The present study focuses on the derivation of effective elastic properties for a two-dimensional elastic continuum containing several different distributions of rec tangular slits. The emphasis of the study is placed on the slit induced anisotropy and com parison of results derived using three different methods belonging to the class of mean field theories. Added is a short study of higher order theories incorporating direct interac tion of adjacent slits.
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References
1.
Aboudi, J. and Y. Benveniste, 1987. "The Effective Moduli of Cracked Bodies in Plane Deformation ," Eng. Fracture Mech., 26:171-184.
2.
Budiansky, B.1965 "On the Elastic Moduli of Some Heterogeneous Materials ," J. Mech. Phys. Solids, 13.223-227.
3.
Budiansky, B. and R.J. O'Connell1976. "Elastic Moduli of a Cracked Solid," Int. J. Solids Structures, 12:81-97.
4.
Chen, T.M. and J.W. Ju. In press. "On Two-Dimensional Statistical Micromechanical Damage Models for Brittle Solids with Interacting Microcracks. Part I: General Formulations."
5.
Chnstensen, R.M. and K.H. Lo.1979. "Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder Models," J. Mech. Phys. Solids, 27:315-330.
6.
Cleary, M.P., I.W. Chen and S.M. Lee.1980. "Self-Consistent Techniques for Heterogeneous Media," J. Eng. Mech. Div., ASCE, 106:861-887.
7.
Delameter, W.R., G. Herrmann and D.M. Barnett.1975. "Weakening of an Elastic Solid by a Rectangular Array of Cracks," J. Appl. Mech. , 42:74-80.
8.
Delameter, W.R., G. Herrmann and D.M. Barnett.1977. Erratum on "Weakening of an Elastic Solid by a Rectangular Array of Cracks," J. Appl. Mech., 44190-191.
9.
Dyskin, A.V.1985. "On the Calculation of the Effective Deformation Characteristics of a Material with Cracks," Izv AN SSSR, Mekhamka Tverdogo Tela, 20:130-135.
10.
Hashm, Z.1983. "Analysis of Composite Materials-A Survey," J. Appl. Mech. , 50:481-505.
11.
Hashm, Z.1988. "The Differential Scheme and Its Application to Cracked Materials," J. Mech. Phys. Solids, 36:719-734.
12.
Horn, H. and S. Nemat-Nasser1983. "Overall Moduli of Solids with Microcracks: Load Induced Anisotropy," J. Mech. Phys. Solids, 31;155-171.
13.
Horii, H. and K. Sahasakmontri .1990. "Mechanical Properties of Cracked Solids. Validity of the Self-Consistent Method," in Micromechanics and Inhomogeneity-The Toshio Mura Anniversary Volume, G. J Weng et al., eds New York, NY. Springer-Verlag, pp 137-159.
14.
Ju, J.W. and T.M. Chen In press. "On Two-Dimensional Statistical Micromechanical Damage Models for Brittle Solids with Interacting Microcracks. Part II: Process Models."
15.
Kachanov, M.1987. "Elastic Solids with Many Cracks: A Simple Method of Analysis ," Int. J. Solids Struct. , 23:23-43.
16.
Krajcinovic, D.1989 "Damage Mechanics," Mech of Materials, 8:117-197.
17.
Krajcinovic, D. and D. Fanella.1986. "A Micromechanical Damage Model for Concrete," Eng. Fract. Mech. , 25:585-596.
18.
Krajcinovic, D. and D. Sumarac.1989. "A Mesomechamcal Model for Brittle Deformation Processes: Part I," J. Appl. Mech. , 56:51-56.
19.
Kreher, W. and W. Pompe.1989Internal Stresses in Heterogeneous SolidsBerlin: Akademie Verlag.
20.
Kunin, I.A. , 1983. Elastic Media with Microstructure II; Three-Dimensional Models. Berlin: Springer Verlag .
21.
Laws, N. and J.R. Brockenbrough .1987. "The Effect of Micro-Crack Systems on the Loss of Stiffness of Brittle Solids," Int. J. Solids Structures, 231247-1268.
22.
Laws, N. and G.J. Dvorak.1987. "The Effect of Fiber Breaks and Aligned Penny-Shaped Cracks on the Stiffness and Energy Release Rates in Unidirectional Composites," Int. J. Solids Structures, 23:1269-1283
23.
Lekhnitskii, S.G.1981. Theory of Elasticity of an Anisotropic Body. MoscowMir Publ.
24.
Ma, S.K.1976Modern Theory of Critical PhenomenaReading, PA: W. A. Benjamin, Inc Publ
25.
Mura, T.1982. Micromechanics of Defects in Solids. The Hague, Netherlands: M. Nijhoff.
26.
Murakami, Y., 1987. Stress Intensity Factors Handbook. New YorkPergamon Press.
27.
Norris, A.N.1985. "A Differential Scheme for the Effective Moduli of Composites ," Mech. Mater., 4:1-16.
28.
Nemat-Nasser, S. and M. Hori.1990. "Elastic Solids with Microdefects," in Micromechanics and Inhomogeneity-The Toshio Mura Anniversary Volume , G. J Weng et al., eds., New York, NY. Springer-Verlag, pp. 297-320.
29.
Rice, J.R.1975. "Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanisms," in Constitutive Equations in Plasticity, A. S. Argon, ed., Cambridge, MA: MIT Press, pp. 23-79.
30.
Salganik, R.L.1973. "Mechanics of Bodies with Many Cracks," Izv AN SSSR, Mekh. Tverdogo Tela, 8:149-158.
31.
Shermergor, T.D.1977. Theory of Elastic Inhomogeneous Media. Moscow: Nauka Publ.
32.
Sih, G.C., P.C. Paris and G.R. Irwin.1965. "On Cracks in Rectilinearly Anisotropic Bodies," Int. J. Fracture Mech. , 1:189-203.
33.
Sumarac, D. and D. Krajcinovic.1987. "A Self-Consistent Model for Microcrack Weakened Solids," Mech. Mater. , 6: 39-52.
34.
Sumarac, D. and D. Krajcinovic.1989. "A Mesomechanical Model for Brittle Deformation Processes: Part II;' J. Appl. Mech. , 56:57-69.
35.
Vavakin, A.S. and R.L. Salganik.1975. "Effective Characteristics of Nonhomogeneous Media with Isolated Nonhomogeneities," Izv. AN SSSR,Mekh. Tverdogo Tela, 10.65-75.