On Gc, Jc and the characterisation of the mode-I fracture resistance in delamination or adhesive debonding

We focus on the mode-I quasi-static crack propagation in adhesive joints or composite laminates, where inelastic behaviour is due to damage on a relatively thin interface that can be effectively modelled with a cohesive-zone model (CZM). We studied the difference between the critical energy release rate, G c , in- troduced in linear elastic fracture mechanics (LEFM), and the work of separation, , i.e. the area under the traction-separation law of the CZM. This difference is given by the derivative, with respect to the crack length, of the energy dissipated ahead of the crack tip per unit of specimen width. For a steady- state crack propagation, in which that energy remains constant as the crack tip advances, this derivative vanishes and =G c . Thus, the difference between and G c depends on how far from steady-state the process is, and not on the size of the damage zone, unlike what is stated elsewhere in the literature. Therefore, even for very ductile interfaces, G c = for a double cantilever beam (DCB) loaded with mo- ments and their difference is extremely small for a DCB loaded with forces. We also show that the proof that the critical value of the J integral, J c , is equal to the nonlinear energy release rate is not valid for a non-homogeneous material. To compute G c for a DCB, we use a method based on the introduction of an equivalent crack length, a eq , where the solution is a product of a closed-form part, which does not require the measurement of the actual crack length, and of a corrective factor where the knowledge of the actual crack length is required. However, we also show that this factor is close to unity and therefore has a very small effect on G c

Master-slave approach for the modelling of joints with dependent degrees of freedom in flexible mechanisms

The analysis of multibody systems requires an exact description of the kinematics of the joints involved. In the present work the master–slave approach is employed and endowed with the possibility of including several more complex types of joints. We present the formulation for joints where some relation between the different released degrees of freedom exists such as the screw joint, the rack‐and‐pinion joint or the cam joint. These joints are implemented in conjunction with geometrically exact beams and an energy‐momentum conserving time‐stepping algorithm

Modelling mixed-mode rate-dependent delamination in layered structures using geometrically nonlinear beam finite elements

Delamination is one of the one most important problems for layered structures, which are widely used in industry (e.g.compositelaminates)andalsooftenpresentinnature(e.g.layeredbiologicaltissue).Inthisworkdelamination is studied using cohesive-zone models (CZMs) where a discontinuous displacement field and a non-linear tractionseparation law on the considered interface are assumed. Authors of the present work have recently shown that beam elements can be used with very good accuracy to model delamination in layered structures both in geometrically linear and non-linear analysis. Beam elements also make use of a smaller number of degrees of freedom, with significant reduction in the overall computational burden. When the fracture process is significantly rate dependent, the traditional fracture-mechanics based approaches can only characterise the phenomenological dependence of the fracture energy on the crack speed. Instead, rate-dependent CZMs, recently developed by the authors, where the different dissipation mechanisms occurring during fracture are separated out, is less phenomenological and better linked to the underlying physics. Combining the highly efficient multi-layer beam model and the novel rate-dependent CZMs is the aim of the project on which the authors of this work are currently collaborating. This work gives a brief overview of authors’ recent work which presents the background for developing a novel multi-layer beam finite element with rate-dependent mixed-mode delaminatio

Energy-momentum dynamic integrator for geometrically exact 3D beams Attempt at a strain-invariant solution

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