Stochastic Damage Model for Brittle Materials Subjected to Monotonic Loading
Publication: Journal of Engineering Mechanics
Volume 122, Issue 8
Abstract
A one-dimensional stochastic micromechanical model is developed for brittle materials subjected to monotonic uniaxial loading. The material is represented by a set of brittle linear-elastic springs of equal stiffness that are joined in parallel. The failure strengths of the springs are modeled as either a discrete or a continuous correlated random field. The statistics of the random force-displacement and damage-displacement functions are analytically derived for the structural element. The stochastic model is shown to be capable of representing the experimentally observed scatter in the structural response. To demonstrate the validity of the model, comparisons are made with experimental data for uniaxial compressive tests on concrete specimens. The present model is shown to offer a viable alternative to empirical methods proposed in the literature for exploring the statistical behavior of brittle materials.
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References
1.
Bazant, Z. P., and Panula, L.(1977). “Statistical stability effects in concrete failure.”J. Engrg. Mech. Div., ASCE, 104(10), 1195–1212.
2.
Burt, N. J., and Dougill, J. W.(1977). “Progressive failure in a model heterogeneous medium.”J. Engrg. Mech. Div., ASCE, 103(6), 365–376.
3.
Carreira, D. J., and Chu, K.-H.(1985). “Stress-strain relationship for plain concrete in compression.”ACI J., 82, 797–804.
4.
Daniels, H. E. (1945). “The statistical theory of the strength of bundles of threads I.”Proc., Royal Soc., London, England, Vol. 183, Ser. A, 405–435.
5.
Desayi, P.(1968). “A model to simulate the strength and deformation of concrete in compression.”Materiaux et Constructions, 1(1), 49–56.
6.
Desayi, P., and Sen, B. R.(1966). “An investigation into the prediction of creep and true ultimate strength of concrete—I.”Indian Concrete J., Thane, India, 40(4), 134–141.
7.
Dougill, J. W.(1967). “A mathematical model for the failure of cement paste and mortars.”Mag. of Concrete Res., 19(60), 135–142.
8.
Dougill, J. W.(1971). “Further consideration of a mathematical model for progressive fracture of a heterogeneous material.”Mag. of Concrete Res., 23(74), 5–10.
9.
Elfgren, L. (ed.). (1989). Fracture mechanics of concrete structures: from theory to applications. Rep., Chapman and Hall, New York, N.Y.
10.
Hohenbichler, M. (1983). “Resistance of large brittle parallel systems.”Proc., 4th Int. Conf. on Applications of Statistics and Probability in Soil and Struct. Engrg., Pitagora, Bologna, Italy, 1301–1311.
11.
Hohenbichler, M., and Rackwitz, R.(1981). “On structural reliability of parallel systems.”Reliability Engrg., 2, 1–6.
12.
Hohenbichler, M., and Rackwitz, R.(1983). “Reliability of parallel systems under imposed uniform strain.”J. Engrg. Mech., ASCE, 109(3), 896–907.
13.
Krajcinovic, D., and Silva, M. A. G.(1982). “Statistical aspects of the continuous damage theory.”Int. J. Solids and Struct., 18(7), 557–562.
14.
Phoenix, S. L., and Taylor, H. M.(1973). “The asymptotic strength distribution of a general fibre bundle.”Advances in Appl. Probability, 5, 200–216.
15.
Suh, M. W., Bhattacharya, B. B., and Grandage, A.(1970). “On the distribution and moments of the strength of a bundle of F fibers.”J. Appl. Probability, 7, 712–720.
16.
Wang, P. T., Shah, S. P., and Naaman, A. E. (1978). “Stress-strain curves of normal and light-weight concrete in compression.”ACI J., 75(Nov.), 603–611.
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Copyright © 1996 American Society of Civil Engineers.
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Published online: Aug 1, 1996
Published in print: Aug 1996
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