Micromechanical and lattice modeling of brittle damage

• Autorzy: Basista M.

Warianty tytułu

PL

Mikromechaniczne i sieciowe modele kruchego uszkodzenia

• Języki publikacji: EN

Abstrakty

EN

This thesis is a multi-aspect study concerned with theoretical modeling of damage in brittle solids with special emphasis on rocks and plain concrete. Motivated by the complex and diverse nature of damage processes in these materials, a integrated approach involving micromechanical, phenomenological and lattice modeling is pursued. it is shown that these seemingly disparete classes of models turn to be complementary in their objectives and utility. The bulk of the work is devoted to the local description of damage problems in rock-like materials under quasi-static mechanical loading (tensile or compressive) at isothermal condition. Slightly of the mainstream but well in tune with the micromechanical damage modeling promoted in this thesis, a type of environmental damage of concrete due to chemically aggressive ambient is also investigated. Application of the methods of physics of critical phenomena to brittle damage and fracture problems constitutes an important part of this study. It is suggested that the percolation and other disorder models be used at large microdefects densities where the traditional methods of micromechanical and continuum damage mechanics cease ti be valid. The individual chapters of the thesis can be summarized al follows.

PL

Niniejsza praca jest wieloaspektowym studium procesów uszkodzenia w skałach i betonie w zakresie deformacji kruchych. Czynnikami wywołującymi wzrost uszkodzenia są tu quasi-statyczne obciążenia rozciągające, ściskające oraz chemicznie agresywne środowisko. Rozważa się izotermiczne procesy deformacji przy założeniu małych odkształceń i pominięciu efektów plastycznych. Zasadniczym celem pracy jest sformułowanie równań konstytutywnych dla powyższych materiałów, przyjmując za punkt wyjścia udokumentowanie doświadczalnie mechanizmy rozwoju uszkodzeń na poziomie mikroskopowym. Modele teoretyczne zostały w pracy podzielone na mikromechaniczne, fenomenologiczne i sieciowe. Odnoszą się one wprawdzie do tych samych zjawisk fizycznych, ale różni je przyjęta metodologia i zakres stosowalności, co uzasadnia taki podział. Zgodnie z tytułem, większa część pracy poświęcona jest mikromechanicznym i sieciowym modelom kruchego uszkodzenia. Model fenomenologiczny przedstawiony w Rozdziale 7 jest przykładem wykorzystania informacji z poziomu mikro do zbudowania modelu makroskopowego, ale nie stanowi jeszcze zamkniętej teorii. Wyprzedzając wnioski końcowe można dodać, że wymieniowe trzy grupy modeli nie są wobec siebie konkurencyjne, ale wzajemnie się uzupełniają. Praca zawiera przykłady zastosowań proponowanych modeli i porównania z wynikami doświadczeń. Rozdziały 1 i 2 mają charakter opisowy, Rozdziały 3, 4, 5, 6, 7, 8 stanowią oryginalną, badawczą część pracy. Rozdział 9 zawiera spis literatury cytowanej w tekście. Niniejsza praca podsumowuje kilkunastoletni okres aktywności badawczej autora w dziedzinie mechaniki uszkodzenia materiałów kruchych.

Słowa kluczowe

EN

materials engineering; dispersion; crushing; disintegration

PL

inżynieria materiałowa; uszkodzenia materiałów kruchych; rozpad; kruszenie; dyspersja

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Prace Instytutu Podstawowych Problemów Techniki PAN
• Rocznik: 2001
• Tom: nr 3
• Strony: 5--237
• Opis fizyczny: Bibliogr. 275 poz.

Twórcy

autor

Basista M.

• Instytut Podstawowych Problemów Techniki PAN

Bibliografia

• Aboudi, J. (1991). Mechanics of Composite Materials - a Unified Micromechanical Approach, Elsevier, Amsterdam.
• Ashby, M.F. (1979). Micromechanics of fracture in static and cyclic failure, in: Fracture Mechanics, R.A. Smith (Ed.), Pergamon Press, Oxford, 1-27.
• Ashby, M.F. and Hallam, S.D. (1986). The failure of brittle solids containing small cracks under compressive stress states, Acta Metall., 34, 497-510.
• ASTM C1012 (1987). Standard test method for: Length change of hydrauliccement mortars exposed to a sulphate solution, Annual Book of ASTM Standards, 04.01.
• ASTM C490 (1986). Standard specification for: Apparatus for use in measurement of length change of hardened cement paste, mortar and concrete, Annual Book of ASTM Standards, 04.01.
• Atkinson, B.K. and Meredith, P.G. (1987). Experimental fracture mechanics data for rocks and minerals, in: Fracture Mechanics of Rock, B.K. Atkinson (Ed.), Academic Press, London, 477-525.
• Balberg, I. (1987). Recent developments in continuum percolation, Phil. Mag. B56, 991-1003.
• Balberg, I., Anderson, C H., Alexander, S. and Wagner, N. (1984). Excluded volume and its relation to the onset of percolation, Phys. Rev. B, 30, 3933-3943.
• Barenblatt, G.I., Zheltov, Iu.P. and Kochina, I.N. (1960). Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, Prikl. Mat. i Mekh., 24, 852-864.
• Basista, M. (1984). Continuum Damage Mechanics - a review of existing theories, IFTR Reports, 40 (in Polish).
• Basista, M. (1988). Damage mechanics: experimental background, Eng. Trans., 36, 707-737.
• Basista, M. (1993). On micromechanical modeling of deformation of compact rock in compression, Eng. TYans., 41, 395-417.
• Basista, M. (1997) Modeling of spall damage in brittle solids, Eng. Trans., 45, 501-527.
• Basista, M (1999). Micromechanical, phenomenological, and lattice modeling of brittle damage, in: Modeling of Damage and Fracture Processes in Engineering Materials, M. Basista and W.K. Nowacki (Eds.), IPPT PAN, Warszawa, 236-298.
• Basista, M. (2000). On interactions of frictional cracks, Arch. Mech., 52, 329-340.
• Basista, M. and Gross, D. (1985). One-dimensional constitutive model of microcracked elastic solid, Arch. Mech., 37, 587-601.
• Basista, M. and Gross, D. (1989). A note on brittle damage description, Mech. Res. Comm., 16, 147-154.
• Basista, M. and Gross, D. (1997). Internal variable representation of microcrack induced inelasticity in brittle materials, Int. J. Damage Mechanics, 6, 300-316.
• Basista, M. and Gross, D. (1998a) The sliding crack model of brittle deformation: an internal variable approach, Int. J. Solids Structures, 35, 487-509.
• Basista, M. and Gross, D. (1998b) The sliding crack model revisited, in: Damage Mechanics in Engineering Materials, G.Z. Voyiadjis, J.W. Ju and J.L. Chaboche (Eds.), Elsevier Science, 125-143.
• Basista, M. and Gross, D. (2000). A note on crack interactions in compression, Int. J. Fracture, 102, L67-L72.
• Basista, M. and Krajcinovic D. (1991). Brittle deformation of disordered solids, Composites Eng., 1, 103-112.
• Basista, M., Krajcinovic, D. and Sumarac D. (1991) Analytical modeling of the brittle deformation of solids, in: Damage Mechanics in Engineering Materials, J.W. Ju, D. Krajcinovic, H. Schreyer (Eds.), ASME Publ., AMD-109, MD-24, New York, 27-40.
• Basista, M., Krajcinovic, D. and Sumarac D. (1992). Micromechanics, phenomenology and statistics of brittle deformation, in: Computational Plasticity - Fundamentals and Applications, D.R.J. Owen, E. Oiiate, E. Hinton (Eds.), Pineridge Press, Swansea, UK., 1479-1490.
• Bazant, Z.P. (1984). Size effect in blunt fracture: concrete, rock, metal, J. Engng Mech. ASCE, 110, 518-535.
• Bazant, Z.P, Bittnar, Z., Jirasek, M. and Mazars, J. (1994). Fracture and Damage in Quasi-brittle Structures, E &: FN Spon, London.
• Bazant, Z.P., Sener, S. and Kim, J.K. (1987). Effect of cracking on drying perme¬ability and diffusivity of concrete, ACI Mater. J., 84-M35, 351-357.
• Beale, P.D. and Srolovitz, D.J. (1988). Elastic fracture in random materials, Phys. Rev. B, 37, 5500-5507.
• Benguigui, L. (1984). Experimental study of the elastic properties of a percolating system, Phys. Rev. Lett., 53, 2028-2030.
• Benguigui, L. (1986a). Elasticity and fracture near a percolation threshold in two dimensions, in: Fragmentation, Form and Flow in Fractured Media, R. Englman and Z. Jaeger, eds., Annals Israel Phys. Soc., 8, 288-293.
• Benguigui, L. (1986b). Lattice and continuum percolation transport exponents: Experiments in two-dimensions, Phys. Rev. B, 34, 8176-8179.
• Bensoussan, A., Lions, J.L. and Ramos, R.R. (1978). Asymptotic Analysis for Periodic Structures, North Holland, New York.
• Benveniste, Y., Dvorak, G.J. and Chen, T. (1991). On diagonal and elastic symmetry of the approximate effective stiffness tensor of heterogeneous media, J. Mech. Phys. Solids, 39, 927 946.
• Benveniste, Y., Dvorak, G.J., Zarzour, J. and Wung, E.C.J. (1989). On interacting cracks and complex crack configurations in linear elastic media, Int. J. Solids Structures, 25, 1279-1293.
• Bettin, A. and Gross, D. (1990). Crack propagation in materials with local inhomogeneities under thermal load, in: Thermal Effects in Fracture of Multiphase Materials, K.P. Herrrmann and Z.S. Olesiak (Eds.), Lecture Notes in Engineering, Springer Verlag, 59, 85-93.
• Biczok, I. (1972). Concrete Corrosion Concrete Protection, Akademiai Kiado, Budapest.
• Bieniawski, Z.T. (1967). Mechanism of brittle fracture of rock, Int. J. Rock Mech. Mm. Sci. 4, 407-423.
• Brace, W.F. and Bombolakis, E.G. (1963). A note on brittle crack growth in compression, J. Geophys. Res., 68, 3709-3713.
• Brace, W.F., Paulding, B.W. and Scholz, C. (1966). Dilatancy in the fracture of crystalline rocks, J. Geophys. Res., 71, 3939-3953.
• Bristow, J.R. (1960). Microcracks and the static and dynamic elastic constants of annealed and heavily cold-worked metals, British J. Appl. Phys., 11, 81-85.
• Broek, D. (1974). Elementary Engineering Fracture Mechanics, Noordhoff, Leyden.
• Brown, P.W. and LaCroix, P. (1989). The kinetics of ettringite formation, Cem. Concr. Res., 19, 879-884.
• Briihwiler, E., Fliickinger, D. and Rosli, H. (1986). Versuche iiber den Einfluss hoher Dehngeschwindigkeiten und Vorbelastungsgeschichten auf die Festigkeit und das Verformungsverhalten von Beton, Versuchsbericht, Eidgenossiche Technische Hochschule, Zurich.
• Budiansky, B. and O’Connell, R.J. (1976). Elastic moduli of cracked solid, Int. J. Solids Structures, 12, 81-97.
• Cannon, N.P., Schulson, E.M., Smith, T.R. and Frost, H.J. (1990). Wing cracks and brittle compressive fracture, Acta Metall. Mater., 38, 1955-1962.
• Chaboche, J.L. (1988). Continuum damage mechanics. Part I and II, J. Appl. Mech., 55, 59-72.
• Chaboche, J.L. (1999). Thermodynamically founded CDM models for creep and other conditions, in: Creep and Damage in Materials and Structures, H. Altenbach and J. Skrzypek (Eds.), Springer, Vienna.
• Charlaix, E. (1986). Percolation thresholds of a random array of discs: A numerical simulation, J. Phys. A, 19, L533-L536.
• Chen, W. F. (1982). Plasticity of Concrete, McGraw-Hill, New York.
• Chen, Y.Z. (1984). General case of multiple crack problems in an infinite plate, Eng. Fracture Mech., 20, 591-597.
• Christensen, R.M. (1990). A critical evaluation for a class of micro-mechanics models, J. Mech. Phys. Solids, 38, 379-404.
• Christensen, R.M. (1991). Mechanics of Composite Materials. Krieger, Malabar, FL.
• Chrzanowski, M. (1976). Use of the damage concept in describing creep-fatigue interaction under prescribed stress, Int. J. Mech. Sci., 18, 69-73.
• Cleary, M.P., Chen, I.W. and Lee, S.M. (1980). Self-consistent techniques for heterogeneous media, J. Eng. Mech. Div. ASCE, 106, 861-887.
• Coon, M.D. and Evans, R.J. (1972). Incremental constitutive laws and their associated failure criteria with application to plain concrete, Int. J. Solids Structures, 8, 1169-1183.
• Costin, L.S. (1983). A microcrack model for the deformation and failure of brittle rock, J. Geophys. Res., 88, 9485-9492.
• Cotterell, B. and Rice, J.R. (1980). Slightly curved or kinked cracks, Int. J. Fract., 16, 155-169.
• Cox, S.J.D. and Paterson, L. (1990). Damage development during rupture of heterogeneous brittle materials: a numerical study, in: Deformation Mechanisms, Rheology and Tectonics, R.J. Knipe and E.H. Rutter (Eds.), Geol. Soc. Lond. Spec. Publ.
• Daniels, H.E. (1945). The statistical theory of the strength of bundles of threads, Proc. Roy. Soc. London. A, 183, 405-435.
• Davison, L. and Stevens, A.L. (1973). Thermomechanical constitution of spalling elastic bodies, J. Appl. Phys., 44, 668-674.
• Dawson, B.E. (1973). Kinetics and Mechanisms of Reactions. Methuen Educational Ltd., London.
• de Arcangelis, L. and Herrmann, H.J. (1989). Scaling and multiscaling laws in random fuse networks, Phys. Rev. B, 39, 2678-2681.
• de Arcangelis, L., Redner S. and Herrmann, H.J. (1985). A random fuse model for breaking process, J. Physique Lett., 46, L585-L590.
• Delaplace, A., Pijaudier-Cabot, G. and Roux, S. (1996). Progressive damage in discrete models and consequences on continuum modelling, J. Mech. Phys. Solids, 44, 99-136.
• Deng, H. and Nemat-Nasser, S. (1992). Dynamic damage evolution in brittle solids, Mech. Mater., 14, 83-103.
• Deng, H. and Nemat-Nasser, S. (1994). Microcrack interaction and shear fault failure, Int. ,J. Damage Mech., 3, 3-37.
• Dienes, J.K. (1982). Permeability, percolation, and statistical crack mechanics, in: Issues on Rock Mechanics, R.E. Goodman and F.E. Heuze (Eds.), Proc. 23rd Symp. on Rock Mech., Berkeley, CA.
• Doliński, K. (1999). Fatigue damage and reliability assessment of cemented hip prosthesis, J. Theor. Appl. Mech., 37, 505-518.
• Dougill, J.W. (1976). On stable progressively fracturing solids, ZAMP, 27, 423-437.
• Dragon, A. and Mroz, Z. (1979). A continuum model for plastic-brittle behavior rock and concrete, Int. J. Eng. Sci., 17, 121-137.
• Dullien, F.A.L. (1979). Porous Media. Fluid Transport and Pore Structure, Academic Press, New York.
• Duxbury, P.M., Leath, P.L. and Beale, P.D. (1987). Breakdown properties of quenched random systems: The random-fuse network, Phys. Rev. B, 36, 367-380.
• Dyskin, A.V., Germanovich, L.N., Jewell, R.J., Joer, H., Krasinski, J.S., Lee, K.K., Roegiers, J.-C., Sahouryeh, E. And Ustinov, K.B. (1995). Some experimental results on three-dimensional crack propagation in compression, in: Mechanics of Jointed and Faulted Rock, Rossmanith (ed.), Balkema Rotterdam, 91-96.
• Eimer, Cz. (1978). Elasticity of cracked medium, Arch. Mech., 30, 827-836.
• Elices, M. and Planas, J. (1992). Size effect in concrete structures: R-curve approach, in: Application of Fracture Mechanics to Reinforced Concrete, A. Carpin- teri (Ed.), Elsevier Applied Science, Torino, Italy, 169-200.
• Englman, R., Gur, Y. and Jaeger, Z. (1983). Fluid flow through a crack network in rocks, J. Appl. Mech., 50, 707-711.
• Erdogan, F. And Sih, G.C. (1963). On the crack extension in plates under plane loading and transverse shear, J. Basic Eng., 85, 519-527.
• Evans, R.H. and Marathe, M.S. (1968). Microcracking and stress-strain curves for concrete in tension, Materiaux et Constructions, 1, 61-64.
• Fanella, D. and Krajcinovic, D. (1988). A micromechanical model for concrete in compression, Eng. Fract. Mech., 29, 49-66.
• Feng, S. and Sen, P.N. (1984). Percolation on elastic networks: New exponents and threshold, Phys. Rev. Lett., 52, 216-280.
• Feng, S., Sen, P.N., Halperin, B.I. and Lobb, C.J. (1984). Percolation on two- dimensional elastic networks with rotationally invariant bond-bending forces, Phys. Rev. B, 30, 5386-5389.
• Feng, X.Q. and Yu, S.W. (1995). Micromechanical modelling of tensile response of elastic-brittle materials, Int. J. Solids Structures, 32, 3359-3372.
• Finlayson, B.A. (1980). Nonlinear Analysis in Chemical Engineering, McGraw-Hill, New York.
• Forster, F. and Scheil, E. (1936). Akustische Untersuchung der Bildung von Martensitnadeln, Z. Metallkunde, 29, 245.
• Gambin, B. and Telega, J.J. (2000). Effective properties of elastic solids with randomly distributed microcracks, Mech. Res. Comm., 27, 697-706.
• Germanovich, L.N., Carter, B.J., Ingraffea, A.R., Dyskin, A.V. and Lee, K.K. (1996). Mechanics of 3-D crack growth under compressive loads, in: Rock Mechanics, Aubertin, Hassani and Mitri (Eds.), Balkema, Rotterdam, 1151-1160.
• Goodman, R.E. (1963). Subaudible noise during compression of rocks, Geol. Soc. Amer. Bull., 74, 487-490.
• Griggs, D.T., Turner, F.J. and Heard, H.C. (1960). Deformation of rocks at 500° to 800°C, in: Rock Deformation. Geol. Soc. A. Mem., 79, 39-104.
• Gross, D. (1982). Spannungsintensitaetsfaktoren von Risssystemen, Ing. Archiv, 51, 301-310.
• Gross, D. (1996). Bruchmechanik, Springer, Berlin-Heidelberg.
• Gross, D., Becker, W. and Basista, M. (1990). A simple mesostructural model for damage-induced inelasticity of brittle materials, in: Yielding, Damage, and Failure of Anisotropic Solids, J.P. Boehler (Ed.), Mechanical Eng. Publ., London, 681-692.
• Gueguen, Y. and Dienes, J. (1989). Transport properties of rocks from statistics and percolation, Math. Geol., 21, 1-13.
• Halm, D. and Dragon, A. (1998). Anisotropic model of damage and frictional sliding for brittle materials, Eur. J. Mechanics A/Solids, 17, 439-460.
• Halperin, B.I., Feng, S. and Sen, P.N. (1985). Differences between lattice and continuum percolation transport exponents, Phys. Rev. Lett., 54, 2391-2394.
• Hansen, A., Hinrichsen, E.L. and Roux, S. (1991). Scale-invariant disorder in fracture and related breakdown phenomena, Phys. Rev. B, 43, 665-678.
• Hansen, A., Roux, S. and Herrmann H.J. (1989). Rupture of central-force lattices, J. Physique, 50, 733-744.
• Hansen, W.C. (1968). The chemistry of sulphate-resisting portland cement, in: Performance of Concrete, E.G. Swenson (Ed.), University of Toronto Press, 18-55.
• Hayakawa, K. and Murakami, S. (1998). Space of damage conjugate force and damage potential of elastic-plastic-damage materials, in: Damage Mechanics in Engineering Materials, G.Z. Voyiadjis, J.W. Ju and J.L. Chaboche (Eds.), Elsevier Science, 27-44.
• Hemmer, P.C. and Hansen, A. (1992). The distribution of simultaneous fiber failures in fiber bundles, J. Appl. Mech., 59, 909-914.
• Herrmann H.J., Hansen, A. and Roux, S. and (1989). Fracture of disordered, elastic lattices in two dimensions, Phys. Rev. B, 39, 637-648.
• Herrmann, H. J. and Roux, S. (1990). Statistical Models for the Fracture of Disordered Media, North-Holland.
• Hill, R. and Rice, J.R. (1973). Elastic potentials and the structure of inelastic constitutive laws, SIAM J. Appl. Math., 25, 448-461.
• Holcomb, D.J. (1983). Using acoustic emissions to determine in-situ stress: problems and promise, in: Geomechanics - AMD, ASME Publ., S. Nemat-Nasser, ed., 57, 11, New York.
• Holcomb, D.J. and Costin, L.S. (1986). Detecting damage surfaces in brittle materials using acoustic emissions, J. Appl. Mech., 53, 536-544.
• Horii, H. and Nemat-Nasser, S. (1983). Overall moduli of solids with microcracks: load induced anisotropy, J. Mech. Phys. Solids, 31, 155-171.
• Horii, H. and Nemat-Nasser, S. (1985a). Compression-induced microcrack growth in brittle solids: axial splitting and shear failure, J. Geophys. Res., 90, 3105-3125.
• Horii, H. and Nemat-Nasser, S. (1985b). Elastic fields of interacting inhomogeneities, Int. J. Solids Structures, 21, 731-745
• Horii, H. and Nemat-Nasser, S. (1986). Brittle failure in compression: splitting, faulting and brittle-ductile transition, Phil. TYans. Roy. Soc. London, 319, 337-374.
• Ingraffea, A.R. (1987). Theory of crack initiation and propagation in rock, in: Fracture Mechanics of Rock, B.K. Atkinson (Ed.), Academic Press, London, 71—110.
• Irwin, G.R. (1957). Analysis of stresses and strains near the end of a crack traversing a plate, J. Appl. Mech., 24, 361-365.
• Jaeger, J.C. and Cook, N.G.W. (1976). Fundamentals of Rock Mechanics, Chapman and Hall, London.
• Janson, J. and Hult, J. (1977). Fracture mechanics and damage mechanics - a combined approach, J. Mec. Appl., 1, 69-84.
• Ju, J.W. (1991). On two-dimensional self-consistent micromechanical damage models for brittle solids, Int. J. Solids Structures, 27, 227-258.
• Ju, J.W. and Tseng, K.H. (1995). An improved two-dimensional micromechanical theory for brittle solids with randomly located interacting microcracks, Int. J. Damage Mech., 4, 23-57.
• Kachanov, L.M. (1958). On the time to rupture in creep conditions, Izv. AN SSSR, Otd. Tekhn Nauk, 8, 26-31.
• Kachanov, L.M. (1976). Introduction to Continuum Damage Mechanics, Nijhoff, Dordrecht.
• Kachanov, M. (1980). Continuum model of medium with cracks, J. Eng. Mech. Div. ASCE, 106, 1039-1051.
• Kachanov, M. (1982). A microcrack model of rock inelasticity, Part I: Frictional sliding on microcracks, Mech. Mater, 1, 19-27.
• Kachanov, M. (1987). Elastic solids with many cracks - a simple method of analysis, Int. J. Solids Structures, 23, 23-43.
• Kachanov, M. (1992). Effective elastic properties of cracked solids. Critical review of some basic concepts, Appl. Mech. Rev., 45, 304-335.
• Kachanov, M. (1993). Elastic solids with many cracks and related problems, in: Advances in Applied Mechanics, J. Hutchinson and T. Wu (Eds.), 30, 259-445, Academic Press, New York, NY.
• Kaiser, J. (1950). An investigation into the occurrence of noises in tensile tests or a study of acoustic phenomena in tensile tests, PhD thesis, Technische Hochschule Miinchen, Germany
• Kasperkiewicz, J. (1983). Modelling of inhomogeneity in certain cement-based composites, Int. J. Cement Composites and Lightweight Concrete, 5, 41-48.
• Kemeny, J.M. and Cook, N.G.W. (1991). Micromechanics of deformation in rocks, in: Toughening Mechanisms in Quasi-Brittle Materials, S. P. Shah, ed., Kluwer, 155-188.
• Kendall, K. (1978). Complexities of compression failure, Proc. R. Soc. London A. 361, 245-263.
• Kestin, J. (1992). Local equilibrium formalism applied to mechanics of solids, Int. J. Solids Structures, 29, 1827-1836.
• Kestin, J. and Bataille, J. (1978). Irreversible thermodynamics of continua and internal variables, in: Continuum Models of Discrete Systems, J.W. Provan (Ed.), Univ. of Waterloo Press, Waterloo, Canada.
• Kestin, J. and Rice, J.R. (1970). Paradoxes in the application of thermodynamics to strained solids, in: Critical Review of Thermodynamics, E. B. Stuart et al., eds., Mono Book Corp., Baltimore, 275-298.
• Knott, J.F. (1973). Fundamentals of Fracture Mechanics, Butterworth, London.
• Krajcinovic D. and Basista, M. (1991b). Rupture of central-force lattices revisited, J. Physique I, 1, 241-245.
• Krajcinovic D., Basista, M. and Sumarac D. (1991a). Micromechanically inspired phenomenological damage model, J. Appl. Mech., 58, 305-310.
• Krajcinovic D., Basista, M. and Sumarac D. (1991b). Micromechanics of brittle composites exposed to chemically aggressive ambients, in: Microcracking Induced Damage in Composites, G. Dvorak and C. Lagoudas (Eds.), ASME Publ., AMD-109, MD-22, New York, 101-112.
• Krajcinovic D., Basista, M. and Sumarac D. (1994). Basic principles of damage mechanics, in: Damage Mechanics of Composite Materials, R. Talreja (Ed.), Elsevier, 1-51.
• Krajcinovic D., Basista, M., Mallick K. and Sumarac D. (1992). Chemo-micromechanics of brittle solids, J. Mech. Phys. Solids, 40, 965-990.
• Krajcinovic D., Mallick K., Basista, M. and Sumarac D. (1992). Elastic moduli of perforated plates in the neighborhood of critical state, Int. J. Solids Structures, 29, 1837-1847.
• Krajcinovic, D. (1979). Distributed damage theory of beams in pure bending, J. Appl. Mech., 46, 592-596.
• Krajcinovic, D. (1984). Continuum damage mechanics, Appl. Mech. Rev., 37, 397-402.
• Krajcinovic, D. (1989). Damage mechanics, Mech. Mater., 8, 117-197.
• Krajcinovic, D. (1995). Continuum damage mechanics: when and how?, Int. J. Damage Mech., 4, 217-229.
• Krajcinovic, D. (1996). Damage Mechanics, Elsevier, Amsterdam.
• Krajcinovic, D. (2000). Damage mechanics: accomplishments, trends and needs, Int. J. Solids Structures, 37, 267-277.
• Krajcinovic, D. and Fanella, D. (1986). A micromechanical damage model for concrete, Eng. Fract. Mech., 25, 585-596.
• Krajcinovic, D. and Fonseka, G.V. (1981). The continuous damage theory of brittle materials. Parts I and II, J. Appl. Mech., 48, 809-824.
• Krajcinovic, D. and Mastilovic, S. (1995). Some fundamental issues of damage mechanics, Mech. Mater., 21, 217-230.
• Krajcinovic, D. and Silva, M. A. G. (1982). Statistical aspects of the continuous damage theory, Int. J. Solids Structures, 18, 551-562.
• Krajcinovic, D. and Sumarac, D. (1987). Micromechanics of damage processes, in: Continuum Damage Mechanics: Theory and Application, D. Krajcinovic and J. Lemaitre (Eds.), Springer, Vienna.
• Krajcinovic, D. and Sumarac, D. (1989). A mesomechanical model for brittle deformation processes, J. Appl. Mech., 56, 51-62.
• Krajcinovic, D. and Vujosevic, M. (1998). Strain localization - short to long correlation length transition. Int. J. Solids Structures, 35, 4147-4166.
• Krajcinovic, D., Lubarda, V. and Sumarac, D. (1993). Fundamental aspects of brittle cooperative phenomena - Effective continua models, Mech. Mater., 15, 99-115.
• Labuz, J.F. and Bridell, J.M. (1993). Reducing frictional constraint in compression testing through lubrication, Int. J. Rock Mech. Min. Sci.& Geomech. Abstr., 30, 451-455.
• Labuz, J.F. and Carvalho, F.C.S. (1998). Micromechanisms in failure of rocklike materials, Paper presented at the 32. Solid Mechanics Conference SolMec ’98, Zakopane, Poland.
• Lauterbach, B. (2001). Zur mikrorissinduzierten Schadigung sproder Materialien, PhD Thesis, Institute of Mechanics, Darmstadt University of Technology, Ger¬many.
• Lauterbach, B. and Gross, D. (1998). Crack growth in brittle solids under compression, Mech. Mater., 29, 81-92.
• Lauterbach, B. and Gross, D. (1999). Analysis of microcrack interaction in brittle solids, in: Fracture and Damage Mechanics, M.H. Aliabadi (Ed.), University of London, UK, 213-222.
• Lawn, B.R. and Wilshaw, T.R. (1975). Fracture of Brittle Solids, Cambridge University Press, Cambridge, UK.
• Lawn. B.R, Marshall, D.B (1998). Nonlinear stress-strain curves for solids containing closed cracks with friction, J. Mech. Phys. Solids, 46, 85-113.
• Lea, F.M. (1970). The Chemistry of Cement and Concrete. Edward Arnold, London.
• Lehner, F. and Kachanov, M. (1996). On modelling of “winged” cracks forming under compression, Int. J. Pract., 77, R69-R75.
• Lemaitre, J. (1996). A Course on Damage Mechanics, Springer, Berlin-Heidelberg.
• Lemaitre, J. and Chaboche, J.L. (1978). Aspect ph6nom6nologique de la rupture per endommagement, J. Mec. Appi. 2, 317-365.
• Lemaitre, J. and Chaboche, J.L. (1985). Mecanique des Materiaux Solides, Dunod, Paris.
• Lemieux, M.A., Bretton, P. and Tremblay, A.M.S. (1985). Unified approach to numerical transfer matrix methods for disordered systems: Application to mixed crystals and to elasticity percolation, J. Phys. Lett., 46, L1-L7.
• Leonhardt, F. And Walter, R. (1962). Beitrage zur Behandlung der Schubprobleme in Stahlbetonbau. Beton- und Stahlbetonbau (Berlin), March, 56-64, and June, 141-149.
• Lewiński, T. and Telega, J.J. (2000). Plates, Laminates and Shells. Asymptotic Analysis and Homogenization, Series on Advances in Mathematics for Applied Sciences, 52, World Scientific, Singapore.
• Litewka, A. (1985). Effective material constants for orthotropically damaged elastic solid, Arch. Mech., 37, 631-642.
• Litewka, A. and Hult, J. (1989). One parameter CDM model for creep rupture prediction, Eur. J. Mech., A/Solids, 8, 185-200.
• Lockner, D. (1993) The role of acoustic emission in the study of rock fracture, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 30, 883-899.
• Lubarda, V. and Krajcinovic, D. (1993). Damage tensors and the crack density distribution, Int. J. Solids Structures, 30, 2859-2877.
• Lubarda, V. and Krajcinovic, D. (1995). Constitutive structure of the rate theory of damage in brittle elastic solids, Appl. Math. Comp., 67, 81-101.
• Mai, Y.W. (1991). Failure characterisation of fibre-reinforced cement composites with R-curve characteristics, in: Toughening Mechanisms in Quasi-Brittle Materials, S.P. Shah (Ed.), Kluwer Publ., New York, 489-527.
• Mai, Y.W. and Cotterell, B. (1982). Slow crack growth and fracture instability in cement composites, Int. J. Cement Composites, 4, 33-37.
• Martin, J.B. (1975). Plasticity. Fundamentals and General Results. MIT Press, Cambridge, MA.
• Matczynski, M. and Sokolowski, M. (1982). Interaction of cracks in elastic media, Arch. Mech., 34, 89-104.
• Mather, B. (1968). Field and laboratory studies of the sulphate resistance of concrete, in: Performance of Concrete, E.G. Swenson (Ed.), University of Toronto Press, 66-76.
• Mauge, C. and Kachanov, M. (1994). Effective elastic properties of an anisotropic material with arbitrary oriented interacting cracks, J. Mech. Phys. Solids, 42, 561-584.
• Mchedlow-Petrosjan, O.P. (1988). The Chemistry of Inorganic Structural Materials, 2nd edition, Stroi-Izdat, Moscow.
• Mehta, P.K. (1983). Mechanism of sulphate attack on portland cement concrete - another look, Cem. Concr. Res., 13, 401-406.
• Meredith, P.G. (1989). Comparative fracture toughness testing of rocks, in: Fracture Toughness and Fracture Energy. Test Methods for Concrete and Rock. Tohoku Univ. Sendai, Japan, 211-223.
• Meredith, P.G., Ayling, M.R., Murrell, S.A.F. and Sammonds, P.R. (1991). Cracking, damage and fracture in stressed rock: a holistic approach, in: Toughening Mechanisms in Quasi-Drittle Materials, S.P. Shah (Ed.), Kluwer, The Netherlands, 67-89.
• Mindess, S. and Young, J.F. (1981). Concrete, Prentince Hall, Englewood Clifs, N.J.
• Mogi, K. (1962). Study of the elastic shocks caused by the fracture of a heterogeneous material and its relation to earthquake phenomena, Bull. Earthquake Res. Inst., 40, 125-173.
• Mogi, K. (1966). Pressure dependence of rock strength and transition form brittle to ductile flow, Bull. Earth. Res. Inst., 44, 215-232.
• Moss, W.C. and Gupta, Y.M. (1982). A constitutive model describing dilatancy and cracking in brittle rock, J. Geophys. Res., 87, 2985-2998.
• Moukwa, M. (1990). Characteristics of the attack of cement paste by MgSC>4 and MgCh from the pore structure measurements, Cem. Concr. Res., 20, 148-158.
• Mróz, Z. and Seweryn, A. (1999) Multiaxial damage and fatigue conditions, in: Modeling of Damage and Fracture Processes in Engineering Materials, M. Basista and W.K. Nowacki (Eds.), IPPT PAN, Warszawa, 117-180.
• Mura, T. (1987). Micromechanics of Defects in Solids, Martinus Nijhoff Publ., The Hague, The Netherlands.
• Murakami, S. (1988). Mechanical modelling of material damage, J. Appl. Mech., 55, 280-286.
• Murakami, S., Hayakawa, K. and Liu, Y. (1998). Damage evolution and damage surface of elastic-plastic-damage materials under multiaxial loading, Int. J. Damage Mech., 7, 103-128.
• Murakami, S. and Kamiya, K. (1997). Constitutive and damage evolution equations of elastic-brittle materials based on irreversible thermodynamics, Int. J. Solids Structures, 39, 473-486.
• Murakami, S. and Ohno, N. (1981). A continuum theory of creep and creep damage, in: Creep in Structures, A.R.S. Ponter and D.R. Hayhurst, (Eds.), 422-444, Springer Verlag, Berlin.
• Murakami, Y. (1987). Stress Intensity Factors Handbook, Pergamon Press, New York.
• Murzewski, J. (1957). Une theorie statistique du corps fragile quasi-homogene, IX-e Congres International de Mecanique Apliquee, Actes, V, 313-320, Univ. De Bruxelles.
• Murzewski, J. (1992). Brittle and ductile damage of stochastically homogeneous solids, Int. J. Damage Mech., 1, 276-289.
• Najar, J. (1987). Continuous damage of brittle solids, in: Continuum Damage Mechanics. Theory and Applications, D. Krajcinovic and J. Lemaitre (Eds.), Springer, Vienna, 233-294.
• Neimitz, A. (1999). Analysis of stable and unstable crack growth, in: Modeling of Damage and Fracture Processes in Engineering Materials, M. Basista and W.K. Nowacki (Eds.), IPPT PAN. Warszawa, 57-89.
• Nemat-Nasser, S. and Horii, H. (1982). Compression-induced nonplanar crack extension with application to splitting, exfoliation and rockburst, J. Geophys. Res. 87, 6805-6821.
• Nemat-Nasser, S. and Hori, M. (1993). Micromechanics: Overall Properties of Heterogeneous Materials, Elsevier, Amsterdam.
• Nemat-Nasser, S. and Hori, M. (1999). Micromechanics: Overall Properties of Heterogeneous Materials, Elsevier, Amsterdam, The Netherlands.
• Nemat-Nasser, S. and Obata, M. (1988). A microcrack model of dilatancy in brittle materials, J. Appl. Mech., 55, 24-35.
• Neville, A.M. (2000). Własciwosci Betonu, Wydanie IV, Polski Cement, Kraków.
• Obert, L. (1941). Use of subaudible noise for the prediction of rock bursts, Rep. RI 3555, US Bureau of Mines, Washington, DC.
• Odler, I. and Gasser, M. (1988). J. Am. Ceram. Soc., 71, 1015-1026.
• Ogawa, K. and Roy, D.M. (1981). C4A3S hydration, ettringite formation, and its expansion mechanism: I. Expansion; ettringite stability, Cem. Concr. Res., 11, 741-750.
• Ortiz, M. (1985). A constitutive theory for the inelastic behavior of concrete, Mech. Mater., 4, 67-93.
• Ostoja-Starzewski, M. (1994). Micromechanics as a basis of continuum random fields, Appl. Mech. Rev., 47, S221-S230.
• Ouyang, Ch., Mobasher, B. and Shah, S.P. (1990). An R-curve approach for fracture of quasi-brittle materials, Eng. Fract. Mech, 37, 901-913.
• Ouyang, C., Nanni, A. and Chang, W.F. (1988). Internal and external sources of sulphate ions in portland cement mortar: two types of chemical attack, Cem. Concr. Res., 18, 699-709.
• Peng, S. and Johnson, J.M. (1972). Crack growth and faulting in cylindrical specimens of Chelmsford granite. Int. J. Rock Mech. Min. Sci., 9, 37 86.
• Perzyna, P. (1986). Internal state variable description of dynamic fracture of ductile solids, Int. J. Solids Structures, 22, 797-818.
• Phoenix, S.L. and Taylor, H.M. (1973). The asymptotic strength distribution of a general fibre bundle, Adv. Appl. Prob., 5, 200-216.
• Pike, G.E. and Seager, C.H. (1974). Percolation and conductivity: A computer study, Phys. Rev. B, 10, 1421-1446.
• Plowman, C. and Cabrera, J.G. (1984). Mechanism and kinetics of hydration of C3A and C4AF extracted from cement, Cem. Concr. Res., 14, 238-248.
• Pommersheim, J. and Chang, J. (1988). Kinetics of hydration of tricalcium aluminate in the presence of gypsum, Cem. Concr. Res., 18, 911-922.
• Ponte-Castaiieda, P. and Suquet, P. (1998). Nonlinear composites, in: Advances in Applied Mechanics, 34, 171-302.
• Raniecki, B. (2001). Private communication.
• Rice, J R. (1968). Mathematical analysis in the mechanics of fracture, in: Fracture - An Advanced Treatise, H. Liebowitz (Ed.), II, 192-308.
• Rice, J.R. (1971). Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity, J. Mech. Phys. Solids, 19, 433-455.
• Rice, J.R. (1975). Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanisms, in: Constitutive Equations in Plas¬ticity, A.S. Argon (Ed.), The MIT Press, Cambridge, MA, 23-79.
• Rice, J.R. (1976). The localization of plastic deformation, in: Proceedings 14th IUTAM Congress, W.T. Koiter (Ed.), North-Holland Publ. Co., 207-220.
• Rice, J.R. (1978). Thermodynamics of the quasi-static growth of Griffith cracks, J. Mech. Phys. Solids, 26, 61-78.
• Rice, J.R. and Cleary, M.P. (1976). Some basic stress diffusion solutions for fluid saturated elastic porous medium with compressible constituents, Rev. Geophys. Space Phys., 14, 227-241.
• Robinson, P.C. (1984). Numerical calculations of critical densities for lines and planes, J. Phys. A, 17, 2823-2830.
• Rudnicki, J.W. and Rice, J.R. (1975). Conditions for the localization of deformation in pressure-sensitive dilatant materials, J. Mech. Phys. Solids, 23, 371-394.
• Sadowski, T. (1994). Modelling of semi-brittle MgO ceramic behaviour under compression, Mech. Mater., 18, 1-16.
• Sahimi, M. (1994). Applications of Percolation Theory, Taylor & Francis Publ. London, UK.
• Sahimi, M. and Goddard, J.D. (1986). Elastic percolation models for cohesive mechanical failure in heterogeneous systems, Phys. Rev. B, 33, 7848-7851.
• Salganik, R.L. (1974). Transport processes in bodies with a large number of cracks, Mech. Solids (Inzhenerno-Fizicheskii Zhurnal), 27, 1534-1538.
• Sammis, C.G. and Ashby, M.F. (1986). The failure of brittle porous solids under compressive stress states. Acta Metall., 34, 511-526.
• Sanchez-Palencia, E. (1981). Non-homogeneous media and Vibration Theory, Lecture Notes in Physics, No. 127, Springer, Berlin.
• Scher, H. and Zallen, R. (1970). Critical density in percolation processes, J. Chem. Phys., 53, 3759-3761.
• Schmidt, R.A. and Lutz, T.J. (1979). A'/c and J/c of Westerly granite - effects of thickness and in-lane dimensions, in: Fracture Mechanics Applied to Brittle Materials, ASTM Spec. Techn. Publ. STP 678, 166-182.
• Scholz, C.H. (1968). Microfracturing and the inelastic deformation of rock in compression, J. Geophys. Res., 73, 1417-1432.
• Scholz, C.H. and Kranz, R. (1974). Notes on dilatancy recovery, J. Geophys. Res., 79, 2132-2135.
• Scott, I.G. (1991). Basic acoustic emission, in: Nondestructive testing Monographs and Tracts, 6, 246 pages, Gordon and Breach, Newark, NJ.
• Seaman, L., Curran, D.R. and Shockey, D.A. (1976). Computational models for ductile and brittle fracture, J. Appl. Phys., 47, 4814-4826.
• Seweryn, A. and Mróz, Z. (1995). A non-local stress failure condition for structural elements under multiaxial loading, Eng. Fract. Mech., 51, 955-973.
• Shante, V.K.S. and Kirkpatrick, S. (1971). An introduction to percolation theory, Adv. Phys., 20, 325-357.
• Shockey, D.A., Curran, D.R., Seaman, L., Rosenberg, J.T. and Petersen, C.F. (1974). Fragmentation of rock under dynamic loads, Int. J. Rock Mech. Sci. & Geomech. Abstr., 11, 303-317.
• Sieradzki, K. and Li, R. (1986). Fracture behavior of a solid with random porosity, Phys. Rev. Lett., 56, 2509-2512
• Sih, G.C. (1973). Handbook of Stress Intensity Factors, Lehigh Univ.
• Skrzypek, J. and Ganczarski, A. (1999). Modeling of Material Damage and Failure of Structures, Springer, Berlin-Heidelberg.
• Skrzypek, J., Kuna-Ciskal, H. and Ganczarski, A. (1999). Continuum damage mechanics modeling of creep-damage and elastic-damage-fracture in materials and structures, in: Modeling of Damage and Fracture Processes in Engineering Materials, M. Basista and W.K. Nowacki (Eds.), IPPT PAN, Warszawa, 181-235.
• Sobczyk, K. and Spencer B.F. (1992). Random Fatigue. From Data to Theory, Academic Press, San Diego.
• Sornette, D. (1988). Critical transport and failure in continuum crack percolation, J. Phys. France, 49, 1365-1377.
• Sornette, D. (1989). Elasticity and failure of a set of elements loaded in parallel, J. Phys. A, 22, L243-L250.
• Sornette, D. (2000). Critical Phenomena in Natural Sciences, Springer, Heidelberg.
• Soroka, I. (1980). Portland Cement Paste and Concrete. Chemical, New York.
• Stauffer, D. (1985). Introduciton to Percolation Theory, Taylor & Francis, London, UK.
• Steif, P. S. (1984). Crack extension under compressive loading, Eng. Fract. Mech., 20, 463 473.
• Steinbrech, R.W., Dickerson, R.M. and Kleist, G. (1991). Characterisation of the fracture behavior of ceramics through analysis of crack propagation studies, in: Toughening Mechanisms in Quasi-Brittle Materials, S.P. Shah (Ed.), Kluwer Publ., New York, 353-375.
• Sumarac, D. (1987). Self-consistent model for the brittle response of solids, PhD Thesis, Civil Eng., Mechanics and Metallurgy Dept., University of Illinois at Chicago Circle, Chicago IL.
• Sumarac, D. and Krajcinovic, D. (1987). A self-consistent model for microcrack weakened solids, Mech. Mater., 6, 39-52.
• Swoboda, G. and Yang, Q. (1999). An energy-based damage model of geoinaterials -II. Deduction of damage evolution laws, Int. J. Solids Structures, 36, 1735-1755.
• Tada, H., Paris, P. and Irwin, G. (1985). The Stress Analysis of Cracks Handbook. Paris Productions Inc., St. Louis, MO.
• Talreja, R. (1985). A continuum mechanics characterization of damage in composite materials, Proc. Roy. Soc. London A 399, 195-216.
• Tapponier, P. and Brace, W.F. (1976). Development of stress-induced microcracks in Westerly granite, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 13, 103-112.
• Tonks, D.L. (1996). Disorder, percolation and wave propagation effects in ductile fracture, in: High-Pressure Shock Compression of Solids II, L. Davison, D.E. Grady and M. Shahinpoor (Eds.), Springer.
• Torelli, L. and Scheidegger, A.E. (1972). Three-dimensional branching-type models of flow through porous media, J. Hydrol., 15, 23-37.
• Vakulenko, A.A. and Kachanov, M. (1971). Continuum theory of cracked media, Izv. AN SSSR, Mckh. Tverdogo Tela, 4, 159 166.
• Vavakin, A.S. and Salganik, R.L. (1975). Effective characteristics of nonhomogeneous media and with isolated nonhomogeneities, Izv AN SSSR, Mekh. Tverdogo Tela, 10, 65-75.
• Wagner, Ch. and Gross, D. (1988). Untersuchungen zur Wechselwirkung zwischen Defekten und einem Einzelriss, DFG-Report, Gr 596/15-1, Institute of Mechanics, Darmstadt University of Technology.
• Walsh, J.B. (1965). The effect of cracks on uniaxial compression of rocks, J. Geophys. Res., 70, 399-411.
• Wang, P.T. (1977). Complete stress-strain curves of concrete and its effects on ductility of reinforced concrete members, PhD Thesis, University of Illinois at Chicago Circle.
• Wang, R. and Kemeny, J.M. (1993). Micromechanical modeling of tuffaceous rock for application in nuclear waste storage, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 30, 1351-1357.
• Weng, J.G., Taya, M. and Abe, H., Eds. (1990). Micromechanics and Inhomogeneity, Springer, New York.
• Wilke, S.E, Guyon, E. and de Maxsily, G. (1985). Water penetration through fractured rocks: test of three-dimensional percolation description, Math. Geol., 17, 17-27.
• Wiliam, K. and Iordache, M.-M. (1994). Fundamental aspects of failure modes in brittle solids, in: Fracture and Damage in Quasi-brittle Structures, E & FN Spon, London, 53-67.
• Woo, C.W. and Li, D.L. (1993). A universal physically consistent definition of material damage, Int. J. Solids Structures, 30, 2097-2108.
• Yazdani, S. and Schreyer, H.L. (1988). An anisotropic damage model with dilatation for concrete, Mech. Mater., 7, 231-244.
• Zaitsev, Yu. (1982). Modelling of Deformation and Strength Using Fracture Me¬chanics Methods (in Russian), Stroiizdat, Moscow.
• Zaitsev, Yu. (1985). Inelastic properties of solids with random cracks, in: Mechanics of Geomaterials, Z. Bazant (Ed.), Wiley.
• Zallen, R. (1983). The Physics of Amorphous Solids, J. Wiley & Sons, New York, NY.
• Zhang, A., Wagner, Ch.F., and Dresen, G. (1996). Acoustic emission, microstructure, and damage model of dry and wet sandstone stressed to failure, J. Geophys. Res., 101, 17507-17524.
• Zhao, Y., Huang, J., and Wang, R. (1993). Real-time SEM observations of the microfracturing process in rock during a compression test, Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 30, 643-652.
• Zoback, M.D. and Byerlee, J.D. (1975). The effect of cyclic differential stress on dilatancy in Westerly granite under uniaxial and triaxial conditions, J. Geophys. Res., 80, 1526-1530.