Cohesive zone modeling in load – unload situations

• Published in: International journal of mechanical sciences 2022-05, Vol.222, p.107205, Article 107205
• Main Authors: Zahr Viñuela, Jorge, Torres, María, Guerra Silva, Rafael
• Format: Article
• Language: English
• Subjects: Cohesive-crack model; Damage; DCB fracture specimen; Displacement control; Force control; Loading-unloading process
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2022.107205

•It is observed for the first time that cohesive elements may erroneously predict an increase in both interface separation and damage during “force-controlled” unloadings.•This effect is partially a consequence of loss of uniqueness in the separation solution for a given decrease in tractions, as there are two possible separations for which force equilibrium is satisfied.•In force-controlled unloadings, the loading/unloading criterion used may induce the Newton-Raphson solution procedure in nonlinear FEM to choose the physically wrong unloading path.•A solution is identified and implemented in a UMAT subroutine (provided in a Mendeley Dataset), using the trial traction concept as a loading/unloading criterion.•It is found that, when formulating and implementing a cohesive model, a validation strategy aimed to verify that the model “returns to the origin during unloadings” should be implemented for both, displacement and force-controlled unloadings. In some circumstances, loss of uniqueness of the stress/displacement solution may arise in cohesive modeling, preventing the use of cohesive elements in simulations involving loading and unloading of solids containing cracks. In these cases, it may be erroneously predicted that the damage of cohesive cracks increases when the external forces acting on the solid containing the cracks are reduced due to a prescribed “load reversal”. This issue is illustrated with various practical examples, including a finite element model of a double cantilever beam fracture specimen. Further numerical experiments are presented, that help to explain the causes of the observed phenomenon and shed some light on possible solutions. It is shown that lack of thermodynamic consistency of the cohesive model is not the cause of the observed behavior. The cause of the unphysical response is finally identified in its relationship with features of the nonlinear solution procedure and material stress update routines, by means of the formulation of a custom one-dimensional cohesive element. Two solutions are proposed based on a redesign of the loading/unloading criterion and a custom material model using one of them is presented. It is used as the material definition for Abaqus cohesive elements via UMAT subroutine, and it is shown that it solves the problem found during unloadings for all the considered numerical examples. [Display omitted]