Asymptotic fields at frictionless and frictional cohesive crack tips in quasibrittle materials

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.