9.3. Nonstandard Cohesive Crack Model Defined by a Fixed KProfile

For sufficiently large structures, functions b ₁, b ₂, ..., c ₁, c ₂, ... may be neglected. Then (9.11) with (9.14) furnish

(9.17)

(9.18)

It will be convenient to write these equations also as

(9.19)

If K _c, c _f and the profile q( ?) are known, equation (9.17) provides a parametric description of the stress-displacement ?( w) curve of the cohesive crack model. Indeed, choosing a series of values of ?, the corresponding pairs of w and ? can be obtained by evaluating the integrals S( ?) and W( ?), which are independent of structure size and shape. Thus, for each K-profile, there exists a corresponding stress-displacement curve (softening law) ?( w) of the cohesive crack model. Vice versa, assuming this relationship to be invertible, one can find for each f _t, w _f and function ? the values K _c, c _f and function q( ?). Therefore, defining the cohesive crack model by a stress-displacement curve or by a fixed asymptotic K-profile is equivalent.

For the sake of simplicity, we will now introduce a nonstandard form of the cohesive crack model defined by the hypothesis that the K-profile q( ?) and its length 2 c _f are material properties, i.e., are fixed. In the perspective...