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Extra resources for Physics- Vibrations and Waves
Example text
Later, the thermodynamics of irreversible processes provided the necessary scientific basis to justify continuum damage mechanics as a theory (before 1993: Chaboche [2-33], Lemaitre and Chaboche [2-22], Leckie and Hayhurst [2-60], Murakami [2-48], Cordebois and Sidoroff [2-181] and Krajcinovic [245]; after 1993: Ibijola [2-2], Zhang and Valliappan [2-74], Voyiadjis [2-124], Tang et al. [2-164]' Massart [2-174], Abdul-Latif [2-180], Carol et al. [2-182 ]' Desmorat [2-183]). Models presented here are in the framework of thermodynamics that provides the possibility of identifying the damage by means of coupling with elasticity and plasticity.
The measure of damage considered by Pieichnik and Pachla [2-176] and Cheng [2-177] was the ratio of strain for damaged and undamaged cases as D = l -c/c* (2-5) The damage variable considered by Rosuselier [2-106] is measured from the mass density of material. From his calculations, the mass density of a damaged 20 2 Review of Damage Mechanics material p* must be less than the original undamaged one Po. Accordingly, the damage variable can be defined as n=1- p* j po (2-6) It should be noted that only in the case of large plastic deformation does this definition becomes valid [2-178].
The microstructure change was defined as the internal state variable due to the irreversible nature of the material behavior. 1 Constitutive Relations for Damaged Materials Due to the importance of the internal state variables they must be included in the constitutive equation for damaged materials. This concept has been previously utilized in continuum mechanics/thermodynamics for ductile and brittle materials by many investigators such as [2-22, 2-39, 2-45 , 2-120, 2-121 , 2-169]. A constitutive model should address equally the two distinct physical modes of irreversible changes and should satisfy the basic postulates of mechanics and thermodynamics, based on which Chow and Wang [2-214], Murakami et al.