Peak Load Determination in Linear Fictitious Crack Model
Publication: Journal of Engineering Mechanics
Volume 120, Issue 2
Abstract
The linear fictitious crack model with linear softening law is a very important special case of the general fictitious crack model proposed by Hillerborg. When the traction‐separation softening curve is assumed linear, the peak load can be determined through the proposed linear eigenvalue problem formalism, referred to as the boundary eigenvalue problem. A detailed description is given of the finite element implementation of the proposed algorithm. It is shown that the first eigenvector can be used to calculate the peak load of the linear fictitious crack model. Furthermore, the first eigenvalue can be related to the critical nondimensional specimen size. Finally, it is elucidated that in the linear fictitious crack model, the peak‐load solutions can be presented in a nondimensional fashion with proper consideration of material properties and specimen sizes. The nondimensional peak‐load solution graphs can be used effectively for quantifying the size effect in the linear fictitious crack model.
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References
1.
Barenblatt, G. I. (1962). “The mathematical theory of equilibrium cracks in brittle fracture.” Adv. Appl. Mech., 7(1), 55–129.
2.
Bažant, Z. P. (1984). “Size effect in blunt fracture: Concrete, rock, metal.” J. Engrg. Mech., ASCE, 110(4), 518–535.
3.
Carpinteri, A. (1984). “Interpretation of the Griffith instability as a bifurcation of the global equilibrium.” Application of Fracture Mechanics to Cementitious Composites, S. P. Shah, ed., Northwestern Univ., Evanston, Ill., 267–316.
4.
Dugdale, D. S. (1960). “Yielding of steel sheets containing slits.” J. Mech. and Physics of Solids, 8(1), 100–104.
5.
Griffith, A. A. (1921). “The phenomenon of rupture and flow in solids.” Philosophical Trans. of Royal Society, A 221, 163–198.
6.
Hillerborg, A., Modeer, M., and Peterson, P. E. (1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.” Cement Concr. Res., 6(6), 773–782.
7.
Hillerborg, A. (1985). “Numerical methods to simulate softening and fracture of concrete. Fracture Mechanics of Concrete: Structural Application and Numerical Calculation, G. C. Sih and A. Di'Tommaso, eds., Martinus Nijhoff Publisher, Dordrecht, Netherlands, 141–170.
8.
Li, Y. N., and Liang, R. Y. (1992). “Stability theory of the cohesive crack model.” J. Engrg. Mech., ASCE, 118(3), 587–603.
9.
Li, Y. N., and Liang, R. Y. (1993). “The theory of boundary eigenvalue problem in the cohesive crack model and its application.” J. Mech. Phys. Solids, 41(2), 331–350.
10.
Liang, R. Y., and Li, Y. N. (1991). “Simulation of nonlinear fracture process zone in cementitious materials—A boundary element approach.” Computational Mech., 7, 413–427.
11.
Tada, H., Paris, P. C., and Irwin, G. R. (1973). Stress analysis of cracks handbook. Del Research Corp., Hellertown, Pa.
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Information
Published In
Journal of Engineering Mechanics
Volume 120 • Issue 2 • February 1994
Pages: 232 - 249
Copyright
Copyright © 1994 American Society of Civil Engineers.
History
Received: Jul 14, 1992
Published online: Feb 1, 1994
Published in print: Feb 1994
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