Integration of finite displacement interface element in reference and current configurations

Abstract

In the present paper the non-linear behaviour a solid body with embedded cohesive interfaces is examined in a nite displacements context. The principal target is the formulation of a two dimensional interface nite element which is referred to a local reference frame, dened by normal and tangential unit vectors to the interface middle surface. All the geometric operators, such as the interface elongation and the reference frame, are computed as function of the actual nodal displacements. The constitutive cohesive law is dened in terms of Helmholtz free energy for unit of undeformed interface surface and, in order to obtain the same nodal force vector and stiness matrix by the two integration schemes, the cohesive law in the deformed conguration is dened in terms of Cauchy traction, as a function of separation displacement and of interface elongation. Explicit expression of the nodal force vector is integrated either over the reference conguration or over the current conguration, which is shown to produce the same analytical nite element operators. No dierences between the integration carried out in the reference and in the current conguration are shown, provided that elongation of the interface is taken in to account.

A coupled plasticity-damage cohesive-frictional interface for low-cycle fatigue analysis

“…[26,27] by suggesting the use of two independent values of fracture energies and extended in Ref. [32,33] to large displacement analysis. An analytical solution for the mode II fracture energy in the 4ENF test with frictional effects has been developed in Ref.…”

Fatigue crack growth of new FML composites for light ship buildings under predominant mode II loading condition

“…A unique damage parameter accounting for static and fatigue degradation is used. In [28][29][30][31], a thermodynamically consistent damage model is proposed for the simulation of progressive delamination in composite materials under mode II loading condition. In particular, a cohesive-frictional model, implemented in the finite element program FEAP, allows to evaluate the influence of frictional phenomena in the Mode II delamination, when the compression of the two interfaces increases the energy dissipation due to the friction.…”

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

“…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.…”