Basic Concepts in Crack Band Models
From the preceding analysis it is clear that, in order to make strain softening an acceptable constitutive relation, localization of strain softening into arbitrarily small regions must be prevented. This is, in general, achieved by some mathematical concept; called the localization limiter. There are various such concepts of varying degrees of generality and complexity. The most general concept is the nonlocal continuum concept, which will be discussed in Chapter 13. Now we describe a rather simple albeit less general concept, known as the crack band model, which was proposed in general terms in Bazant (1976), and was developed in full detail for sudden cracking in Bazant and Cedolin (1979, 1980, 1983) and Cedolin and Bazant (1980), and for gradual strain softening in Bazant (1982) and Bazant and Oh (1983a). The basic attribute of the crack band model is that the given constitutive relation with strain softening must be associated with a certain width hc of the crack band, which represents a reference width and is treated as a material property. Mere we discuss the most basic aspects only, with the help of simple uniaxial models. The three-dimensional analysis is deferred until Section 8.6.