Browse > Article
http://dx.doi.org/10.12989/cac.2017.19.5.501

Theoretical formulation of double scalar damage variables  

Xue, Xinhua (State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resource and Hydropower, Sichuan University)
Zhang, Wohua (College of Civil Engineering and Architecture, Zhejiang University)
Publication Information
Computers and Concrete / v.19, no.5, 2017 , pp. 501-507 More about this Journal
Abstract
The predictive utility of a damage model depends heavily on its particular choice of a damage variable, which serves as a macroscopic approximation in describing the underlying micromechanical processes of microdefects. In the case of spatially perfectly randomly distributed microcracks or microvoids in all directions, isotropic damage model is an appropriate choice, and scalar damage variables were widely used for isotropic or one-dimensional phenomenological damage models. The simplicity of a scalar damage representation is indeed very attractive. However, a scalar damage model is of somewhat limited use in practice. In order to entirely characterize the isotropic damage behaviors of damaged materials in multidimensional space, a system theory of isotropic double scalar damage variables, including the expressions of specific damage energy release rate, the coupled constitutive equations corresponding to damage, the conditions of admissibility for two scalar damage effective tensors within the framework of the thermodynamics of irreversible processes, was provided and analyzed in this study. Compared with the former studies, the theoretical formulations of double scalar damage variables in this study are given in the form of matrix, which has many features such as simpleness, directness, convenience and programmable characteristics. It is worth mentioning that the above-mentioned theoretical formulations are only logically reasonable. Owing to the limitations of time, conditions, funds, etc. they should be subject to multifaceted experiments before their innovative significance can be fully verified. The current level of research can be regarded as an exploratory attempt in this field.
Keywords
double scalar damage variables; damage energy release rate; isotropic; irreversible thermodynamics; theoretical analysis;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Alexandrov, S. and Jeng, Y.R. (2011), "Damage evolution in an expanding/contracting hollow sphere at large strains", Contin. Mech. Thermodyn., 23(6), 573-580.   DOI
2 Alexander, M., Tomas, R. and Marita, T. (2012), "From damage to delamination in nonlinearly elastic materials at small strains", J. Elast., 109(2), 235-273.   DOI
3 Cauvin, A. and Testa, R. (1999), "Damage mechanics: Basic variables in continuum theories", J. Sol. Struct., 36(5), 747-761.   DOI
4 Chow, C.L. and Wei, Y. (1999), "Constitutive modeling of material damage for fatigue failure prediction", J. Damage Mech., 8(4), 355-375.   DOI
5 D'Annibale, F. and Luongo, A. (2013), "A damage constitutive model for sliding friction coupled to wear", Contin. Mech. Thermodyn., 25(2-4), 503-522.   DOI
6 Fan, X.Q., Hu, S.W. and Lu, J. (2016), "Damage and fracture processes of concrete using acoustic emission arameters", Comput. Concrete, 18(2), 267-278.   DOI
7 Jaric, J., Kuzmanovic, D. and Numarac, D. (2012), "On anisotropic elasticity damage mechanics", J. Damage Mech., 22(7), 1023-1038.
8 Ju, J.W. (1990), "Isotropic and anisotropic damage variables in continuum damage mechanics", J. Eng. Mech., 116(12), 2764-2770.   DOI
9 Kachanov, L.M. (1958), "Time of the rupture process under creep conditions", Izv. Akad. Nauk, USSR, 8, 26-31.
10 Lemaitre, J. (1984), "How to use damage mechanics", Nucl. Eng. Des., 80(2), 233-245.   DOI
11 Lemaitre, J. (1985), "A continuous damage mechanics model for ductile fracture", J. Eng. Mater.-T ASME., 107(1), 83-89.   DOI
12 Li, R. and Li, X. (2010), "A coupled chemo-elastoplastic-damage constitutive model for plain concrete subjected to high temperature", J. Damage Mech., 19(8), 971-1000.   DOI
13 Mao, Y.Q., Fu, Y.M. and Tian, Y.P. (2012), "Nonlinear dynamic response and active control of piezoelastic laminated shallow spherical shells with damage", J. Damage Mech., 21(6), 783-809.   DOI
14 Mitsuru, O., Takuya, F., and Fumiyoshi, M. (2010), "Damage model for predicting the effect of steel properties on ductile crack growth resistance", J. Damage Mech., 19(4), 441-459.   DOI
15 Misra, A. and Singh, V. (2013), "Micromechanical model for viscoelastic materials undergoing damage", Contin. Mech. Thermodyn., 25, 343-358.   DOI
16 Ohata, M. and Toyoda, M. (2006), "Damage mechanism for controlling ductile cracking of structural steel with heterogeneous microstructure", Mater. Sci. For., 512, 31-36.
17 Pham, K. and Marigo, J.J. (2013), "From the onset of damage to rupture: Construction", Contin. Mech. Thermodyn., 25, 147-171.   DOI
18 Rabotnov, I.N. (1963), On the Equations of State for Creep, Progress in Applied Mechanics-the Prager Anniversary Volume, Macmillan, New York, U.S.A.
19 Rinaldi, A. (2013), "Bottom-up modeling of damage in heterogeneous quasi-brittle solids", Contin. Mech. Thermodyn., 25, 359-373.   DOI
20 Tan, K.T. and Watanabe, N. (2012), "Impact damage resistance, response, and mechanisms of laminated composites reinforced by through-thickness stitching", J. Damage Mech., 21(1), 51-80.   DOI
21 Voyiadjis, G.A., Taqieddin, Z.N. and Kattan, P.I. (2009), "Theoretical formulation of a coupled elastic-plastic anisotropic damage model for concrete using the strain energy equivalence concept", J. Damage Mech., 18(7), 603-638.   DOI
22 Thakkar, B.K. and Panley, P.C.A. (2007), "Isotropic continuum damage evolution model", J. Damage Mech., 16, 403-426.   DOI
23 Tang, C.Y., Shen, W., Peng, L.H. and Lee, T.C. (2002), "Characterization of isotropic damage using double scalar variables", J. Damage Mech., 11(1), 3-25.   DOI
24 Umit, C., Voyiadjis, G.Z. and Rashid, K.A.A.R. (2007), "A plasticity and anisotropic damage model for plain concrete", J. Plastic., 23(10), 1874-1900.   DOI
25 Voyiadjis, G.A., Taqieddin, Z.A. and Kattan, P.I. (2008), "Anisotropic damage-plasticity model for concrete", J. Plastic., 24(10), 1946-1965.   DOI
26 Voyiadjis, G.A. and Kattan, P.I. (2009), "A comparative study of damage variables in continuum damage echanics", J. Damage Mech., 18(4), 315-340.   DOI
27 Selvadurai, A.P.S. (2004), "Stationary damage modeling of poroelastic contact", J. Sol. Struct., 41(8), 2043-2064.   DOI
28 Wang, S.S., Ren, Q.W. and Qiao, P.Z. (2006), "Structural damage detection using local damage factor", J. Vibr. Control, 12(9), 955-973.   DOI
29 Xue, X.H. (2008), "Non-linear damage mechanics theory of coupled fluid-solid with numerical analysis of geo-materials", Ph.D. Dissertation, Zhejiang University, Hangzhou, China.
30 Xue, X.H., Yang, X.G., Zhang, W.H. and Dai, F. (2014), "A soil damage model expressed by a double scalar and its applications", Acta Mech., 225(9), 2667-2683.   DOI
31 Zhang, W.H. and Cai, Y.Q. (2010), Continuum Damage Mechanics and Numerical Applications, Zhejiang University Press, Hangzhou, China.
32 Xiong, C.S., Jiang, L.H., Zhang, Y. and Chu, H.Q. (2015), "Modeling of damage in cement paste subjected to external sulfate attack", Comput. Concrete, 16(6), 865-880.   DOI
33 Zhou, W.Y., Zhao, J.D., Liu, Y.G. and Yang, Q. (2002), "Simulation of localization failure with strain-gradientenhanced damage mechanics", J. Numer. Anal. Meth. Geomech., 26(8), 793-813.   DOI