys. Solids, 42, pp. 1397-1434.
    • (1994) J. Mech. Phys. Solids , vol.42 , pp. 1397-1434
    • Xu, X.P.1    Needleman, A.2
  • 64
    • 0035802969 scopus 로고    scopus 로고
    • Grain Level Analysis of Crack Initiation and Propagation in Brittle Materials
    • Zavattieri, P. D., and Espinosa, H. D., 2001, "Grain Level Analysis of Crack Initiation and Propagation in Brittle Materials," Acta Mater, 49, pp. 4291-4311.
    • (2001) Acta Mater , vol.49 , pp. 4291-4311
    • Zavattieri, P.D.1    Espinosa, H.D.2
  • 65
    • 0035136653 scopus 로고    scopus 로고
    • A Micromechanical Model for a Viscoelastic Cohesive Zone
    • Allen, D. H., and Searcy, C. R., 2001, "A Micromechanical Model for a Viscoelastic Cohesive Zone," Int. J. Fract., 107, pp. 159-176.
    • (2001) Int. J. Fract , vol.107 , pp. 159-176
    • Allen, D.H.1    Searcy, C.R.2
  • 66
    • 0035922150 scopus 로고    scopus 로고
    • A Discrete Dislocation Analysis of Near-Thresold Fatigue Crack Growth
    • Deshpande, V. S., Nedlemann, A., and van der Giessen, E., 2001, "A Discrete Dislocation Analysis of Near-Thresold Fatigue Crack Growth," Acta Mater., 49, pp. 3189-3203.
    • (2001) Acta Mater , vol.49 , pp. 3189-3203
    • Deshpande, V.S.1    Nedlemann, A.2    van der Giessen, E.3
  • 67
    • 0029346176 scopus 로고
    • Size Effects in Nominal Tensile Strength of Concrete Structures: Multifractality of Material Ligaments and Dimensional Transition From Order to Disorder
    • Carpinteri, A., Chiaia, B., and Ferro, G., 1995, "Size Effects in Nominal Tensile Strength of Concrete Structures: Multifractality of Material Ligaments and Dimensional Transition From Order to Disorder," Mater. Struct., 28, pp. 311-317.
    • (1995) Mater. Struct , vol.28 , pp. 311-317
    • Carpinteri, A.1    Chiaia, B.2    Ferro, G.3
  • 68
    • 0035930866 scopus 로고    scopus 로고
    • A Scale-Invariant Cohesive Crack Model for Quasi-Brittle Materials
    • Carpinteri, A., Chiaia, B., and Cometti, P., 2002, "A Scale-Invariant Cohesive Crack Model for Quasi-Brittle Materials," Eng. Fract. Mech., 69, pp. 207-217.
    • (2002) Eng. Fract. Mech , vol.69 , pp. 207-217
    • Carpinteri, A.1    Chiaia, B.2    Cometti, P.3
  • 69
    • 0033333802 scopus 로고    scopus 로고
    • Van Mier, 1. 0. M., and Van Vliet, M. R. A., I999, Effect of Strain Gradients on the Size Effect of Concrete in Uniaxial Tension, Int. J. Fract., 94, pp. 195-219.
    • Van Mier, 1. 0. M., and Van Vliet, M. R. A., I999, "Effect of Strain Gradients on the Size Effect of Concrete in Uniaxial Tension," Int. J. Fract., 94, pp. 195-219.
  • 70
    • 33846345258 scopus 로고
    • Nonlinear Phenomena Associated With Fracture in Strain-Softening Materials
    • M. P. Wnuk, ed, Springer Verlag, Wien, pp
    • Carpinteri, A., 1990, "Nonlinear Phenomena Associated With Fracture in Strain-Softening Materials," in Nonlinear Fracture Mechanics, M. P. Wnuk, ed., Springer Verlag, Wien, pp. 61-121.
    • (1990) Nonlinear Fracture Mechanics , pp. 61-121
    • Carpinteri, A.1
  • 71
    • 0038549429 scopus 로고
    • A Numerical Method for the Analysis of Stable T. P. B. T. Test: Comparison With Some Experimental Data
    • Turin, pp
    • Colombo, G., and Limido, E., 1983, "A Numerical Method for the Analysis of Stable T. P. B. T. Test: Comparison With Some Experimental Data," in XI Convegno Nazionale per I'Analisidelle Sollecitazioni, Turin, pp. 233-243.
    • (1983) XI Convegno Nazionale per I'Analisidelle Sollecitazioni , pp. 233-243
    • Colombo, G.1    Limido, E.2
  • 72
    • 0024737155 scopus 로고
    • Fracture Mechanics of Brick Masonry: Size Effect and Snap-Back Analysis
    • Bocca, P., Carpinteri, A., and Valente, S., 1989, "Fracture Mechanics of Brick Masonry: Size Effect and Snap-Back Analysis," Mater. Struct., 22, pp. 364-373.
    • (1989) Mater. Struct , vol.22 , pp. 364-373
    • Bocca, P.1    Carpinteri, A.2    Valente, S.3
  • 73
    • 33846359212 scopus 로고    scopus 로고
    • Determination of the fracture energy of mortar and concrete by means of three-point bending tests in notched beams. Technical Report No. 18, Materials and Structures R.I.L.E.M, 1985
    • Determination of the fracture energy of mortar and concrete by means of three-point bending tests in notched beams. Technical Report No. 18, Materials and Structures (R.I.L.E.M.), 1985.
  • 74
    • 0037535317 scopus 로고
    • Fracture, Path Bifurcations and Instabilities in Elastic Cohesive Softening Models: A Boundary Elements Approach
    • J. G. M. van Mier, I. G. Rots, and A. Bakker, eds, E&FN Spon, pp
    • Maier, O., Cen, Z., Novati, O., and Tagliaferri, R., 1991, "Fracture, Path Bifurcations and Instabilities in Elastic Cohesive Softening Models: A Boundary Elements Approach," in Fracture Processes in Concrete, Rock, Ceramics, J. G. M. van Mier, I. G. Rots, and A. Bakker, eds., E&FN Spon, pp. 695-704.
    • (1991) Fracture Processes in Concrete, Rock, Ceramics , pp. 695-704
    • Maier, O.1    Cen, Z.2    Novati, O.3    Tagliaferri, R.4
  • 75
    • 0015200918 scopus 로고
    • Optimizing the Control of Rock Failure in Servo-Controlled Laboratory Test
    • Fairhurst, C., Hudson, J. A., and Brown, E. T., 1971, "Optimizing the Control of Rock Failure in Servo-Controlled Laboratory Test," Rock Mech., 3, pp. 217-224.
    • (1971) Rock Mech , vol.3 , pp. 217-224
    • Fairhurst, C.1    Hudson, J.A.2    Brown, E.T.3
  • 77
    • 0024767517 scopus 로고
    • Snapback Softening Instability in High Strength Concrete Beams
    • Biolzi, L., Cangiano, S., Tognon, G. P., and Carpinteri, A., 1989, "Snapback Softening Instability in High Strength Concrete Beams," Mater. Struct., 22, pp. 429-436.
    • (1989) Mater. Struct , vol.22 , pp. 429-436
    • Biolzi, L.1    Cangiano, S.2    Tognon, G.P.3    Carpinteri, A.4
  • 78
    • 0003956031 scopus 로고
    • Damage Accumulation and Crack Growth in Bilinear Materials With Softening
    • Carpinteri, A., and Sib, G. C., 1984, "Damage Accumulation and Crack Growth in Bilinear Materials With Softening," Theor. Appl. Fract. Mech., 1, pp. 145-159.
    • (1984) Theor. Appl. Fract. Mech , vol.1 , pp. 145-159
    • Carpinteri, A.1    Sib, G.C.2
  • 79
    • 0023305945 scopus 로고
    • Tensile Behaviour of Concrete
    • Cedolin, L., Dei Poli, S., and lori, I., 1987, "Tensile Behaviour of Concrete," I. Eng. Mech., 113, 431-449.
    • (1987) I. Eng. Mech , vol.113 , pp. 431-449
    • Cedolin, L.1    Dei Poli, S.2    lori, I.3
  • 80
    • 0006360402 scopus 로고
    • Fracture Toughness Tests for Concrete
    • Barr, B., and Bear, T. J., 1977, "Fracture Toughness Tests for Concrete," Int. J. Fract., 13, pp. 92-96.
    • (1977) Int. J. Fract , vol.13 , pp. 92-96
    • Barr, B.1    Bear, T.J.2
  • 81
    • 0021899628 scopus 로고
    • Numerical Modeling of Discrete Crack Propagation in Plain and Reinforced Concrete
    • G. C. Sih and A. Di Tommaso, eds, Martinus Nijhoff Publishers, pp
    • Ingraffea, A. R., and Saouma, V., 1985, "Numerical Modeling of Discrete Crack Propagation in Plain and Reinforced Concrete," in Fracture Mechanics of Concrete: Structural Application and Numerical Calculation, G. C. Sih and A. Di Tommaso, eds., Martinus Nijhoff Publishers, pp. 171-225.
    • (1985) Fracture Mechanics of Concrete: Structural Application and Numerical Calculation , pp. 171-225
    • Ingraffea, A.R.1    Saouma, V.2
  • 82
    • 33846342820 scopus 로고
    • Structural Effects in the Fracture of Concrete
    • A. M. Brandt, I. H. Marshall, eds, Elsevier Applied Science, pp
    • Kasperkiewicz, J., Dalhuisen, D., and Stroeven, P., 1986, "Structural Effects in the Fracture of Concrete," in Brittle Matrix Composites, A. M. Brandt, I. H. Marshall, eds., Elsevier Applied Science, pp. 537-548.
    • (1986) Brittle Matrix Composites , pp. 537-548
    • Kasperkiewicz, J.1    Dalhuisen, D.2    Stroeven, P.3
  • 83
    • 0022733727 scopus 로고
    • Fracture Processes in Concrete and Fiber Reinforced Cementitious Composites
    • Li, V. C., and Liang, E., 1986, "Fracture Processes in Concrete and Fiber Reinforced Cementitious Composites," J. Eng. Mech., 112, pp. 566-586.
    • (1986) J. Eng. Mech , vol.112 , pp. 566-586
    • Li, V.C.1    Liang, E.2
  • 84
    • 0023347801 scopus 로고
    • Experimental Determination of the Tension-Softening Relations for Cementitious Composites
    • Li, V. C., Chan, C. M., and Leung, K. Y., 1987, "Experimental Determination of the Tension-Softening Relations for Cementitious Composites, Cetn. Concr. Res., 17, pp. 441-452.
    • (1987) Cetn. Concr. Res , vol.17 , pp. 441-452
    • Li, V.C.1    Chan, C.M.2    Leung, K.Y.3
  • 85
    • 0039395175 scopus 로고
    • Dependence of Concrete Fracture Toughness on Specimen Geometry and on Composition
    • A. Carpinteri, and A. R. Ingraffea, eds, Martinus Nijhoff, pp
    • Shah, S. P., 1984, "Dependence of Concrete Fracture Toughness on Specimen Geometry and on Composition," in Fracture Mechanics of Concrete: Material Characterization and Testing, A. Carpinteri, and A. R. Ingraffea, eds., Martinus Nijhoff, pp. 135-1115.
    • (1984) Fracture Mechanics of Concrete: Material Characterization and Testing , pp. 135-1115
    • Shah, S.P.1
  • 86
    • 0015430783 scopus 로고
    • Fracture of Plain Concrete
    • Walsh, P. F., 1972, "Fracture of Plain Concrete," Indian Concr. J., 44, pp. 469-470.
    • (1972) Indian Concr. J , vol.44 , pp. 469-470
    • Walsh, P.F.1
  • 87
    • 33846384222 scopus 로고
    • Effect of Specimen Geometry Stress State and Structure Heterogeneity of Cementitious Composite Materials on KK
    • A. M. Brandt and I. H. Marshall, eds, Elsevier Applied Science, pp
    • Zaitsev, Y. V., and Kovler, K. L., 1986, "Effect of Specimen Geometry Stress State and Structure Heterogeneity of Cementitious Composite Materials on KK" in Brittle Matrix Composites, A. M. Brandt and I. H. Marshall, eds., Elsevier Applied Science, pp. 559-570.
    • (1986) Brittle Matrix Composites , pp. 559-570
    • Zaitsev, Y.V.1    Kovler, K.L.2
  • 88
    • 0019059250 scopus 로고
    • A Model Law for the Notch Sensitivity of Brittle Materials
    • Ziegeldorf, S., Muller, H. S., and Hilsdorf, H. K., 1987, "A Model Law for the Notch Sensitivity of Brittle Materials," Cem. Concr. Res., 10, pp. 589-599.
    • (1987) Cem. Concr. Res , vol.10 , pp. 589-599
    • Ziegeldorf, S.1    Muller, H.S.2    Hilsdorf, H.K.3
  • 89
    • 0008140626 scopus 로고
    • Size-Scale Transition From Ductile to Brittle Fracture: A Dimensional Analysis Approach
    • J. Mazars, and Z. P. Bazant, eds, Elsevier Applied Science, pp
    • Carpinteri, A., and Valente, S, 1989, "Size-Scale Transition From Ductile to Brittle Fracture: A Dimensional Analysis Approach," in Cracking and Damage Strain-Localization and Size Effect, J. Mazars, and Z. P. Bazant, eds., Elsevier Applied Science, pp. 477-490.
    • (1989) Cracking and Damage Strain-Localization and Size Effect , pp. 477-490
    • Carpinteri, A.1    Valente, S.2
  • 91
    • 6244232696 scopus 로고
    • Fractal Character of Fracture Surfaces of Metals
    • Paullay, A. J., Maier, B. B., Passoja, D. E., 1984, "Fractal Character of Fracture Surfaces of Metals," Nature (London), 308, pp. 721-722.
    • (1984) Nature (London) , vol.308 , pp. 721-722
    • Paullay, A.J.1    Maier, B.B.2    Passoja, D.E.3
  • 92
    • 0022779409 scopus 로고
    • The Fractal Nature of Slip in Crystals
    • Kleiser, T., and Bocek, M., 1986, "The Fractal Nature of Slip in Crystals," Z. Metallkd., 77, pp. 582-587.
    • (1986) Z. Metallkd , vol.77 , pp. 582-587
    • Kleiser, T.1    Bocek, M.2
  • 93
    • 0025386644 scopus 로고
    • On the Interpretation of the Fractal Character of Fracture Surfaces
    • Haubensal, F., Dauskardt, R. H., and Ritchie, R. O., 1990, "On the Interpretation of the Fractal Character of Fracture Surfaces, Acta Metall, Mater., 38, pp. 143-159.
    • (1990) Acta Metall, Mater , vol.38 , pp. 143-159
    • Haubensal, F.1    Dauskardt, R.H.2    Ritchie, R.O.3
  • 95
    • 0001824316 scopus 로고
    • Fractal Surfaces: Measurement and Applications in the Earth Sciences
    • Cox, B. L., and Wang, J. S. Y., 1993, "Fractal Surfaces: Measurement and Applications in the Earth Sciences," Fractals, 1 pp. 87-115.
    • (1993) Fractals , vol.1 , pp. 87-115
    • Cox, B.L.1    Wang, J.S.Y.2
  • 96
    • 0042121430 scopus 로고    scopus 로고
    • On the Mechanics of QuasiBrittle Materials With a Fractal Microstructure
    • Carpinteri, A., Chiaia, B., and Cornetti, P., 2003, "On the Mechanics of QuasiBrittle Materials With a Fractal Microstructure," Eng. Fract. Mech., 70, pp. 2321-2349.
    • (2003) Eng. Fract. Mech , vol.70 , pp. 2321-2349
    • Carpinteri, A.1    Chiaia, B.2    Cornetti, P.3
  • 97
    • 4444223931 scopus 로고    scopus 로고
    • A Stereological Analysis of Aggregate Grading and Size Effect on Concrete Tensile Strength
    • Carpinteri, A., Cornetti, P., and Puzzi, S., 2004, "A Stereological Analysis of Aggregate Grading and Size Effect on Concrete Tensile Strength," Int. J. Fract., 128, pp. 233-242.
    • (2004) Int. J. Fract , vol.128 , pp. 233-242
    • Carpinteri, A.1    Cornetti, P.2    Puzzi, S.3
  • 99
    • 0036819132 scopus 로고    scopus 로고
    • Mechanism of Formation of Fractal Mesostructure at the Surface of Polycrystals Upon Cyclic Loading
    • Phys. Met. Metallogr
    • "Mechanism of Formation of Fractal Mesostructure at the Surface of Polycrystals Upon Cyclic Loading," Phys. Met. Metallogr., 94, pp. 402-412.
    • , vol.94 , pp. 402-412
  • 100
    • 33744968760 scopus 로고
    • Multifractal Fracture and Size Effect
    • Mosolov, A., 1994, "Multifractal Fracture and Size Effect," Fractals, 2, pp. 5-8.
    • (1994) Fractals , vol.2 , pp. 5-8
    • Mosolov, A.1
  • 101
    • 0031061907 scopus 로고    scopus 로고
    • Some Fractal Models of Fracture
    • Borodich, F. M., 1997, "Some Fractal Models of Fracture," J. Mech. Phys. Solids, 45, pp. 239-259.
    • (1997) J. Mech. Phys. Solids , vol.45 , pp. 239-259
    • Borodich, F.M.1
  • 102
    • 0031131244 scopus 로고    scopus 로고
    • Physics of Fracture and Mechanics of Self Affine Cracks
    • Balankin, A. S., 1997, "Physics of Fracture and Mechanics of Self Affine Cracks," Eng. Fract. Mech., 57, pp. 135-203.
    • (1997) Eng. Fract. Mech , vol.57 , pp. 135-203
    • Balankin, A.S.1
  • 103
    • 0027085539 scopus 로고
    • Fractal Geometry in Solids and Structures
    • Panagiotopoulos, P. D., 1992, "Fractal Geometry in Solids and Structures," Int. J. Solids Struct., 29, pp. 2159-2175.
    • (1992) Int. J. Solids Struct , vol.29 , pp. 2159-2175
    • Panagiotopoulos, P.D.1
  • 104
    • 0036505741 scopus 로고    scopus 로고
    • The Mechanics of Self-Similar and Self-Affine Fractal Cracks
    • Moyer, E. T., Jr., Yavari, A., Sarkani, S., 2002, "The Mechanics of Self-Similar and Self-Affine Fractal Cracks," Int. J. Fract., 114, pp. 1-27.
    • (2002) Int. J. Fract , vol.114 , pp. 1-27
    • Moyer Jr., E.T.1    Yavari, A.2    Sarkani, S.3
  • 105
    • 0035243367 scopus 로고    scopus 로고
    • Fracture Surface-Fractal or Multi-fractal?
    • Chmiela, J., Stach, S., Cybo, J., 2001, "Fracture Surface-Fractal or Multi-fractal? Mater. Charact., 46, pp. 163-167.
    • (2001) Mater. Charact , vol.46 , pp. 163-167
    • Chmiela, J.1    Stach, S.2    Cybo, J.3
  • 106
    • 11944269290 scopus 로고
    • Experimental Measurements of the Roughness of Brittle Cracks
    • Måløy, K. I., Hansen, A., Hinrichsen, E. L., and Roux, S., 1992, "Experimental Measurements of the Roughness of Brittle Cracks," Phys. Rev. Lett., 68, pp. 213-215.
    • (1992) Phys. Rev. Lett , vol.68 , pp. 213-215
    • Måløy, K.I.1    Hansen, A.2    Hinrichsen, E.L.3    Roux, S.4
  • 107
    • 0029486280 scopus 로고
    • Scaling Invariance of Crack Surfaces
    • Schmittbuhl, J., Schmitt, F., and Scholz, C, 1995, "Scaling Invariance of Crack Surfaces," J. Geophys. Res., 100, pp. 5953-5974.
    • (1995) J. Geophys. Res , vol.100 , pp. 5953-5974
    • Schmittbuhl, J.1    Schmitt, F.2    Scholz, C.3
  • 108
    • 0027510911 scopus 로고
    • Field Measurements of the Roughness of Fault Surfaces
    • Schmittbuhl, I., Gentler, S., and Roux, S., 1985, "Field Measurements of the Roughness of Fault Surfaces," Geophys. Res. Lett., 20, 639-641.
    • (1985) Geophys. Res. Lett , vol.20 , pp. 639-641
    • Schmittbuhl, I.1    Gentler, S.2    Roux, S.3
  • 109
    • 77955588873 scopus 로고
    • Development of Roughness in Crack Propagation
    • Schmittbuhl, I., Roux, S., and Berthaud, Y., 1994, "Development of Roughness in Crack Propagation," Europhys. Lett., 28, pp. 585-590.
    • (1994) Europhys. Lett , vol.28 , pp. 585-590
    • Schmittbuhl, I.1    Roux, S.2    Berthaud, Y.3
  • 110
    • 1942515806 scopus 로고
    • Fractal Diamension of Fractured Surfaces: A Universal Value
    • Bouchaud, E., Lapasset, G., and Planés, J., 1990, "Fractal Diamension of Fractured Surfaces: A Universal Value," Europhys. Lett., 13, pp. 73-79.
    • (1990) Europhys. Lett , vol.13 , pp. 73-79
    • Bouchaud, E.1    Lapasset, G.2    Planés, J.3
  • 111
    • 0001060524 scopus 로고    scopus 로고
    • Pinning and Depinning of Crack Fronts in Heterogeneous Materials
    • Daguier, P., Nghiem, B., Bouchaud, E., and Creuzet, F., 1997, "Pinning and Depinning of Crack Fronts in Heterogeneous Materials," Phys. Rev. Lett., 78, pp. 1062-1065.
    • (1997) Phys. Rev. Lett , vol.78 , pp. 1062-1065
    • Daguier, P.1    Nghiem, B.2    Bouchaud, E.3    Creuzet, F.4
  • 112
    • 0001705597 scopus 로고
    • Surface Measurement and Fractal Characterization of Naturally Fractured Rocks
    • Poon, C. Y., Sayles, R. S., and Jones, T. A., 1992, "Surface Measurement and Fractal Characterization of Naturally Fractured Rocks," J. Phys. D, 25, pp. 1269-1275.
    • (1992) J. Phys. D , vol.25 , pp. 1269-1275
    • Poon, C.Y.1    Sayles, R.S.2    Jones, T.A.3
  • 113
    • 0345582417 scopus 로고    scopus 로고
    • Origin of the Universal Roughness Exponent of Brittle Fracture Surfaces: Stress-Weighted Percolation in the Damage Zone
    • Hansen, A., and Schmittbuhl, J., 2003, "Origin of the Universal Roughness Exponent of Brittle Fracture Surfaces: Stress-Weighted Percolation in the Damage Zone," Phys. Rev. Lett., 90, pp. 045504.
    • (2003) Phys. Rev. Lett , vol.90 , pp. 045504
    • Hansen, A.1    Schmittbuhl, J.2
  • 114
    • 0022130960 scopus 로고
    • The Fractal Nature of the Surface of Cement Paste
    • Winslow, D. N., 1985, "The Fractal Nature of the Surface of Cement Paste," Cem. Concr. Res., 15, pp. 817-824.
    • (1985) Cem. Concr. Res , vol.15 , pp. 817-824
    • Winslow, D.N.1
  • 115
    • 0037216668 scopus 로고    scopus 로고
    • Fractal Dimension - A Measure of Fracture Roughness and Toughness of Concrete
    • Islam, Md. S., Issa, Mo. A., Issa, Ma. A., and Chudnovsky, A., 2003, "Fractal Dimension - A Measure of Fracture Roughness and Toughness of Concrete," Eng. Fract. Mech., 70, 125-137.
    • (2003) Eng. Fract. Mech , vol.70 , pp. 125-137
    • Islam, M.S.1    Issa, M.A.2    Issa, M.A.3    Chudnovsky, A.4
  • 116
    • 0038604259 scopus 로고    scopus 로고
    • Cohensive Crack Model Description of Ductile to Brittle Size-Scale Transition: Dimensional Analysis vs Renormalization Group Theory
    • Carpinteri, A., Cornetti, P. Barpi, F., and Valente, S., 2003, "Cohensive Crack Model Description of Ductile to Brittle Size-Scale Transition: Dimensional Analysis vs Renormalization Group Theory," Eng. Fract. Mech., 70, pp. 1809-1839.
    • (2003) Eng. Fract. Mech , vol.70 , pp. 1809-1839
    • Carpinteri, A.1    Cornetti, P.2    Barpi, F.3    Valente, S.4
  • 117
    • 0022659241 scopus 로고
    • Determination of Fracture Properties From Size Effect Tests
    • Bažant, Z. P., Kirn, J. K., and Pfeiffer, P. A., 1984, "Determination of Fracture Properties From Size Effect Tests," J. Struct. Eng., 112, pp. 289-307.
    • (1984) J. Struct. Eng , vol.112 , pp. 289-307
    • Bažant, Z.P.1    Kirn, J.K.2    Pfeiffer, P.A.3
  • 118
    • 33846356630 scopus 로고    scopus 로고
    • Van Mier, J. G. M., and Van Vliet, M. R. A., 1998, Experimental Investigation of Size Effect in Concrete Under Uniaxial Tension, in Proceedings of FRAMCOS-3, H. Mihashi, and K. Rokugo, eds., AEDIFICATIO, pp. 1923-1936.
    • Van Mier, J. G. M., and Van Vliet, M. R. A., 1998, "Experimental Investigation of Size Effect in Concrete Under Uniaxial Tension," in Proceedings of "FRAMCOS-3", H. Mihashi, and K. Rokugo, eds., AEDIFICATIO, pp. 1923-1936.
  • 119
    • 0031223809 scopus 로고    scopus 로고
    • Complex Fracture Energy Dissipation in Concrete Under Different Loading Conditions
    • Carpinteri, A., Chiaia, B., and Nemati, K. M., 1997, "Complex Fracture Energy Dissipation in Concrete Under Different Loading Conditions," Mech. Mater., 26, pp. 93-108.
    • (1997) Mech. Mater , vol.26 , pp. 93-108
    • Carpinteri, A.1    Chiaia, B.2    Nemati, K.M.3
  • 120
    • 0032672354 scopus 로고    scopus 로고
    • Three Dimensional Fractal Analysis of Concrete Fracture at the Mesolevel
    • Carpinteri, A., Chiaia, B., and Invemizzi, S., 1999, "Three Dimensional Fractal Analysis of Concrete Fracture at the Mesolevel," Theor. Appl. Fract. Mech., 31, pp. 163-172.
    • (1999) Theor. Appl. Fract. Mech , vol.31 , pp. 163-172
    • Carpinteri, A.1    Chiaia, B.2    Invemizzi, S.3
  • 121
    • 0037535289 scopus 로고    scopus 로고
    • Size Effects on Concrete Tensile Fracture Properties: An Interpretation of the Fractal Approach Based on the Aggregate Grading
    • Carpinteri, A., and Cornetti, P., 2002, "Size Effects on Concrete Tensile Fracture Properties: An Interpretation of the Fractal Approach Based on the Aggregate Grading," J. Mech. Behav. Mater., 13, pp. 233-246.
    • (2002) J. Mech. Behav. Mater , vol.13 , pp. 233-246
    • Carpinteri, A.1    Cornetti, P.2
  • 122
    • 0000879722 scopus 로고    scopus 로고
    • Power Scaling Laws and Dimensional Transitions in Solid Mechanics
    • Carpinteri, A., and Chiaia, B., 1996, "Power Scaling Laws and Dimensional Transitions in Solid Mechanics," Chaos, Solitons Fractals, 7, pp. 1343-1364.
    • (1996) Chaos, Solitons Fractals , vol.7 , pp. 1343-1364
    • Carpinteri, A.1    Chiaia, B.2
  • 123
    • 0000111514 scopus 로고    scopus 로고
    • Multifractal Scaling Laws in the Breaking Behavior of Disordered Materials
    • Carpinteri, A., and Chiaia, B., 1997, "Multifractal Scaling Laws in the Breaking Behavior of Disordered Materials," Chaos, Solitons Fractals, 8, pp. 135150.
    • (1997) Chaos, Solitons Fractals , vol.8 , pp. 135150
    • Carpinteri, A.1    Chiaia, B.2
  • 124
    • 0032154734 scopus 로고    scopus 로고
    • Scale Dependence of Tensile Strength of Concrete Specimens: A Multifractal Approach
    • Carpinteri, A., Chiaia, B., and Ferro, O., 1998, "Scale Dependence of Tensile Strength of Concrete Specimens: A Multifractal Approach," Mag. Concrete Res., 50, pp. 237-246.
    • (1998) Mag. Concrete Res , vol.50 , pp. 237-246
    • Carpinteri, A.1    Chiaia, B.2    Ferro, O.3
  • 125
    • 0006811828 scopus 로고    scopus 로고
    • Size Effects on Concrete Fracture Energy: Dimensional Transition From Order to Disorder
    • Carpinteri, A., and Chiaia, B., 1996. "Size Effects on Concrete Fracture Energy: Dimensional Transition From Order to Disorder," Mater. Struct., 29, pp. 259-266.
    • (1996) Mater. Struct , vol.29 , pp. 259-266
    • Carpinteri, A.1    Chiaia, B.2
  • 126
    • 0030465094 scopus 로고    scopus 로고
    • Crack-Resistance Behavior as a Consequence of Self-Similar Fracture Topologies
    • Carpinteri, A., and Chiaia, B., 1996, "Crack-Resistance Behavior as a Consequence of Self-Similar Fracture Topologies," Int. J. Fract., 76, pp. 327-340.
    • (1996) Int. J. Fract , vol.76 , pp. 327-340
    • Carpinteri, A.1    Chiaia, B.2
  • 127
    • 0031098082 scopus 로고    scopus 로고
    • A New Explanation for Size Effects on the Flexural Strength of Concrete
    • Carpinteri, A., Chiaia, B., and Ferro, G., 1997, "A New Explanation for Size Effects on the Flexural Strength of Concrete," Mag. Concrete Res, 49, pp. 45-53.
    • (1997) Mag. Concrete Res , vol.49 , pp. 45-53
    • Carpinteri, A.1    Chiaia, B.2    Ferro, G.3
  • 128
    • 0032682449 scopus 로고    scopus 로고
    • Scale Effects in Uniaxially Compressed Concrete Specimens
    • Carpinteri, A., Ferro, G., and Monetto, I., 1999, "Scale Effects in Uniaxially Compressed Concrete Specimens," Mag. Concrete Res., 51, pp. 217-225.
    • (1999) Mag. Concrete Res , vol.51 , pp. 217-225
    • Carpinteri, A.1    Ferro, G.2    Monetto, I.3
  • 129
    • 0012374613 scopus 로고    scopus 로고
    • Size Effects on Tensile Strength and Fracture Energy in Concrete: Wavelet vs Fractal Approach
    • Konstantinidis, A., Frantziskonis, G., Carpinteri, A., and Aifantis, E. C., 2001, "Size Effects on Tensile Strength and Fracture Energy in Concrete: Wavelet vs Fractal Approach," J. Mech. Behav. Mater., 12, pp. 63-75.
    • (2001) J. Mech. Behav. Mater , vol.12 , pp. 63-75
    • Konstantinidis, A.1    Frantziskonis, G.2    Carpinteri, A.3    Aifantis, E.C.4
  • 130
    • 0012638198 scopus 로고    scopus 로고
    • Multifractal Scaling Law Versus Gradient Elasticity in the Evaluation of Disordered Materials Compressive Strength
    • Efraimidis, G., Carpinteri, A., Aifantis, E. C., 2001, "Multifractal Scaling Law Versus Gradient Elasticity in the Evaluation of Disordered Materials Compressive Strength," J. Mech. Behav. Mater., 12, pp. 107-120.
    • (2001) J. Mech. Behav. Mater , vol.12 , pp. 107-120
    • Efraimidis, G.1    Carpinteri, A.2    Aifantis, E.C.3
  • 131
    • 0036028181 scopus 로고    scopus 로고
    • A Fractional Calculus Approach to the Description of Stress and Strain Localization in Fractal Media
    • Carpinteri, A., and Comettri, P., 2002, "A Fractional Calculus Approach to the Description of Stress and Strain Localization in Fractal Media," Chaos, Solitons Fractals, 13, pp. 85-94.
    • (2002) Chaos, Solitons Fractals , vol.13 , pp. 85-94
    • Carpinteri, A.1    Comettri, P.2
  • 133
    • 33846382972 scopus 로고    scopus 로고
    • Kolwankar, K. M., 1998, Studies of Fractal Structures and Processes Using Methods of Fractional Calculus, Ph.D. thesis, University of Pune.
    • Kolwankar, K. M., 1998, "Studies of Fractal Structures and Processes Using Methods of Fractional Calculus, Ph.D. thesis, University of Pune.
  • 134
    • 0035834542 scopus 로고    scopus 로고
    • Static- Kinematic Duality and the Principle of Virtual Work in the Mechanics of Fractal Media
    • Carpinteri, A., Chiaia, B., and Cornetti, P., 2001, "Static- Kinematic Duality and the Principle of Virtual Work in the Mechanics of Fractal Media," Comput. Methods Appl. Mech. Eng., 191, pp. 3-19.
    • (2001) Comput. Methods Appl. Mech. Eng , vol.191 , pp. 3-19
    • Carpinteri, A.1    Chiaia, B.2    Cornetti, P.3
  • 135
    • 1142264110 scopus 로고    scopus 로고
    • A Fractional Calculus Approach to the Mechanics of Fractal Media
    • Carpinteri, A., Chiaia, B., and Cornetti, P., 2004, "A Fractional Calculus Approach to the Mechanics of Fractal Media," Z, Angew. Math. Mech., 84, pp. 128-135.
    • (2004) Z, Angew. Math. Mech , vol.84 , pp. 128-135
    • Carpinteri, A.1    Chiaia, B.2    Cornetti, P.3
  • 136
    • 1342264358 scopus 로고    scopus 로고
    • Calculation of the Tensile and Flexural Strength of Disordered Materials Using Fractional Calculus
    • Carpinteri, A., Cornetti, P., and Kolwankar, K. M., 2004, "Calculation of the Tensile and Flexural Strength of Disordered Materials Using Fractional Calculus," Chaos, Solitons Fractals, 21, pp, 623-632.
    • (2004) Chaos, Solitons Fractals , vol.21 , pp. 623-632
    • Carpinteri, A.1    Cornetti, P.2    Kolwankar, K.M.3
  • 137
    • 0032098838 scopus 로고    scopus 로고
    • Scaling Behaviour and Dual Renormalization of Experimental Tensile Softening Responses
    • Carpinteri, A., and Ferro, G., 1998, "Scaling Behaviour and Dual Renormalization of Experimental Tensile Softening Responses," Mater. Struct., 31, pp. 303-309.
    • (1998) Mater. Struct , vol.31 , pp. 303-309
    • Carpinteri, A.1    Ferro, G.2
  • 139
    • 33846383286 scopus 로고    scopus 로고
    • Miller, K. S., and Ross, B., 1993, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York.
    • Miller, K. S., and Ross, B., 1993, An Introduction to the Fractional Calculus and Fractional Differential Equations, Wiley, New York.
  • 142
    • 0030464353 scopus 로고    scopus 로고
    • Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena
    • Mainardi, F., 1996, "Fractional Relaxation-Oscillation and Fractional Diffusion-Wave Phenomena," Chaos, Solitons Fractals, 7, pp. 1461-1477.
    • (1996) Chaos, Solitons Fractals , vol.7 , pp. 1461-1477
    • Mainardi, F.1
  • 143
    • 0001219948 scopus 로고
    • Fractional Differentiation of Devil's Staircases
    • Schellnhuber, H. J., and Seyler, A., 1992, "Fractional Differentiation of Devil's Staircases, Physica A. 191, pp. 491-500.
    • (1992) Physica A , vol.191 , pp. 491-500
    • Schellnhuber, H.J.1    Seyler, A.2
  • 144
    • 36149036329 scopus 로고
    • Fractional Diffusion Equation on Fractals: One-Dimensional Case and Asymptotic Behavior
    • Giona, M., and Roman, H. E., 1992, "Fractional Diffusion Equation on Fractals: One-Dimensional Case and Asymptotic Behavior," J. Phys. A. 25, pp. 2093-2105.
    • (1992) J. Phys. A , vol.25 , pp. 2093-2105
    • Giona, M.1    Roman, H.E.2
  • 145
    • 0001102649 scopus 로고
    • Fractional Integral and Differential Equations for a Class of Lévy-Type Probability Densities
    • Nonnenmacher, T. F., 1990, "Fractional Integral and Differential Equations for a Class of Lévy-Type Probability Densities," J. Phys. A, 23, pp. L697-L700.
    • (1990) J. Phys. A , vol.23
    • Nonnenmacher, T.F.1
  • 146
    • 0040655648 scopus 로고    scopus 로고
    • Fractional Differentiability of Nowhere Differentiable Functions and Dimensions
    • Kolwankar, K. M., and Gangal, A. D., 1996, "Fractional Differentiability of Nowhere Differentiable Functions and Dimensions," Chaos, 6, pp. 505-523.
    • (1996) Chaos , vol.6 , pp. 505-523
    • Kolwankar, K.M.1    Gangal, A.D.2
  • 147
    • 0030671988 scopus 로고    scopus 로고
    • Holder Exponents of Irregular Signals and Local Fractional Derivatives
    • Kolwankar, K. M., and Gangal, A. D., 1997, "Holder Exponents of Irregular Signals and Local Fractional Derivatives," Pramana, J. Phys., 48, pp. 49-68.
    • (1997) Pramana, J. Phys , vol.48 , pp. 49-68
    • Kolwankar, K.M.1    Gangal, A.D.2
  • 148
    • 0001707390 scopus 로고    scopus 로고
    • Local Fractional Fokker-Planck Equations
    • Kolwankar, K. M., and Gangal, A. D., 1998, "Local Fractional Fokker-Planck Equations," Phys. Rev. Lett., 80, pp. 214-217.
    • (1998) Phys. Rev. Lett , vol.80 , pp. 214-217
    • Kolwankar, K.M.1    Gangal, A.D.2
  • 150
    • 0742324870 scopus 로고    scopus 로고
    • The Elastic Problem for Fractal Media: Basic Theory and Finite Element Formulation
    • Carpinteri, A., Chiaia, B., and Cornetti, P., 2004, "The Elastic Problem for Fractal Media: Basic Theory and Finite Element Formulation," Comput. Struct., 82, pp. 499-508.
    • (2004) Comput. Struct , vol.82 , pp. 499-508
    • Carpinteri, A.1    Chiaia, B.2    Cornetti, P.3
  • 151
    • 0021410063 scopus 로고
    • Size Effect in Blunt Fracture: Concrete, Rock, Metal
    • Bazant, Z. P., 1984, "Size Effect in Blunt Fracture: Concrete, Rock, Metal." J. Eng. Mech., 110. pp. 518-535.
    • (1984) J. Eng. Mech , vol.110 , pp. 518-535
    • Bazant, Z.P.1
  • 152
    • 0007720067 scopus 로고
    • Effettti di Scala sulla Resistenza a Trazionc del Materiali
    • Ph.D. thesis, Politccnico di Torino
    • Ferro, G., 1994, "Effettti di Scala sulla Resistenza a Trazionc del Materiali." Ph.D. thesis, Politccnico di Torino.
    • (1994)
    • Ferro, G.1
  • 153
    • 0003509778 scopus 로고    scopus 로고
    • Size Effect in Tensile Fracture of Concrete and Rock,
    • Ph.D. thesis. Technical University of Delft, The Netherlands
    • Van Vliet, M. R. A., 2000, "Size Effect in Tensile Fracture of Concrete and Rock," Ph.D. thesis. Technical University of Delft, The Netherlands.
    • (2000)
    • Van Vliet, M.R.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.