This paper is devoted to the numerical simulation of the dynamic propagation of non-planar 3D cracks under transient loadings. For that purpose, in an explicit finite element code, the X-FEM with only discontinuous enrichment is used coupled with level sets to represent the crack geometry. We show on a complex example that the commonly used Hamilton-Jacobi based level set updating algorithm lacks robustness and numerical efficiency to model such types of problems. To circumvent this, we introduce a simple geometric updating algorithm that does not involve any equation solving, and is therefore numerically cheap. The robustness of this updating algorithm is demonstrated on several virtual propagation examples. Finally common benchmark used in the literature as well as a complex experiment involving the dynamic propagation of a non-planar 3D crack under impact loading are used to demonstrate the efficiency of the approach.

This paper is devoted to the modeling of crack propagation under impact loadings in thick shells composed of metallic materials using X-FEM. The proposed thick shell element is based on the existing Q4 gamma 24 4-node shell element for fast transient loadings that is enriched in the present work using X-FEM. The shell is considered to be always cut by a through the thickness crack. This element is hence enriched only with jump Heaviside functions on all degrees of freedom (displacements as well as rotations). The mass matrix corresponding to all added DOF is simply a copy of the usual continuous DOF diagonal mass matrix. The crack is discretized explicitly with a simple 1D mesh that lives on the shell's mid-surface and independently of the finite element mesh. Plasticity as well as stress field used for crack propagation criterion is evaluated using 5 Simpson points across the thickness. The crack propagation criterion is based on the measure of an equivalent stress at the crack tip and can predict both tensile and shear driven fracture as well as transitions between those two regimes. Comparisons with elastoplastic crack propagation experiments involving fracture under transient loadings show that the method is able to reproduce experimental fracture quite well.

SummaryWe propose a method to couple smoothed particle hydrodynamics and finite elements methods for nonlinear transient fluid–structure interaction simulations by adopting different time‐steps depending on the fluid or solid sub‐domains. These developments were motivated by the need to simulate highly non‐linear and sudden phenomena requiring the use of explicit time integrators on both sub‐domains (explicit Newmark for the solid and Runge–Kutta 2 for the fluid). However, due to critical time‐step required for the stability of the explicit time integrators in, it becomes important to be able to integrate each sub‐domain with a different time‐step while respecting the features that a previously developed mono time‐step coupling algorithm offered. For this matter, a dual‐Schur decomposition method originally proposed for structural dynamics was considered, allowing to couple time integrators of the Newmark family with different time‐steps with the use of Lagrange multipliers. Copyright © 2016 John Wiley & Sons, Ltd.

In this study, visco-hyperelastic Landau's model, which is widely used in acoustical physic field, is introduced into a finite element formulation. It is designed to model the nonlinear behaviour of finite amplitude shear waves in soft solids, typically, in biological tissues. This law is used in finite element models based on elastography, experiments reported in Jacob et al, the simulations results show a good agreement with the experimental study: It is observed in both that a plane shear wave generates only odd harmonics and a nonplane wave generates both odd and even harmonics in the spectral domain. In the second part, a parametric study is performed to analyse the influence of different factors on the generation of odd harmonics of plane wave. A quantitative relation is fitted between the odd harmonic amplitudes and the non-linear elastic parameter of Landau's model, which provides a practical guideline to identify the non-linearity of homogeneous tissues using elastography experiment.

New computational approach for hydrogen leakage with wall crack propagation problem was conducted by using a hybrid of the coupled particle and Eulerian methods. This computational method provides useful safety information for predicting crack propagation and hydrogen leakage in pressure vessels as an important part of assessing hydrogen as an energy vector. The present computational analysis procedures consisted of two main parts. The first part was crack propagation analysis of a thin square plate, which simulated the wall of a high-pressure hydrogen vessel by using a particle method. The crack propagation was analyzed in high-pressure tank walls under two different types of initial conditions, and in both cases, the direction of crack propagation was freely determined by the direction of the stress field. This confirms the superiority of particle methods for modeling destructive phenomena. After the crack propagation analysis, the particle location and coordinate data of the barrier wall were converted to Euler mesh data. The geometric data of particle location were fitted to Euler numerical space, which was used for simulating high-pressure hydrogen leakage into air at atmospheric pressure. The differences and features of hydrogen diffusion during hydrogen leakage were analyzed for two types of wall data and two types of boundary conditions, as a result, the effect of wall boundaries on the hydrogen concentration distribution was computationally predicted.

SummaryThis paper describes a selective mass scaling method which is designed for the analysis of wave propagation problems in nearly incompressible materials. The incompressibility of materials leads to a high value of the compressional wave speed, which makes the time step extremely small in explicit time integration method. The proposed selective mass scaling method selects the eigenfrequencies related to volumetric deformation modes to decrease them, while it keeps the shear eigenmodes unchanged. This makes the time step no longer limited by the compressional wave speed but by the shear wave speed. A significant reduction of CPU time is obtained with a good accuracy for transient problems in small strains on free or largely prestressed media. Copyright © 2016 John Wiley & Sons, Ltd.

SummaryThe hyper‐reduced‐order model (HROM) is proposed for the thermal calculation with a constant moving thermal load. Firstly, the constant velocity transient process is simplified to a steady‐state process in the moving frame. Secondly, the control volume is determined by the temperature rate, and the thermal equilibrium equation in the moving frame is derived by introducing an advective term containing the loading velocity. Thirdly, the HROM is performed on the control volume with a moving frame formulation. This HROM has been applied to the thermal loading on brick and ring disk specimens with a CPU gain of the order of 7 (107). In addition, two strategies are proposed for the HROM to improve its precision. Moreover, the high efficiency and high accuracy are kept for the parametric studies on thermal conductivity and amplitude of heat flux based on the developed HROM. Copyright © 2016 John Wiley & Sons, Ltd.

The aim of this work is to understand the erosion mechanism caused by repeated water droplets impingement on a metallic structure, and then perform numerical simulations of the damage. When a high velocity water droplet with small diameter impacts a rigid surface, interaction is driven by inertial effects. Upon impact, the "water-hammer" pressure appears by inertial effect at the center of the contact though the maximum pressure occurs on the envelope of the contact area. Lateral jetting occurs by compression when the wave front travelling inside droplet overtakes the contact area. Concerning the structure, erosion is due to fatigue cracking. First, material grains are weakened during an "incubation" phase. After a large number of impacts, micro-cracks emerge and lead to ejection or fracture of grains, what is called "amplification" phase. Numerical simulation including rigid solid allows to locate the most loaded zones of the area, by observing the pressure and mainly the impulse. A 2-way coupling computation with fluid-structure interaction at macroscopic scale allows to confirm the fatigue-based mechanism by observing the hydrostatic stress. Finally, erosion program developed with Dang Van criterion provides the location of the most eroded zones of the structure during a loading cycle. They locate at the edge of jetting zone, which shows the influence of microjets in the erosion mechanism.

This paper is dedicated to creep buckling predictions. Thin walled cylinders having an aspect ratio of one are subjected to an uniform external pressure. The material is a special type of nickel which "creeps" at ambient temperature. The material parameters for the creep law are identified from experimental results. The creep failure experiments are described and corresponding failure times are given. The paper then compares three alternatives of finite element modeling of the experiments (3D Shell with integration through the thickness with a periodic or non periodic initial imperfection are compared with COMU quasi axi-symmetric imperfect shell element). These 3 modeling show consistent predictions. The simulation time is a hundred times faster with the COMU model. It is shown that the prediction of failure time of these experiments is extremely sensitive to the initial imperfection amplitude. The effect of creep law modeling is also important. Finally a parametric analysis on different types of cylinders is given: some general trends are proposed for this type of delicate predictions. (C) 2017 Elsevier Ltd. All rights reserved.

Objective: Validation of a numerical method to compute arterial deformations under the insertion of an “extra-siff” guidewire during Endovascular Repair of Abdominal Aortic Aneurysm. Methods: We propose the validation of a previously developed simulation method. The model is calibrated using anatomical hypothesis and intraoperative observations. Simulation results are blindly evaluated against 3-D imaging data acquired during the surgical procedure on 28 patients, based on the predicted position of the intraoperative guidewire. Results: Simulation was successfully conducted on the 28 patients. The mean position error given by the Modified Hausdorff Distance for the 28 cases was 3.8 ± 1.9 mm, which demonstrates very good results for most of the cases. Conclusion: The work reported here shows that numerical simulation can predict some rather large variations in the vascular geometry due to tools insertion, for a wide variety of aorto-iliac morphologies. This is a new step toward clinically applicable mechanical simulation. Significance: Validation on 3-D intraoperative data on a large number of cases—robustness on adverse anatomies.

The objective of this paper is to show, in a specific case, the importance of modeling adhesive forces when simulating the bouncing of very small particles impacting a substrate at high speed. The implementation of this model into a fast-dynamics SPH code is described. Taking the example of an impacted elastic cylinder, we show that the adhesive forces, which are surface forces, play a significant role only if the particles are sufficiently small. The effect of the choice of the type of interaction law in the cohesive zone is studied and some conclusions on the relevance of the modeling of the adhesive forces for fast-dynamics impacts are drawn. Then, the adhesion model is used to simulate the Cold Spray process. An aluminum particle is projected against a substrate made of the same material at a velocity ranging from 200 to 1000m⋅s−1. We study the effects of the various modeling assumptions on the final result: bouncing or sticking. Increasingly complex models are considered. At a 200m⋅s−1 impact velocity, elastic behavior is assumed, the substrate being simply supported at its base and supplied with absorbing boundaries. The same absorbing boundaries are also used for all the other simulations. Then, plasticity is introduced and the impact velocity is increased up to 1000m⋅s−1. At the highest velocities, the resulting strains are very significant. The calculations show that if the adhesion model is appropriately chosen, it is possible to reproduce the experimental observations: the particles stick to the substrate in a range of impact velocities surrounded by two velocity ranges in which the particles bounce.

A new adhesion model for numerical simulation of single particle impact in the context of Cold Spray is introduced. As in other studies, cohesive forces are put between the particle and substrate to account for adhesion. In this study however, the forces are put only when a local physical criterion is met. The physical phenomenon most often attributed to Cold Spray adhesion is a shear stress instability. The Johnson-Cook material law is used with a shear damage softening law to enable strong localization at the interface without the need for an extremely fine mesh. This localization is then detected as a drop in local yield stress value by the algorithm, which then implements a local cohesive force. The evolution of this cohesive force is defined by an energy dissipative cohesive model, using a surface adhesion energy as a material parameter. Each cohesive link is broken once all its associated surface energy is dissipated. A criterion on the damage value is also used to break a cohesive bond prematurely, to account for the effect of erosion at higher speeds. This model is found to reproduce the Cold Spray-like adhesion behavior with observed critical and maximum speeds.

Multiscale methods and homogenization techniques are usually compared to full field simulations. The accuracy of the full field simulations is well controlled in the linear elastic regime and for small strain. With non-linear behavior, large strain or multi-axial strain states the comprehension is hampered by the lack of experimental results. In this study, the way to enforce the microscopic boundary conditions from the macroscopic scale is investigated by comparison to experimental results. A series of tests has been carried out on a model multiscale structure over which the displacement field is captured at microscopic and macroscopic scales. These experimental results allow to analyze the results of different homogenization methods such as classical or higher order ones. The study focuses and exhibits different conclusions about the unit cells with periodic or non-periodic kinematics.

This article deals with the development of a multiaxial "plasticity" criterion for the simulation of the macroscopic behavior of light closed-cell foams. The paper proposes a numerical methodology for the determination of the mechanical macroscopic properties given the geometry of the cells (whose walls are assumed to be thin) and the properties of the bulk material. The focus is on foams with relative densities ranging from 0.0526 to 0.1525. The bulk material is assumed to be isotropic with perfectly plastic behavior. We consider tetrakaidecahedron cells having three planes of symmetry in three orthogonal directions. As expected for a material having a cubic symmetry, one observes that the elastic homogenized material is fully described by three parameters (E*, V*, G*) and not only two as for the isotropic bulk material (E, v). We propose a formula which, starting from only a knowledge of the two elastic properties and density of the bulk material, leads to the three macroscopic elastic properties of the thin-wall regular tetrakaidecahedral foam. Their yield and failure strengths in tension, compression and shear are also calculated. Two types of macroscopic behavior can be clearly identified.The first type characterizes foams made of a high-yield-strength bulk material: the foam's macroscopic behavior is determined mainly by buckling of the cell walls.The second type applies when the bulk material has a low yield strength. In that case, yielding of the cell walls is the main failure mechanism. A loading surface of the Wang and Pan form is proposed for all these cases, both in the early nonlinear stage and at ultimate failure. Lastly the effect of irregularity of the geometries on the load surface is presented for the two previous extreme cases. It is observed that these irregularities play a crucial role in tensile case for the lightest foams having the highest yield strength.It is interesting to note that such a loading surface also leads to a good approximation of the "yield" strength obtained experimentally for both open-cell foams Combaz et al. (2010, 2011) and closed-cell foams Wang and Pan (2006). (C) 2015 Elsevier Ltd. All rights reserved.

We propose a non-intrusive numerical coupling method for transient fluid-structure interaction (FSI) problems simulated by means of different discretization methods: smoothed particle hydrodynamics (SPH) and finite element (FE) methods for the fluid and the solid sub-domains, respectively. As a partitioned coupling method, the present algorithm can ensure a zero interface energy during the whole period of numerical simulation, even in the presence of large interface motion. In other words, the time integrations of the two sub-domains (second order Runge–Kutta scheme for fluid and Newmark integrator for solid) are synchronized. Thanks to this energy-conserving feature, one can preserve the minimal order of accuracy in time and the numerical stability of the FSI simulations, which are validated with a 1D and a 2D trivial numerical test cases. Additionally, some other 2D FSI simulations involving large interface motion have also been carried out with the proposed SPH–FE coupling method. Finally, an example of aquaplaning problem is given in order to show the feasibility of such coupling method in multi-dimensional applications with complicated structural geometries.

"Estimation of clinically relevant indicators for EVAR using patient-specific finite element simulation." Computer Methods in Biomechanics and Biomedical Engineering, 18(sup1), pp. 1950–1951

The time integration procedure selected in computational structural dynamics must possess at least the stability and accuracy properties required for the convergence to the exact solution. Other desired properties are the unconditional stability for linear namics, second-order of accuracy, high frequency dissipation capabilities, self-starting, no overshoot, one step method and no more than one set of implicit equations to be solved for each time step (single-step-single-solve format). In linear dynamics, the stability is classically assessed by a spectral study of the amplification matrix, whereas physical energy bounds are preferred in nonlinear dynamics. Popular a-schemes (HHT-o, WBZ-o, CH-a) are second-order accurate and provides numerical dissipation for spurious high frequencies due to the finite element discretization. To go beyond the standard approach based on the same time integration scheme (homogeneous time integration scheme) and the same time step for all the finite elements of the mesh (synchronous time integration), the purpose of this paper is to describe a general methodology for building Heterogeneous (different time integration schemes such as Newmark or a-schemes) Asynchronous (different time steps) Time Integrators (HATI) for computational dynamics. The key point for building the HATI methods is to cancel the interface pseudo-energy as introduced by Hughes in the so-called energy method employed for proving the stability of implicit-explicit algorithms in its pioneer works on heterogeneous time integrators. By canceling the pseudo-energy at the interface between subdomains and assuming a linear time variation of the Lagrange multipliers at the coarse time scale, the HATI method, called BCG-macro method, iS derived. It can handle any dissipative a-schemes (HHT-a, WBZ-a, CH-a), while preserving the second-order of accuracy when adopting different time steps. In addition to the energy argument (cancelation of the interface pseudo-energy), the stability and order oft accuracy is proved by the spectral study of the amplification matrix.

L'elastographie transitoire par ultrasons est une methode non-invasive pour determiner la rigidite des tissus mous basee sur la propagation d'ondes de cisaillement. La simulation par elements finis de cette technologie pourrait permettre une meilleure comprehension de certains resultats experimentaux et l'etude des effets de differents parametres. Cependant, la simulation de la propagation des ondes est rendue difficile par la quasi-incompressibilite des tissus mous. Dans ce travail, une methode de pas de temps fractionne est introduite pour resoudre ce probleme.