Steam generator inner tubes are subjected to clearance impacts during their service life, ultimately leading to wear. The present work aims to better understand the influence of the clearance symmetry on the dynamical response of these tubes as well as to establish the minimum ingredients needed by a model to faithfully represent their dynamical behavior. A proof-of-concept has been designed for this purpose: a doubly clamped tube vibrating inside an annular clearance. The experiment directly demonstrates the coexistence of in-plane and annular vibrational regimes of the tube. On the other hand, a two degree-of-freedom vibro-impact is solved using a harmonic balance method continuation algorithm to carry out a bifurcation analysis. Initially, a frictionless model shows how clearance symmetry govern the onset and disappearance of different dynamical regimes found experimentally. Increasing the clearance eccentricity in any direction other than the forcing one shifts the main branching point bifurcation. Further on, sliding friction is added, mitigating the annular nonlinear resonance and evidencing the existence of an isolated branch. This study evidences experimentally how the stability of these branches depend on the systems parameters like clearance symmetry and friction parameters.

Fluid-elastic instability is the main source of concern during the design of heat-exchanger tube bundles. The associated research has focused on the understanding of the physical mechanisms behind this phenomenon and the establishing of models capable of predicting its onset; also some concomitant work has been done to establish post-instability behaviour and to prevent from excessive wear in possible sliding contacts. Moreover, the existing studies make use of time-integration methods alone for this purpose, through which it is difficult to get a comprehensive insight of global dynamics. Continuation methods, which give access to unstable branches and precise bifurcation information, are a precious tool to unfold the attainable dynamic regimes. In this paper, the parametric behaviour of two representative systems under cross-flow excitation is explored through pseudo arc-length continuation with mean flow velocity as a main driving parameter, wherein the nonlinear modal equations of motion are solved by harmonic balance at each step. As the quasi-unsteady model used for fluid-elastic coupling introduces convolution integrals, this approach is quite natural and we show that, despite some difficulties regarding the treatment of stiff intermittent contacts, it allows for a thorough exploration of the system’s response. For the first case -a benchmark model-, increasingly complex dynamics arise as more modes are kept in the truncated modal basis, which is due to a series of modal interactions as the impacts distribute mechanical energy from the linearly-unstable first mode to the higher ones. This can be anticipated by studying the nonlinear normal modes of the system, as they expose the allowed internal resonances. In the second case, consisting of a realistic heat-exchanger tube configuration, a similar pattern is observed.

Fretting motion between two contacting solids can, under gross slip conditions, induce wear. A finite element model and a simulation strategy aiming at predicting wear under fretting motion are presented. The numerical results obtained are compared with experimental data from the literature. The proposed simulation process is particularly suitable for computing high numbers of cycles. To this end, a cycle jump technique is used, and different integration schemes are investigated. Results show that instabilities may arise when an explicit scheme is used, which limits the size of the cycle jump. On the other hand, using an implicit scheme involves a trade-off between the possibility of considering a larger cycle jump and the number of iterations required for convergence. It is shown that the more cycles we perform, the faster the implicit scheme converges. Therefore, the implicit scheme is especially appropriate for high-cycle computations. Moreover, an adaptive cycle jump is used with the implicit scheme, enabling to accelerate the computations for high numbers of cycles.

A phase-field approach was used in order to model the complex mechanisms of fatigue crack nu-cleation and growth. This popular method enables a flexible framework that recovers accurately expected crack patterns. However, it usually suffers from several efficiency drawbacks, such as the need for a very fine mesh, and the heavy computational cost associated with the cycle by cycle approach. For this reason, we put forward the coupling of adaptive mesh refinement and cycle jumps, to significantly accelerate computing time, at a given level of accuracy. Several numerical examples were studied to showcase the abilities of the proposed coupling and some qualitative numerical/experimental comparisons were made. In the end, the proposed coupling was able to recover non accelerated results with significant computing gains.

Commercial finite element software follow cautiously the numerical methods developed by the scientific community. Even though the phase-field method is not a default option in Abaqus, the code proposes a unique way to implement and test complex, extraneous models. In the last five years, phase-field fracture models in Abaqus have gained unbelievable popularity among scientists and engineers alike. However, most implementations are based on the quadratic crack representation function, which is easy to solve but has no elastic threshold. Various solutions have been proposed as a workaround to implement the linear damage function, however, none of them obtain consistent results to the original Griffith solution when the length scale is reduced to zero. This paper presents an energetically consistent linear damage gradient model in Abaqus. The bound constrained optimization is achieved using Lagrange multipliers as an additional degree of freedom. We show that when the necessary energy corrections are applied, the phase-field simulations are in agreement with the analytical results of linear elastic fracture mechanics. Furthermore, through elaborate benchmark tests, we verified our code and experimentally demonstrated the validity of our implementation.

When subjected to some anti-plane shear mode III loading, segmentation of the crack front frequently occurs during propagation: even if the crack is initially planar, propagation produces facets/segments rotated toward the shear free direction [1]. These facets induce some modifications in the local loading of the crack tips that can be captured through a multi-scale cohesive zone model [2]: Assuming that the width of the facets is small in comparison to their length, the facets can be considered at the microscale, as a bidimensional periodic array of tilted cracks perpendicularly to the direction of propagation, and at the macroscale, as a growing Cohesive Zone. The model was developed initially supposing a constant period, small tilt angles and non-overlapping facets. We relaxed recently these assumptions to deal with more realistic cases including coarsening of the facets, large tilt angles and overlap. For this, the microscale problem is solved using XFEM and the outputs are further incorporated into the model to get some results on the macroscale, in particular the effective fracture energy. By comparing the results to some experiments [3], we demonstrate the ability of the approach (i) to determine the inclination of the facets and (ii) to quantify, in both fatigue and brittle fracture, the toughening due to the decrease of the crack opening driven by the unbroken ligaments between the facets.

This work presents a recently developed implementation of numerical methods for vibration problems involving nonlinear mechanical systems in the finite element software Cast3M. Branches of periodic solutions (as well as their bifurcations) are found through a combination of harmonic balance and pseudo arc-length continuation. Current tests show promising results in terms of performance and accuracy, namely regarding strong nonlinearities such as impacts.