Multi-timescale analysis of fatigue crack growth on interfaces via cohesive-zone models

The paper describes a new non-linear finite-element formulation to analyse fatigue debonding or delamination, along predefined interfaces, which is multi-scale in time. At the small timescale level, cyclic loading and the related oscillating response are considered in an explicit way, whereas at the large timescale level, both the real loading actions and the related response in terms of displacement and stress fields are replaced with minimum and maximum functions over the time of the analysis, which also implies doubling the degrees of freedom of the finite-element model. A cohesive-zone model capable of simulating sub-critical damage growth and hysteretic local response is used on the interface. With a conventional cycle-by-cycle incremental procedure, the analysis would require a number of increments significantly higher than the number of cycles, and would be therefore unfeasible for most industrial applications. Instead, with the developed multi-timescale method, the cycle-by-cycle time integration is transferred from the structural level to the local, integration-point level, whereby the time step can be, and in fact should better be, much larger than the period of the applied actions. The consequent significant saving in terms of computational cost largely offsets the shortcoming of having to double the degrees of freedom of the model and makes the analysis not only feasible but relatively inexpensive in many cases, while retaining excellent accuracy as showed by the presented numerical results. © 2014 Taylor and Francis

An analytical insight into the buckling paradox for circular cylindrical shells under axial and lateral loading

A large number of authors in the past have concluded that the flow theory of plasticity tends to overestimate significantly the buckling load for many problems of plates and shells in the plastic range, while the deformation theory generally provides much more accurate predictions and is consequently used in practical applications. Following previous numerical studies by the same authors focused on axially compressed cylinders, the present work presents an analytical investigation which comprises the broader and different case of nonproportional loading. The analytical results are discussed and compared with experimental and numerical findings and the reason for the apparent discrepancy on the basis of the so-called “buckling paradox” appears once again to lay in the overconstrained kinematics on the basis of the analytical and numerical approaches present in the literature

A novel rate-dependent cohesive-zone model combining damage and visco-elasticity

This is the author’s post-print version of a work that was accepted for publication in Computers & Structures. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.The published paper is available from the link below.This paper presents a novel rate-dependent cohesive-zone model combining damage and visco-elasticity and based on two fundamental assumptions. Firstly we postulate the existence of an intrinsic (i.e. rate-independent) fracture energy. Secondly, within a thermodynamically consistent damage-mechanics framework we assume that the evolution of the damage variable is related to the current free energy and to the intrinsic fracture energy. The underlying idea is that the energy of the bonds at the micro-level is rate-independent and that the rate-dependence of the overall dissipated energy during crack propagation is a natural by-product of the visco-elastic dissipation lumped on the zero-thickness interface. Quite good agreement within an expected range of loading rates was obtained between numerical and experimental results for a DCB specimen with steel arms bonded through a rubber interface. This is despite the fact that for this application the model has been kept as simple as possible using a quadratic elastic energy and linear visco-elasticity with one relaxation time only. Therefore, the presented results support the fundamental principles behind the proposed approach and indicate that the model has the potential to be refined into a highly accurate tool of analysis based on sound physical arguments.EPSR

Reduction of gear pair transmission error with tooth profile modification

The gear noise problem that widely occurs in power transmission systems is typically characterised by one or more high amplitude acoustic signals. The noise originates from the vibration of the gear pair system caused by transmission error excitation that arises from tooth profile errors, misalignment and tooth deflections. This paper aims to further research the effect of tooth profile modifications on the transmission error of gear pairs. A spur gear pair was modelled using finite elements, and the gear mesh was simulated and analysed under static conditions. The results obtained were used to study the effect of intentional tooth profile modifications on the transmission error of the gear pair. A detailed parametric study, involving development of an optimisation algorithm to design the tooth modifications, was performed to quantify the changes in the transmission error as a function of tooth profile modification parameters as compared to an unmodified gear pair baseline

A thermodynamically consistent derivation of a frictional-damage cohesive-zone model with different mode i and mode II fracture energies

The present paper deals with the derivation of an interface model characterized by macroscopic fracture energies which are different in modes I and II, the macroscopic fracture energy being the total energy dissipated per unit of fracture area. It is first shown that thermo-dynamical consistency for a model governed by a single damage variable, combined with the choice of employing an equivalent relative displacement and of a linear softening in the stress-relative displacement law, leads to the coincidence of fracture energies in modes I and II. To retrieve the experimental evidence of a greater fracture energy in mode II, a micro-structured geometry is considered at the typical point of the interface where a Representative Interface Element (RIE) characterized by a periodic arrangement of distinct inclined planes is introduced. The interaction within each of these surfaces is governed by a coupled damage-friction law. A sensitivity analysis of the correlation between micromechanical parameters and the numerically computed single-point microstructural response in mode II is reported. An assessment of the capability of the model in predicting different mixed mode fracture energies is carried out both at the single microstructural interface point level and with a structural example. For the latter a double cantilever beam with uneven bending moments has been analyzed and numerical results are compared with experimental data reported in the literature for different values of mode mixity. © 2014 Elsevier Masson SAS. All rights reserved

Numerical derivation of constitutive models for unbonded flexible risers

This is the post-print version of the final paper published in International Journal of Mechanical Sciences. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication.In this paper a new constitutive model for flexible risers is proposed and a procedure for the identification of the related input parameters is developed using a multi-scale approach. The constitutive model is formulated in the framework of an Euler–Bernoulli beam model, with the addition of suitable pressure terms to the generalized stresses to account for the internal and external pressures, and therefore can be efficiently used for large-scale analyses. The developed non-linear relationship between generalized stresses and strains in the beam is based on the analogy between frictional slipping between different layers of a flexible riser and frictional slipping between micro-planes of a continuum medium in non-associative elasto-plasticity. Hence, a linear elastic relationship is used for the initial response in which no-slip occurs; an onset-slip function is introduced to define the ‘no-slip’ domain, i.e. the set of generalized stresses for which no slip occurs; a non-associative rule with linear kinematic hardening is used to model the full-slip phase. The results of several numerical simulations for a riser of small-length, obtained with a very detailed (small-scale) non-linear finite-element model, are used to identify the parameters of the constitutive law, bridging in this way the small scale of the detailed finite-element simulations with the large scale of the beam model. The effectiveness of the proposed method is validated by the satisfactory agreement between the results of various detailed finite-element simulations for a short riser, subject to internal and external uniform pressure and uniform cyclic bending loading, with those given by the proposed constitutive law.Lloyds Register EME

Bond-slip analysis via a cohesive-zone model simulating damage, friction and interlocking

A recently proposed cohesive-zone model which effectively combines damage, friction and mechanical interlocking has been revisited and further validated by numerically simulating the pull-out test, from a concrete block, of a ribbed steel bar in the post-yield deformation range. The simulated response is in good agreement with experimental measurements of the bond slip characteristics in the post-yield range of deformed bars reported in the literature. This study highlights the main features of the model: with physically justified and relatively simple arguments, and within the sound framework of thermodynamics with internal variables, the model effectively separates the three main sources of energy dissipation, i.e. loss of adhesion, friction along flat interfaces and mechanical interlocking. This study provides further evidence that the proposed approach allows easier and physically clearer procedures for the determination of the model parameters of such three elementary mechanical behaviours, and makes possible their interpretation and measurement as separate material property, as a viable alternative to lumping these parameters into single values of the fracture energy. In particular, the proposed approach allows to consider a single value of the adhesion energy for modes I and II

Outage Information Rate of Spatially Correlated Multi-Cluster Scattering MIMO Channels

A one-sided spatially-correlated multi-cluster scattering Rayleigh MIMO channel is considered in this work and its outage probability is derived in an analytic form based on Meijer function determinants. First, the spatially-uncorrelated case is addressed and the Moment Generating Function (MGF) of the information rate is expressed in an analytic closed-form. The MGF is then used to obtain the outage probability. A few special cases are addressed to provide a confirmation of the analytic results. Next, the MGF in the one-sided spatially correlated case is derived with the constraint of distinct positive spatial correlation eigenvalues. Numerical results are included to provide confirming evidence of the analytic results. These results are then used to assess the outage probability degradation due to spatial correlation in a selected exampl

Closed-form performance analysis of linear MIMO receivers in general fading scenarios

Linear precoding and post-processing schemes are ubiquitous in wireless multi-input-multi-output (MIMO) settings, due to their reduced complexity with respect to optimal strategies. Despite their popularity, the performance analysis of linear MIMO receivers is mostly not available in closed form, apart for the canonical (uncorrelated Rayleigh fading) case, while for more general fading conditions only bounds are provided. This lack of results is motivated by the complex dependence of the output signal-to-interference and noise ratio (SINR) at each branch of the receiving filter on both the squared singular values as well as the (typically right) singular vectors of the channel matrix. While the explicit knowledge of the statistics of the SINR can be circumvented for some fading types in the analysis of the linear Minimum Mean-Squared Error (MMSE) receiver, this does not apply to the less complex and widely adopted Zero-Forcing (ZF) scheme. This work provides the first-to-date closed-form expression of the probability density function (pdf) of the output ZF and MMSE SINR, for a wide range of fading laws, encompassing, in particular, correlations and multiple scattering effects typical of practically relevant channel models.Comment: 16 pages, 2 figures, contents submitted to IEEE/VDE WSA 201

Nonlinear multi-scale homogenization with different structural models at different scales

We present an extension of the computational homogenization theory to cases where different structural models are used at different scales and no energy potential can be defined at the small scale. We observe that volumetric averaging, which is not applicable in such cases unless similarities exist in the macro-scale and micro-scale models, is not a necessary prerequisite to carry out computational homogenization. At each material point of the macro-model, we replace the conventional representative volume element with a representative domain element (RDE). To link the large-scale and small-scale problems, we then introduce a linear operator, mapping the smooth part of the small-scale displacement field of each RDE to the large-scale strain field and a trace operator to impose boundary conditions in the RDE. The latter is defined on the basis of engineering judgement, analogously to the conventional theory. A generalized Hill’s condition, rather than being invoked, is derived from duality principles and is used to recover the stress measures at the large scale. For the implementation in a nonlinear finite-element analysis, ‘control nodes’ and constraint equationsare used. The effectiveness of the procedure is demonstrated for three beam-to-truss example problems, for which multi-scale convergence is numerically analysed.Lloyd’s Register EME