A new anisotropic damage model for brittle solid inelasticity is developed to accommodate observed behavior in applications where the preloading effects are involved. The shortcomings of conventional damage formulations using the "cumulative damage parameter" is outlined, and a new formulation based on the concept of "effective damage parameter" is proposed. The rate of the effective damage parameter is obtained from the consistency condition associated with a damage surface. The cumulative damage parameter is still used as a measure of total dissipated energy. Anisotropy, dilatation, and strength degradation due to pre-loading effects are captured within the formulation. The model is illustrated for concrete in both proportional and nonproportional stress paths in mode I.
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References
1.
Budiansky, B. and R. J. O'Connell. 1976. "Elastic Moduli of a Cracked Solid,"Int. J. Solids Struct., 12(2):81-97.
2.
Chaboche, J. L.1993. "Development of Continuum Damage Mechanics for Elastic Solids Sustaining Anisotropic and Unilateral Damage,"Int. J. Damage Mech., 2:311-329.
3.
Coleman, B. D. and M. E. Gurtin. 1967. "Thermodynamics with Internal State Variables,"J. Chem. Phys., 47(2):597-613.
4.
Coleman, B. D. and V. J. Mizel. 1964. "Existence of Caloric Equations of State in Thermodynamics,"J. Chem. Phys., 40(4):1116-1125.
5.
Costin, L. S. and C. M. Stone. 1987. "A Finite Element Material Model for Microfracture-Damaged Brittle Rock,"Sandia Lab. Report, Sand87-1227 Sandia National Laboratory, Albuquerque, NM.
6.
Germain, P. , Q. S. Nguyen and P. Suquet. 1983. "Continuum Thermodynamics,"J. App. Mech., ASME, 50:1010-1020.
7.
Gopalaratnam, V. S. and S. P. Shah. 1985. "Softening Response of Plain Concrete in Direct Tension,"Proc. ACI, 87:310-325.
8.
Horri, H. and S. Nemat-Nasser. 1983. "Overall Moduli of Solids with Microcracks: Load-Induced Anisotropy,"J. Mech. Phys. Solids, 31(2):155-177.
9.
Ilankamban, R. and D. Krajcinovic. 1987. "A Constitutive Theory for Progressively Deteriorating Brittle Solids,"Int. J. Solids Struct., 23(11):1521-1534.
10.
Ju, J. W.1989. "On Energy-Based Coupled Elastoplastic Damage Theories: Constitutive Modeling and Computational Aspects,"Int. J. Solids Struct., 25(7):803-833.
11.
Kestin, J. and J. R. Rice. 1970. "Paradoxes in the Application of Thermodynamics to Strained Solids,"A Critical Review of Thermodynamics, E. B. Stuartet al., eds., Baltimore, MD: Mono Book Corp., pp. 275-297.
12.
Krajcinovic, D.1995. "Continuum Damage Mechanics: When and How?"Int. J. Damage Mech., 4:217-229.
13.
Krajcinovic, D.1989. "Damage Mechanics,"Mech. of Mat., 8:117-197.
14.
Krajcinovic, D. , M. Basista and D. Sumarac. 1991. "Micromechanically Inspired Phenomonelogical Damage Model,"J. Appl. Mech., ASME, 58(2):305-310.
15.
Lubliner, J.1972. "On the Thermodynamic Foundations of Non-Linear Solid Mechanics,"Int. J. Non-Linear Mech., 7(3):237-254.
Nemat-Nasser, S.1976. "On Nonequilibrium Thermodyanmics of Continua,"Mechanics Today, Vol. 2, S. Nemat-Nasser, ed., New York, NY: Pergamon Press Inc., pp. 94-158.
18.
Ortiz, M.1985. "A Constitutive Theory for the Inelastic Behavior of Concrete,"Mech. Mater., 4(1):67-93.
19.
Resende, L.1987. "A Damage Mechanics Constitutive Theory for the Inelastic Behavior of Concrete,"Comp. Method App. Mech. Engng., 60(1):57-93.
20.
Rice, J. R.1975. "Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanics,"Constitutive Equations in Plasticity, ed., A. S. Argon, MIT Press.
21.
Schreyer, H. L.1995. "Continuum Damage Based on Elastic Projection Operators,"Int. J. Damage Mech., 4:171-195.
22.
Simo, J. C. and J. W. Ju. 1987. "Strain and Stress Based Continuum Damage Models: Part I-Formulation,"Int. J. Solids Struct., 23(7):821-840.
23.
Suaris, W. , C. Quyang and V. M. Ferando. 1990. "Damage Model for Cyclic Loading of Concrete,"J. Engng. Mech., ASCE, 116(5):1020-1035.
24.
Stankowski, T. 1990. "Numerical Simulation of Progressive Failure in Particle Composites," Ph.D. dissertation, University of Colorado, Boulder.
25.
Truesdell, C.1984. Rational Thermodynamics, 2nd Ed., New York, NY: Springer-Verlag.
26.
van Mier, J. G. M. 1984. "Strain-Softening of Concrete under Multiaxial Loading Conditions," Ph.D. dissertation, De Technische Hogeschool Eindehoven, The Netherlands.
27.
William, K. , T. Stankowski and S. Sture. 1990. "Theory and Basic Concepts for Modeling Concrete Behavior,"26th CEB Plenary Session, Bulletin Information No. 194, Dubrovnik, Yugoslavia.
28.
Yazdani, S. and H. S. Schreyer. 1988. "An Anisotropic Damage Model with Dilatation for Concrete,"Mech. of Mat., 7(3):231-244.
29.
Yazdani, S.1993. "On a Class of Continuum Damage Mechanics Theories,"Int. J. Damage Mech., 2:162-176.
30.
Yazdani, S. and S. R. Karnawat. 1996. "A Constitutive Theory for Brittle Solids with Application to Concrete,"Int. J. Damage Mech., 5:93-110.
