Non associative damage interface model for mixed mode delamination and frictional contact

Abstract

The present paper proposes a new interface constitutive model based on the nonassociative damage mechanics and frictional plasticity. The model is developed in a thermodynamically consistent framework, with three independent damage variables. The non associative ow rules drive the concurrent evolution of the three damage variables. The interface model provides two independent values for the mode I fracture energy and the mode II fracture energy and it is able to accurately reproduce arbitrary mixed mode fracture conditions. The model can also take into account the presence of frictional eects both at the fully debonded zones and at the partially debonded ones. The experimental tests developed by Benzeggagh and Kenane with seven dierent mixed mode ratios have been numerically simulated with a unique set of constitutive parameters. The split shear torsion, for the evaluation of the mode III delamination toughness, has been analysed by a three-dimensional numerical simulation.

Hybrid equilibrium element with interelement interface for the analysis of delamination and crack propagation problems

“…The convergence of the nonlinear consistency condition problem in Equations (57) and (58) is quite effective as can be observed from the following numerical example, which reproduces the pure tensile test represented in Figure 5A of a specimen subjected to a uniform horizontal displacement at the right side (nodes 25,26,27). Constrained degrees of freedom (at node 1, 2, 3) are marked in red and the extrinsic interface Γ 0 is embedded at one side of element 4, of nodes 13, 14, 15.…”

“…Moreover, the two modes are fully coupled in the CZM for the dependence of the damage activation condition in Equation (38) on the energy release rate Y, which is defined in Equation (35) in terms of the two separation displacement components (normal and tangential) and in Equation (39) in terms of the traction components. The model could be also extended to a more general formulation, in order to account for different response in pure modes, by an extrinsic formulation of the nonassociative damage model proposed by the author in Reference 25. The interface elastic stiffness matrix and its inverse are diagonal and defined as k el = k 0 I and with I being the identity matrix and k 0 a stiffness parameter.…”

“…The CZMs, initially proposed in the pioneering works of Dugdale 18 and Barenblatt, 19 allow us to overcome the mathematical issue of the stress singularity ahead of the crack tip of linear elastic fracture mechanics. 20 The literature is extremely rich in cohesive interface models, and several points of view have been thoroughly investigated, such as the following: isotropic and orthotropic cohesive interface models, 21 coupling damage and plasticity, 22 different mode I and mode II fracture energies, [23][24][25] thermodynamic consistency, [26][27][28] with smooth transition from cohesive behavior to frictional one, 26,29 under finite displacement conditions, 23,30 and so on. The references cited represent a short and largely incomplete review of the interface models available in literature.…”

Hybrid equilibrium element with high‐order stress fields for accurate elastic dynamic analysis

“…In this case the analysis is limited to elastic static problems and its application to dynamic analysis of fracture and fragmentation phenomena would be of great interest. Indeed, analysis of such problems with classic intrinsic interface elements (see, e.g., References 11‐13), with a penalty approach in the pre‐failure regime, introduces additional compliance in elastic behavior with the relevant wave propagation issues. The dynamic fragmentation problem is approached by References 14,15 using the interelement fracture governed by means of a discontinuous Galerkin method, combined with an extrinsic interface.…”

Inter-Element Crack Propagation with High-Order Stress Equilibrium Element

“…The numerical modelling of nonlinear behaviours in brittle materials can be approached in the framework of continuum damage mechanics, by using suitable regularization techniques to avoid pathological mesh dependency, or by adopting discrete crack models, such as the zero-thickness interface element, strong or embedded discontinuity (EFEM) approaches 1,2,3,4 and the eXtended-generalized FEM (XFEM, GFEM) 5,6,7,8 . Discrete crack models are often combined with Cohesive Zone Models (CZMs) 9,10,11,12,13,14,15,16,17,18,19,20 , which describe the Traction Separation Law (TSL) at the discontinuity surface.…”