Modelling post-crack tension-softening behavior of fiber-reinforced materials

• We analyze fracture behavior of fiber-reinforced materials under stochastic viewpoints.
• We provide a constitutive equation for the crack opening behavior of such materials.
• We demonstrate the effect of random fiber length and orientation numerically.
• We study correlations of fiber length and orientation in this context.

We present a general method for the traction-separation law for the cohesive model of fiber reinforced materials with brittle matrix. The proposed approach is based on results from the theories of marked point and fiber processes. The application of stochastic notions in the field of traction-separation laws and tension-softening curves for fiber reinforced composites allows the thorough investigation of the random effect of the fiber reinforcement on cohesive behavior. The presented method accounts for correlations between length and orientation as may be the case in real fiber reinforced composites. We study the influence of randomness of fiber length and degree of anisotropy on the post-crack tension softening curves. It turns out that fiber length and orientation distributions have a tremendous effect on the crack-opening behavior.