Mesh-independent discrete numerical representations of cohesive-zone models

The importance of the cohesive-zone approach to analyse localisation and fracture in engineering materials is emphasised and ways to incorporate the cohesive-zone methodology in computational methods are discussed. Until recently, numerical implementations of cohesive-zone models have suffered from a certain mesh bias. For discrete representations this is caused by the initial mesh design, while for smeared representations it is rooted in the ill-posedness of the rate boundary value problem that arises upon the introduction of decohesion. A proper representation of the discrete character of cohesive-zone formulations which avoids any mesh bias is obtained by exploiting the partition-of-unity property of finite element shape functions. The recently developed cohesive segments method, which is well-suited for simulating the entire process of crack nucleation, growth and coalescence is reviewed. The effectiveness of this approach is illustrated by some examples for crack nucleation and growth in heterogeneous materials and for fast crack growth.