INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng (2012) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nme.4281 Inverse extraction of cohesive zone laws by field projection method using numerical auxiliary fields Hyun-Gyu Kim 1, * ,† , Huck Beng Chew 2 and Kyung-Suk Kim 3 1 Department of Mechanical Engineering, Seoul National University of Science and Technology, Seoul 139-743, South Korea 2 Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA 3 School of Engineering, Brown University, Providence, RI 02912, USA SUMMARY The cohesive zone law relates the cohesive tractions with the cohesive separations within the fracture pro- cess 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 gen- erated 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. Copyright © 2012 John Wiley & Sons, Ltd. Received 4 August 2011; Revised 13 December 2011; Accepted 16 December 2011 KEY WORDS: FEMs; inverse analysis; cohesive zone law; interaction integrals; field projection method 1. INTRODUCTION Micromechanics models describe the relationship between the cohesive tractions acting on the crack faces and the associated cohesive separations, which constitutes the rate of energy release in the cohesive zone during crack propagation in a material. In conventional cohesive zone models, the cohesive traction initially increases with the cohesive separation until a peak traction is reached, beyond which the cohesive traction decreases continuously until it vanishes to complete separation [1, 2]; the peak traction denotes the cohesive strength, whereas the area enclosed by the traction– separation profile represents the cohesive energy, that is, the energy-release rate of crack growth, in the fracture process zone. Although the cohesive strength and the fracture energy are often suffi- cient to determine the global fracture behavior of the material, the shape of the traction–separation relationship is sensitive to micromechanisms of fracture processes [3, 4]. A number of numerical methods [5–8] have been developed to simulate cohesive crack growth with predefined functional forms of cohesive zone laws. However, an efficient method of experimentally measuring the exact form of the cohesive traction–separation relationship is needed to understand the micromechanisms of crack growth. *Correspondence to: Hyun-Gyu Kim, Department of Mechanical Engineering, Seoul National University of Science and Technology, 172 Gongneung-2dong, Nowon-gu, Seoul, 139-743, South Korea. † E-mail: khg@snut.ac.kr Copyright © 2012 John Wiley & Sons, Ltd.