On deformation and failure of brittle solids: Some outstanding issues

Abstract Certain fundamental issues concerning the experimental basis for current phenomenological constitutive models of rock and concrete are discussed. Problems related to both quasi-static and dynamic response are treated. Within the first category are included the topics of strain softening, strain hardening, failure states, and failure modes below the brittle-ductile transition. The second category focuses upon the task of determining the strain rate-dependent of material properties. In addition to the above, a class of theoretical modeling problems is discussed. Emphasis here is placed on the application of homogenization techniques in conjunction with micromechanics to develop nonphenomenological models of rock and concrete. An example application of this methodology to reinforced concrete is presented in an effort to demonstrate the superior modeling capabilities that can evolve from such an approach.

[1]  Zdenek P. Bazant,et al.  ENDOCHRONIC THEORY OF INELASTICITY AND FAILURE OF CONCRETE , 1976 .

[2]  Kiyoo Mogi,et al.  Fracture and flow of rocks under high triaxial compression , 1971 .

[3]  Poul V. Lade,et al.  Modelling rock strength in three dimensions , 1984 .

[4]  Kurt H. Gerstle,et al.  Behavior of Concrete Under Biaxial Stresses , 1969 .

[5]  L. Morland Continuum model of regularly jointed mediums , 1974 .

[6]  W. R. Wawersik,et al.  Post-failure behavior of a granite and diabase , 1971 .

[7]  W. S. Brown,et al.  An observation of loading path independence of fracture in rock , 1971 .

[8]  A. J. Watson,et al.  Compressive strength and ultimate strain of concrete under impact loading , 1978 .

[9]  Wai-Fah Chen,et al.  CONSTITUTIVE RELATIONS FOR CONCRETE , 1975 .

[10]  James Chinn,et al.  BEHAVIOR OF PLAIN CONCRETE UNDER VARIOUS HIGH TRIAXIAL COMPRESSION LOADING CONDITIONS. , 1965 .

[11]  M. Coon,et al.  Incremental constitutive laws and their associated failure criteria with application to plain concrete , 1972 .

[12]  L. Cedolin,et al.  Triaxial Stress-Strain Relationship for Concrete , 1977 .

[13]  Zdeněk P. Bažant,et al.  Hysteretic Fracturing Endochronic Theory for Concrete , 1980 .

[14]  Poul V. Lade,et al.  Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces , 1977 .

[15]  Michael N. Fardis,et al.  Monotonic and Cyclic Constitutive Law for Concrete , 1983 .

[16]  F. E. Richart,et al.  A study of the failure of concrete under combined compressive stresses , 1928 .

[17]  R. M. Zimmerman,et al.  Compressive Strength of Plain Concrete Under Multiaxial Loading Conditions , 1970 .

[18]  B. P. Hughes,et al.  CONCRETE SUBJECTED TO HIGH RATES OF LOADING IN COMPRESSION , 1972 .

[19]  S. J. Green,et al.  Uniaxial stress behavior of porphyritic tonalite at strain rates to 103/second , 1970 .

[20]  Lynn Seaman,et al.  Lagrangian analysis for multiple stress or velocity gages in attenuating waves , 1974 .

[21]  Leonard R. Herrmann,et al.  A Bounding Surface Plasticity Model for Concrete , 1985 .

[22]  Surendra P. Shah,et al.  STRAIN-RATE DEPENDENT DAMAGE MODEL FOR CONCRETE. , 1983 .

[23]  Kiyoo Mogi,et al.  Effect of the intermediate principal stress on rock failure , 1967 .

[24]  H. Furr,et al.  STRENGTH AND ENERGY ABSORPTION CAPABILITIES OF PLAIN CONCRETE UNDER DYNAMIC AND STATIC LOADINGS , 1967 .

[25]  Kurt H. Gerstle,et al.  Strength of Concrete under Multiaxial Stress States , 1978 .

[26]  K. C. Valanis,et al.  On the Uniqueness of Solution of the Initial Value Problem in Softening Materials , 1985 .

[27]  C. Young,et al.  Lateral Inertia Effects On Rock Failure In Split-Hopkinson-Bar Experiments , 1979 .

[28]  Y. Gupta,et al.  Local response of reinforced concrete to missile impacts , 1978 .

[29]  W. Janach The role of bulking in brittle failure of rocks under rapid compression , 1976 .

[30]  Arthur H. Nilson,et al.  Stress-Strain Response and Fracture of Concrete in Uniaxial and Biaxial Compression , 1972 .

[31]  Sia Nemat-Nasser,et al.  Compression‐induced microcrack growth in brittle solids: Axial splitting and shear failure , 1985 .

[32]  Z. Bažant,et al.  Plastic-Fracturing Theory for Concrete , 1979 .

[33]  Uriel Frisch,et al.  WAVE PROPAGATION IN RANDOM MEDIA. , 1970 .

[34]  Michael Ortiz,et al.  A constitutive theory for the inelastic behavior of concrete , 1985 .

[35]  James D. Byerlee,et al.  Frictional characteristics of granite under high confining pressure , 1967 .

[36]  G. A. Hegemier,et al.  Strain softening of rock, soil and concrete — a review article , 1984 .

[37]  R. M. Zimmerman,et al.  Behavior of concrete under multiaxial stress states , 1980 .

[38]  R. F. Williams,et al.  Determination of Constitutive Relationships with Multiple Gauges in Nondivergent Waves , 1971 .

[39]  Zdeněk P. Bažant,et al.  Endochronic model for nonlinear triaxial behavior of concrete , 1978 .

[40]  Ted Belytschko,et al.  Continuum Theory for Strain‐Softening , 1984 .

[41]  F. Rummel,et al.  Effect of confining pressure on the fracture behaviour of a porous rock , 1980 .

[42]  K. C. Valanis,et al.  An endochronic plasticity theory for concrete , 1986 .

[43]  A unified view of bulk property theories for stochastic and periodic media , 1981 .

[44]  Dan E. Branson,et al.  DESIGN PROCEDURES FOR COMPUTING DEFLECTIONS , 1968 .

[45]  P S Rao,et al.  TRISEGMENTAL MOMENT-CURVATURE RELATIONS FOR REINFORCED CONCRETE MEMBERS , 1973 .

[46]  Egor P. Popov,et al.  Plain concrete as a composite material , 1982 .

[47]  L A Clark,et al.  TENSION STIFFENING IN REINFORCED CONCRETE BEAMS AND SLABS UNDER SHORT-TERM LOAD , 1978 .

[48]  J. Handin,et al.  Chapter 13: Observations on Fracture and a Hypothesis of Earthquakes , 1960 .

[49]  D. Watstein Effect of Straining Rate on the Compressive Strength and Elastic Properties of Concrete , 1953 .

[50]  J. C. Jaeger,et al.  Fundamentals of rock mechanics , 1969 .

[51]  Poul V. Lade,et al.  Three-Parameter Failure Criterion for Concrete , 1982 .