Constitutive relationships during softening

After the softening initiation, a smeared band of microcracks is assumed to appear in the direction perpendicular to the principal tensile strain. The material reference axis system, referred as the local axis system, is aligned with the principal strain directions at that instant [directions n-p in Figure 5.10-c. The constitutive matrix, relating the local stresses to local strains is defined as:

where the parameter n (0 < n ^ 1) is the ratio between the softening Young's modulus En, [Figure 5.10-d], in the direction normal to a fracture plane and E, is the initial isotropic elastic modulus; and ¡i is the shear resistance factor. The following options are considered with respect to the orientation of crack bands in finite element analyses.

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