Damage-induced anisotropy of quasi-brittle materials is investigated using component assembling model in this study. Damage-induced anisotropy is one significant character of quasi-brittle materials coupled with nonlinearity and strain softening. Formulation of such complicated phenomena is a difficult problem till now. The present model is based on the component assembling concept, where constitutive equations of materials are formed by means of assembling two kinds of components' response functions. These two kinds of components, orientational and volumetric ones, are abstracted based on pair-functional potentials and the Cauchy—Born rule. Moreover, macroscopic damage of quasi-brittle materials can be reflected by stiffness changing of orientational components, which represent grouped atomic bonds along discrete directions. Simultaneously, anisotropic characters are captured by the naturally directional property of the orientational component. Initial damage surface in the axial-shear stress space is calculated and analyzed. Furthermore, the anisotropic quasi-brittle damage behaviors of concrete under uniaxial, proportional, and nonproportional combined loading are analyzed to elucidate the utility and limitations of the present damage model. The numerical results show good agreement with the experimental data and predicted results of the classical anisotropic damage models.
Basista, M. (2003). Micromechanics of Damage in Brittle Solids, Anisotropic Behaviour of Damaged Materials, pp. 221-258, Berlin: Springer.
2.
Bazănt, Z.P. and Planas, J. (1998). Fracture and Size Effect in Concrete and Other Quasibrittle Materials, CRC Press, Boca Raton.
3.
Chaboche, J.L. (1993). Development of Continuum Damage Mechanics for Elastic Solids Sustaining Anisotropic and Unilateral Damage, International Journal of Damage Mechanics, 2(4): 311-329.
4.
Chaboche, J.L., Lesne, P.M. and Maire, J.F. (1995). Continuum Damage Mechanics, Anisotropy and Damage Deactivation for Brittle Materials like Concrete and Ceramic Composites, International Journal of Damage Mechanics, 4(1): 5-22.
5.
Chow, C.L. and Wang, J. (1987). An Anisotropic Theory of Continuum Damage Mechanics for Ductile Fracture, Engineering Fracture Mechanics, 27(5): 547-558.
6.
Deng, S.C., Liu, J.X., Zhang, J. and Liang, N.G. (2006). Component Assembling Model and its Application to Quasi-brittle Damage, Theoretical and Applied Fracture Mechanics, 46(3): 232-242.
7.
Dragon, A. (2002). Continuum Damage Mechanics Applied to Quasi-brittle Materials, Continuum Damage Mechanics of Materials and Structures, pp. 165-202, Amsterdam: Elsevier.
8.
Dragon, A., Halm, D. and Desoyer, T. (2000). Anisotropic Damage in Quasi-brittle Solids: Modeling, Computational Issues and Applications, Computer Methods in Applied Mechanics and Engineering, 183(3/4): 331-352.
9.
Feng, X.Q., Qin, Q.H. and Yu, S.W. (2004). Quasi-micromechanical Damage Model for Brittle Solids with Interacting Microcracks, Mechanics of Materials , 36(3): 261-273.
10.
Gao, H.J. and Klein, P. (1998). Numerical Simulation of Crack Growth in an Isotropic Solid with Randomized Internal Cohesive Bonds, Journal of Mechanics and Physics of Solids, 46(2): 187-218.
11.
Gopalaratnam, V.S. and Shah, S.P. (1985). Softening Response of Plain Concrete in Direct Tension, ACI Journal, 82(3): 310-323.
12.
Halm, D. and Dragon, A. (1998). An Anisotropic Model of Damage and Frictional Sliding for Brittle Materials, European Journal of Mechanics - A/Solids, 17(3): 439-460.
13.
Horii, H. and Nemat-Nasser, S. (1983). Overall Moduli of Solids with Microcracks: Load-induced Anisotropy, Journal of the Mechanics and Physics of Solids, 31(2): 155-171.
14.
Kachanov, M. (1992). Effective Elastic Properties of Cracked Solids: Critical Review of Some Basic Concepts, Applied Mechanics Reviews, 45(8): 304-335.
15.
Krajcinovic, D. (1989). Damage Mechanics, Mechanics of Materials, 8(2/3): 117-197.
16.
Krajcinovic, D. (1998). Selection of Damage Parameter-Art or Science? Mechanics of Materials, 28(1/4): 165-179.
17.
Krajcinovic, D. (2000). Damage Mechanics: Accomplishments, Trends and Needs, International Journal of Solids and Structures, 37(1/2): 267-277.
18.
Krajcinovic, D. (2002). Essential Damage Mechanics-bridging the Scales, Continuum Damage Mechanics of Materials and Structures, pp. 17-47, Amsterdam : Elsevier.
19.
Krajcinovic, D. and Fonseka, G.U. (1981). The Continuous Damage Theory of Brittle Materials Part 1: General Theory, Journal of Applied Mechanics, 48(4): 809-815.
20.
Krajcinovic, D. and Mastilovic, S. (1995). Some Fundamental Issues of Damage Mechanics, Mechanics of Materials, 21(3): 217-230.
21.
Lemaitre, J. (1992). A Course on Damage Mechanics, Springer-Verlag, Berlin.
22.
Leukart, M. and Ramm, E. (2003). A Comparison of Damage Models Formulated on Different Material Scales, Computational Materials Science, 28(3/4): 749-762.
23.
Litewka, A. (1986). On Stiffness and Strength Reduction of Solids due to Crack Development, Engineering Fracture Mechanics, 25(5/6): 637-643.
24.
Litewka, A. and Dębiński, J. (2003). Load-induced Oriented Damage and Anisotropy of Rock-like Materials, International Journal of Plasticity, 19(12): 2171-2191.
25.
Litewka, A., Bogucka, J. and Dębiński, J. (2003). Anisotropic Behaviour of Damaged Concrete and Fiber Reinforced Concrete, Anisotropic Behaviour of Damaged Materials, pp. 185-219, Berlin: Springer.
26.
Miller, R., Ortiz, M., Phillips, R., Shenoy, V. and Tadmor, E.B. (1998). Quasicontinuum Models of Fracture and Plasticity , Engineering Fracture Mechanics, 61(3/4): 427-444.
27.
Murakami, S. and Kamiya, K. (1997). Constitutive and Damage Evolution Equations of Elastic-brittle Materials Based on Irreversible Thermodynamics, International Journal of Mechanics & Science, 39(4): 473-486.
28.
Pensee, V. and Kondo, D. (2003). Micromechanics of Anisotropic Brittle Damage: Comparative Analysis between a Stress Based and a Strain Based Formulation , Mechanics of Materials, 35(8): 747-761.
29.
Phillips, R. (2001). Crystals, Defects and Microstructures: Modeling Across Scales, Cambridge: Cambridge University Press.
30.
Skrzypek, J. and Gancarski, A. (1998). Application of the Orthotropic Damage Growth Rule to Variable Principal Directions, International Journal of Damage Mechanics, 7(2): 180-206.
31.
Simo, J.C. and Ju, J.W. (1987). Strain- and Stress-based Continuum Damage Models-I. Formulation, International Journal of Solids and Structures , 23(7): 821-840.
32.
Singh, U.K. and Digby, P.J. (1989). A Continuum Damage Model for Simulation of the Progressive Failure of Brittle Rocks, International Journal of Solids and Structures, 25(6): 647-663.
33.
Steinmann, P., Elizondo, A. and Sunyk, R. (2007). Studies of Validity of the Cauchy-Born Rule by Direct Comparison of Continuum and Atomistic Modelling, Modelling and Simulations in Materials Science and Engineering, 15(1): S271-S281.
34.
Woo, C.W. and Li, D.L. (1993). A Universal Physically Consistent Definition of Material Damage, International Journal of Solids and Structures , 30(15): 2097-2108.
