An Improved Method to Calculate the Direction and Weight in Microplane Constitutive Model

Abstract:

This paper analyzes the calculation method on microplane direction and weight in current literature based on introducing numerical discretization algorithm in the microplane model. The characteristics and disadvantages of current methods are given out. In response to the issue that the orientation of microplane is not enough uniform and the shape and physical meaning of microplane is not clear, it is given out a kind of method that carrying out projection on the spherical surface after dividing the surface grid of regular polyhedron to calculate the orientation of microplane, then using the knowledge of spherical geometry to calculate the weight of microplane. Comparing and selecting the dividing scheme of microplane that obtained by different regular polyhedron and the grid levels, the optimization objective of fitting macroscopic elastic stiffness matrix is given out. The calculation results indicate that the method provided in this paper can obtain the dividing scheme that the shape and size of microplane are fully uniform, and the calculation result is more accurate than the optimal solution in the literature.

• Periodical: Applied Mechanics and Materials (Volume 238)
• Pages: 121-128
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.238.121
• Online since: November 2012
• Authors: Ming Xiao Jia, Shu Shan Li, Wei Xie
• Keywords: Microplane Constitutive Model, Numerical Discrete, Orientation, Spherical Geometry, Weight

References

[1] Z.P. Bažant, B.H. Oh, Microplane model for fracture analysis of concrete structures. Proc., Symp. On the Interactions of Non-Nuclear Munitions with Structure. U.S. Air Force Academy, Colorado Springs, Colorado, 1 (1983) 49-53.

[2] Z.P. Bažant, B.H. Oh, Microplane model for progressive fracture of concrete and rock. Journal of Engineering Mechanics, 114 (1985) 559-582.

DOI: 10.1061/(asce)0733-9399(1985)111:4(559)

[3] Z.P. Bažant, P.C. Prat, Microplane model for brittle plastic material: I. Theory, Journal of Engineering Mechanics, 114 (1988) 1672-1688.

DOI: 10.1061/(asce)0733-9399(1988)114:10(1672)

[4] Z.P. Bažant, P.C. Prat, Microplane model for brittle plastic material: II. Verification, Journal of Engineering Mechanics, 114 (1988) 1689-1702.

DOI: 10.1061/(asce)0733-9399(1988)114:10(1689)

[5] Z.P. Bažant, Y. Xiang, P.C. Prat, Microplane model for concrete. I. Stress-strain boundaries and finite strain, Journal of Engineering Mechanics, 122 (1996) 245-254.

DOI: 10.1061/(asce)0733-9399(1996)122:3(245)

[6] Z.P. Bažant, M.D. Fellow, ASCE, C.C. Ferhun, et al, Microplane model M4 for concrete: I. Formulation with work-conjugate deviatoric stress, Journal of Engineering Mechanics, 126 (2000) 944-953.

DOI: 10.1061/(asce)0733-9399(2000)126:9(944)

[7] Z.P. Bažant, C.C. Ferhun, Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity I: Theory, Journal of Engineering Mechanics, 131 (2005) 31-40.

DOI: 10.1061/(asce)0733-9399(2005)131:1(31)

[8] Z.P. Bažant, C.C. Ferhun, Microplane Model M5 with Kinematic and Static Constraints for Concrete Fracture and Anelasticity II: Computation, Journal of Engineering Mechanics, 131 (2005) 41-47.

DOI: 10.1061/(asce)0733-9399(2005)131:1(41)

[9] I. Carol, P.C. Prat, Z.P. Bažant, New explicit microplane model for concrete: Theoretical aspects and numerical implementation, International Journal of Solids and Structures, 29 (1992) 1173-1191.

DOI: 10.1016/0020-7683(92)90141-f

[10] W. Xiang, Basic Geometry, People's Education Press, Beijing, 2004.