The lack of any work on the asymptotic fields at the tips of cohesive cracks belies the
widespread use of cohesive crack models. This study is concerned with the solution of
asymptotic fields at cohesive crack tips in quasibrittle materials. Only normal
cohesive separation is considered, but the effect of Coulomb friction on the cohesive
crack faces is studied. The special case of a pure mode I cohesive crack is fully
investigated. The solution is valid for any separation law that can be expressed in a
special polynomial form. It is shown that many commonly used separation
laws of quasibrittle materials, for example, rectangular, linear, bilinear, and
exponential, can be easily expressed in this form. The asymptotic fields
obtained can be used as enrichment functions in the extended/generalized
finite element method at the tip of long cohesive cracks, as well as short
branches/kinks.