On Damage Effective Stress and Equivalence Hypothesis

Abstract

The concepts of damage effective stress and damage equivalence hypothesis play an important role in the development of continuum damage mechanics. Based on a generalization of the damage equivalence hypothesis, the so-called damage isotropy principle, it is found that the effective stress as a second-order tensor-valued function of the usual stress tensor and the damage tensor(s) has to be isotropic. Particularly, this property is regardless of the initial material symmetry (isotropy or anisotropy) and the type of damage variables; and thus, it allows general invariant modeling of the effective stress by the use of theory of tensor function representations. Damage material constants are then consistently introduced to the invariant models of the effective stress and the damage effect tensors. Three new models of the damage effect tensor capable of including realistic dimensionless damage material constants are proposed. The significance of the damage material constants is examined by micromechanical analysis and computer experiments on effective elastic moduli.

Experimental investigation of damage evolution by data-driven stochastic subspace identification and iterative finite element model updating

“…Several effective stress concepts in tensorial forms have been discussed by Betten et al [7,37] in more detail. Rewriting Equation (30) we obtain the damage variable…”

A viscoplastic model including anisotropic damage for the time dependent behaviour of rock

“…The description of material damage is based on the concept of effective stress [22][23][24]. Various proposals can be found in the literature regarding the formulation of a symmetrical effective stress tensor linked to a second-order damage tensor.…”

Creep Mechanics

“…Fatigue damage COFFIN (1954) CHABOCHE (1974 DUFAILLY and LEMAITRE (1995) KRAJCINOVIC (1996) LEMAITRE (1992 LEMAITRE and CHABOCHE (1990) MANSON (1979) NAJAR (1994) SKOCZEN (1996) BETTEN (1983b) CHABOCHE (1981 H. ALTENBACH et al (1990;1997) HAYHURST and LECKIE (1973) HAYHURST et al(1984) J. KACHANOV (1958) KOWALESKI (1996a,b,c) KRAJCINOVIC (19831996) LECKIE andHAYHURST (1974) MURAKAMI (1983) NAUMENKO (1996) NEEDLEMAN et al (1995) QI (1998 QI and BERTRAM (1997) RABOTNOV (1969) STIGH (1985 TRAMPCZYNSKI et al (1981) ZHENG and BETTEN (1996) Nucleation and growth of microscopic transgranular cracks in the vicinity of surface. High cycle fatigue (number of cycles to failure larger than 10 5 ): effect of macroscopic plastic strain is negligible.…”