Issue 29

R. Dimitri et alii, Frattura ed Integrità Strutturale, 29 (2014) 266-283; DOI: 10.3221/IGF-ESIS.29.23 283 unloading are defined independently. Actually, neither unloading nor the transition to the contact regime were tackled in the original presentation of the model [7]. Moreover, it is not clear whether thermodynamical consistency can be formally proved. Thus, in the second part of the paper, a reformulated and improved version of the model is presented in a rigorous thermodynamical framework. Based on a predefined Helmoltz energy, the interface model is derived by applying the Coleman and Noll procedure, in accordance with the second law of thermodynamics, whereby the inelastic nature of the decohesion process is accounted for by means of damage variables. The model accounts monolithically for loading and unloading conditions, as well as for decohesion and contact. Its performance is demonstrated through suitable examples such as the diagonal patch test, and the matrix/fiber debonding test under mixed-mode conditions. A CKNOWLEDGEMENTS he authors have received funding for this research from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013), ERC Starting Researcher Grant “INTERFACES”, G.A. n° 279439. R EFERENCES [1] Dugdale, D.S., Yielding of Steel Sheets Containing Slits, J. Mech. Phys. Solids., 8 (1960) 100–104. [2] Barenblatt, GI., The formation of equilibrium cracks during brittle fracture. General ideas and hypotheses. Axially- symmetric cracks, J. Appl. Math. Mech. (PMM), 23(3) (1959) 622–36. [3] Chandra, N., Li, H., Shel, C., Ghonem H., Some issues in the application of cohesive zone models for metal–ceramic interfaces, Int. J. Solids Struct., 39(10) (2002) 2827–55. [4] Volokh, KY., Comparison between cohesive zone models, Commun. Numer. Methods Eng., 20 (2002) 845-856. [5] Alfano, G., On the influence of the interface law on the application of cohesive-zone models, Compos. Sci. Technol., 66 (2006) 723-730. [6] Alfano, M., Furgiuele, F., Leonardi, A., Maletta, C., Paulino, G. H., Mode I fracture of adhesive joints using tailored cohesive zone models, Int. J. Fract., 157 (2009) 193–204. [7] van den Bosch, M.J., Schreurs, P.J.G., Geers M.G.D., An improved description of the exponential Xu and Needleman cohesive zone law for mixed-mode decohesion, Eng. Fract. Mech., 73 (2006) 1220–1234. [8] Xu, X.P., Needleman, A., Void nucleation by inclusions debonding in a crystal matrix, Model. Simul. Mater. Sc. Engng., 1 (1993) 111–132. [9] McGarry, J.P., Máirtín, É.Ó., Parry, G., Beltz, G.E., Potential-based and non-potential-based cohesive zone formulations under mixed-mode separation and over-closure. Part I: Theoretical analysis, J. Mech. Phys. Solids, 63 (2014) 336–362. [10] Högberg, J.L., Mixed mode cohesive law, Int. J. Fract., 141 (2006) 549–559. [11] Camanho, P.P., Dàvila, C.G., De Moura, M.F., Numerical simulation of mixed-mode progressive delamination in composite materials, J. Compos. Mater., 37(16) (2003) 1415–1438. [12] Wriggers, P., Zavarise, G., Zohdi, T.I., A computational study of interfacial debonding damage in fibrous composite materials, Comput. Mater. Sci., 12 (1998) 39–56. [13] Wu, E.M., Reuter, Jr. R.C., Crack Extension in Fiberglass Reinforced Plastics, T. & AM Report No. 275, University of Illinois (1965). [14] Benzeggagh, M.L., Kenane, M., Measurement of Mixed-Mode Delamination Fracture Toughness of Unidirectional Glass/Epoxy Composites With Mixed-Mode Bending Apparatus, Compos Sci Technol, 56 (1996) 439–449. [15] Mosler, J., Scheider, I., A thermodynamically and variationally consistent class of damage-type cohesive models. J. Mech. Phys. Solids, 59 (2011) 1647–1668. [16] Simo, J.C., Numerical analysis of classical plasticity. In: Ciarlet, P.G., Lions, J.J. (Eds.), Handbook for Numerical Analysis, Elsevier, Amsterdam, 4 (1998). T