[Dxy [TT [Dnp[T

where [T] is strain transformation matrix defined as follows in terms of the inclination of the normal to it crack plane, 6 [Figure 5.10-c]:

cos2 0 sin2 0 sin dcosd sin2 0 cos2 0 — sin 0cos0

With an increasing strain softening, the damaged Young's modulus, En, (Figure 5.10-d), and hence the parameters n and p decrease gradually, and may eventually reach zero values after the complete fracture (en > £f or ef). The constitutive matrix in equation 5.26 is updated as the parameters n and p change their values. In the CRCM, a change in the global constitutive relationship may also be caused by a rotation of the local axis system, which is always kept aligned with the directions of coaxial principal stresses and strains. During unloading/reloading, when the strain, en, is less than the previously attained maximum value, emax [Figure 5.10-d], the secant modulus, En, remains unchanged; the parameter p, however, may change during that process.

The change in global constitutive relations is also caused by a rotation of the local axis system, which is always kept aligned with the directions of principal strains to keep the principal stresses and strains coaxial. The CRCM is very effective in alleviating the stress locking generally observed in fixed crack models. During unload ing/reloading, when the strain, en, is less than the previously attained maximum value, emax[Figure 5.10-f], the secant modulus, En, remains unchanged; the parameter p, however, changes during that process.

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