Inverse extraction of cohesive zone laws by field projection method using numerical auxiliary fields

The cohesive zone law relates the cohesive tractions with the cohesive separations within the fracture process zone of a material and is used to quantify the strength and toughness of the material. Determining the material's cohesive zone law, however, is a nontrivial inverse problem of finding unknown tractions and separations from measurement data. Previously, a field projection method was established to extract the cohesive zone laws from far-field data using interaction J-integrals between the physical field of interest and auxiliary analytical probing fields. Here, we extend the universality of the field projection method and its ease of numerical implementation by using numerical auxiliary fields. These numerical fields are generated by systematically imposing uniform surface tractions element-by-element along the crack faces in finite element models. Then, interaction J- and M-integrals between these auxiliary probing fields and the measurement field are used to reconstruct the traction and separation relationship along the crack faces. The effectiveness of this method in extracting the cohesive zone law from measured displacements in the far-field region is demonstrated through numerical experiments.