User login


You are here

Mixed mode cohesive zone model formulation in Abaqus

I am having some difficulty understanding the particulars of the implementation of Abaqus' cohesive zone model (CZM). I also see some differences in what is available in the Abaqus User's Guide (Section 32.5.6) and what is reported for Abaqus' CZM in highly regarded academic literature.

(A) I understand that there have been some discrepancies between LEFM predictions and Abaqus' CZM under mixed mode loading conditions due to path dependence of the loading history, as reported by [1,2]. As far as I understand, this issue was addressed by implementing a default non-accumulated energy measure for the definition of the mode mix ratio, such that the new definition relies only on the current deformation state, and not on the history of the deformation, in order to achieve better alignment with LEFM predictions. This is reported in [7], although, for some reason, the non-accumulated energy measure of the mode mix ratio is not discussed as extensively in the Abaqus User's Guide.

(B) Other sources highlight that due to the coupled, mixed-mode formulation of Abaqus' CZM, it suffers from inaccurate energy dissipation when the pure mode I fracture toughness and the pure mode II toughness are set to different values. There is also inaccuracy when the normal and tangential cohesive strengths or the initial elastic stiffnesses are unequal. This can result in “restoration of the cohesive state” under changing mode-mixity, after an element has failed, and has been highlighted in [2,3,4,5]. Turon et al. [5] proposed a modification to the CZM formulation but it requires the normal and shear cohesive strengths to be set at a certain ratio to ensure correct energy dissipation under changing mode-mixity.

(C) Campilho et al. [6] report on the use of Abaqus' CZM in an uncoupled, mixed-mode manner, such that: the initiation of damage is coupled between tension and shear through the quadratic stress criterion, but upon the initiation of damage an uncoupled tensile/shear behaviour was used, in which the tensile and shear behaviours of the CZM elements are independent up to failure. This constitutes the use of two separate damage variables, one for tension and one for shear, to degrade the material stiffness in each respective direction. However, they present contour plots of a single damage variable (SDEG). Additionally, Abaqus User's Guide (Section 32.5.6) states under the heading “Evaluating damage when multiple criteria are active”, that “when multiple damage initiation criteria and associated evolution definitions are used for the same material, each evolution definition results in its own damage variable”. However, it is not possible to specify separate damage evolution criteria based on one quadratic stress damage initiation criterion, and similarly, it is not possible to specify two quadratic stress damage initiation criterion under the one material. Thus, I cannot see how Campilho et al. [6] are able to determine the use of two separate damage variables, one for tension and one for shear. Their description of Abaqus' CZM also negates the use of the “effective displacement” to define material damage based on mixed mode loading, as defined in the Abaqus User's Guide (Section 32.5.6).

My questions are:
1. Are (A) and (B) one of the same issue? Has this been rectified through the non-accumulated energy measure for the definition of the mode mix ratio?
2. Can the CZM formulation described in [6] actually be achieved in Abaqus? If so, what does the damage variable (SDEG) represent in this case? It would also make sense that this formulation would not be subject to (A) and (B), is this correct?

[1] Song, K., Dávila, C.G. and Rose, C.A., 2008, May. Guidelines and parameter selection for the simulation of progressive delamination. In ABAQUS User’s Conference (Vol. 41, pp. 43-44).
[2] Sarrado, C., Turon, A., Renart, J. and Urresti, I., 2012. Assessment of energy dissipation during mixed-mode delamination growth using cohesive zone models. Composites Part A: Applied Science and Manufacturing, 43(11), pp.2128-2136.
[3] Goutianos, S. and Sørensen, B.F., 2012. Path dependence of truss-like mixed mode cohesive laws. Engineering Fracture Mechanics, 91, pp.117-132.
[4] Turon, A., Camanho, P.P., Costa, J. and Dávila, C.G., 2006. A damage model for the simulation of delamination in advanced composites under variable-mode loading. Mechanics of Materials, 38(11), pp.1072-1089.
[5] Turon, A., Camanho, P.P., Costa, J. and Renart, J., 2010. Accurate simulation of delamination growth under mixed-mode loading using cohesive elements: definition of interlaminar strengths and elastic stiffness. Composite structures, 92(8), pp.1857-1864.
[6] Campilho, R.D., Banea, M.D., Neto, J.A.B.P. and da Silva, L.F., 2013. Modelling adhesive joints with cohesive zone models: effect of the cohesive law shape of the adhesive layer. International Journal of Adhesion and Adhesives, 44, pp.48-56.
[7] Bose, K., Hurtado, J., Krishna, S., and Xia, L., 2013, July. Validation of cohesive-zone based mixed-mode formulations in Abaqus. U.S. National Congress on Computational Mechanics, Raleigh, NC.

Subscribe to Comments for "Mixed mode cohesive zone model formulation in Abaqus"

More comments


Subscribe to Syndicate