Native arteriovenous fistula placement in three patients after implantation of a left ventricular assist device with non‐pulsatile blood flow

Patients with left ventricular assist device have an increased risk for postoperative acute kidney injury and long‐term requirement of dialysis. As a chronic access for dialysis, native arteriovenous fistulae are uncommon options due to suspected maturation failure. We present three patients who received successful arteriovenous fistulae placement after left ventricular assist device implantation with assisted long term patency.     

A cumulative damage model for fatigue life estimation of high‐strength steels in high‐cycle and very‐high‐cycle fatigue regimes

A cumulative fatigue damage model is presented to estimate fatigue life for high‐strength steels in high‐cycle and very‐high‐cycle fatigue regimes with fish‐eye mode failure, and a simple formula is obtained. The model takes into account the inclusion size, fine granular area (FGA) size, and tensile strength of materials. Then, the ‘equivalent crack growth rate’ of FGA is proposed. The model is used to estimate the fatigue life and equivalent crack growth rate for a bearing steel (GCr15) of present investigation and four high‐strength steels in the literature. The equivalent crack growth rate of FGA is calculated to be of the order of magnitude of 10^?14–10^?11 m/cycle. The estimated results accord well with the present experimental results and prior predictions and experimental results in the literature. Moreover, the effect of inclusion size on fatigue life is discussed. It is indicated that the inclusion size has an important influence on the fatigue life, and the effect is related to the relative size of inclusion for FGA. For the inclusion size close to the FGA size, the former has a substantial effect on the fatigue life. While for the relatively large value of FGA size to inclusion size, it has little effect on the fatigue life.     

Prediction of apparent properties with uncertain material parameters using high‐order fictitious domain methods and PGD model reduction

This contribution presents a numerical strategy to evaluate the effective properties of image‐based microstructures in the case of random material properties. The method relies on three points: (1) a high‐order fictitious domain method; (2) an accurate spectral stochastic model; and (3) an efficient model‐reduction method based on the proper generalized decomposition in order to decrease the computational cost introduced by the stochastic model. A feedback procedure is proposed for an automatic estimation of the random effective properties with a given confidence. Numerical verifications highlight the convergence properties of the method for both deterministic and stochastic models. The method is finally applied to a real 3D bone microstructure where the empirical probability density function of the effective behaviour could be obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

A nonparametric probabilistic approach for quantifying uncertainties in low‐dimensional and high‐dimensional nonlinear models

A nonparametric probabilistic approach for modeling uncertainties in projection‐based, nonlinear, reduced‐order models is presented. When experimental data are available, this approach can also quantify uncertainties in the associated high‐dimensional models. The main underlying idea is twofold. First, to substitute the deterministic reduced‐order basis (ROB) with a stochastic counterpart. Second, to construct the probability measure of the stochastic reduced‐order basis (SROB) on a subset of a compact Stiefel manifold in order to preserve some important properties of a ROB. The stochastic modeling is performed so that the probability distribution of the constructed SROB depends on a small number of hyperparameters. These are determined by solving a reduced‐order statistical inverse problem. The mathematical properties of this novel approach for quantifying model uncertainties are analyzed through theoretical developments and numerical simulations. Its potential is demonstrated through several example problems from computational structural dynamics. Copyright © 2016 John Wiley & Sons, Ltd.     

A multilevel projection‐based model order reduction framework for nonlinear dynamic multiscale problems in structural and solid mechanics

A reduction/hyper reduction framework is presented for dramatically accelerating the solution of nonlinear dynamic multiscale problems in structural and solid mechanics. At each scale, the dimensionality of the governing equations is reduced using the method of snapshots for proper orthogonal decomposition, and computational efficiency is achieved for the evaluation of the nonlinear reduced‐order terms using a carefully designed configuration of the energy conserving sampling and weighting method. Periodic boundary conditions at the microscales are treated as linear multipoint constraints and reduced via projection onto the span of a basis formed from the singular value decomposition of Lagrange multiplier snapshots. Most importantly, information is efficiently transmitted between the scales without incurring high‐dimensional operations. In this proposed proper orthogonal decomposition–energy conserving sampling and weighting nonlinear model reduction framework, training is performed in two steps. First, a microscale hyper reduced‐order model is constructed in situ, or using a mesh coarsening strategy, in order to achieve significant speedups even in non‐parametric settings. Next, a classical offline–online training approach is performed to build a parametric hyper reduced‐order macroscale model, which completes the construction of a fully hyper reduced‐order parametric multiscale model capable of fast and accurate multiscale simulations. A notable feature of this computational framework is the minimization, at the macroscale level, of the cost of the offline training using the in situ or coarsely trained hyper reduced‐order microscale model to accelerate snapshot acquisition. The effectiveness of the proposed hyper reduction framework at accelerating the solution of nonlinear dynamic multiscale problems is demonstrated for two problems in structural and solid mechanics. Speedup factors as high as five orders of magnitude are shown to be achievable. Copyright © 2017 John Wiley & Sons, Ltd.     

Matched interface and boundary (MIB) for the implementation of boundary conditions in high‐order central finite differences

High‐order central finite difference schemes encounter great difficulties in implementing complex boundary conditions. This paper introduces the matched interface and boundary (MIB) method as a novel boundary scheme to treat various general boundary conditions in arbitrarily high‐order central finite difference schemes. To attain arbitrarily high order, the MIB method accurately extends the solution beyond the boundary by repeatedly enforcing only the original set of boundary conditions. The proposed approach is extensively validated via boundary value problems, initial‐boundary value problems, eigenvalue problems, and high‐order differential equations. Successful implementations are given to not only Dirichlet, Neumann, and Robin boundary conditions, but also more general ones, such as multiple boundary conditions in high‐order differential equations and time‐dependent boundary conditions in evolution equations. Detailed stability analysis of the MIB method is carried out. The MIB method is shown to be able to deliver high‐order accuracy, while maintaining the same or similar stability conditions of the standard high‐order central difference approximations. The application of the proposed MIB method to the boundary treatment of other non‐standard high‐order methods is also considered. Copyright © 2008 John Wiley & Sons, Ltd.     

Using Krylov‐Padé model order reduction for accelerating design optimization of structures and vibrations in the frequency domain

In many engineering problems, the behavior of dynamical systems depends on physical parameters. In design optimization, these parameters are determined so that an objective function is minimized. For applications in vibrations and structures, the objective function depends on the frequency response function over a given frequency range, and we optimize it in the parameter space. Because of the large size of the system, numerical optimization is expensive. In this paper, we propose the combination of Quasi‐Newton type line search optimization methods and Krylov‐Padé type algebraic model order reduction techniques to speed up numerical optimization of dynamical systems. We prove that Krylov‐Padé type model order reduction allows for fast evaluation of the objective function and its gradient, thanks to the moment matching property for both the objective function and the derivatives towards the parameters. We show that reduced models for the frequency alone lead to significant speed ups. In addition, we show that reduced models valid for both the frequency range and a line in the parameter space can further reduce the optimization time. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparison between the modal identification method and the POD‐Galerkin method for model reduction in nonlinear diffusive systems

This paper presents a comparison between the modal identification method (MIM) and the proper orthogonal decomposition‐Galerkin (POD‐G) method for model reduction. An example of application on a nonlinear diffusive system is used to illustrate the study. The study shows that in both methods, the state formulation of the nonlinear diffusive equation may be similar. However, the ideas behind both methods are completely different. The considered example shows that, for both methods, reducing the order up to 99.5% gives enough accuracy to simulate the dynamic of the original system. It is also seen in this example that the reduced model given through the MIM are slightly faster and more accurate than the ones given through the POD‐G method. Copyright © 2006 John Wiley & Sons, Ltd.     

Non‐reflecting boundary conditions for acoustic propagation in ducts with acoustic treatment and mean flow

We consider a time‐harmonic acoustic scattering problem in a 2D infinite waveguide with walls covered with an absorbing material, in the presence of a mean flow assumed uniform far from the source. To make this problem suitable for a finite element analysis, the infinite domain is truncated. This paper concerns the derivation of a non‐reflecting boundary condition on the artificial boundary by means of a Dirichlet‐to‐Neumann (DtN) map based on a modal decomposition. Compared with the hard‐walled guide case, several difficulties are raised by the presence of both the liner and the mean flow. In particular, acoustic modes are no longer orthogonal and behave asymptotically like the modes of a soft‐walled guide. However, an accurate approximation of the DtN map can be derived using some bi‐orthogonality relations, valid asymptotically for high‐order modes. Numerical validations show the efficiency of the method. The influence of the liner with or without mean flow is illustrated. Copyright © 2011 John Wiley & Sons, Ltd.     

Study based on the analysis of valence electron structure for adiabatic shear sensitivity of 30CrMnMo and C45E4 steel in process of high‐speed penetration

In this paper, the influence of valence electron structure parameters on the adiabatic shearing sensitivity has been studied for two grade steels (30CrMnMo and C45E4) as a function of covalent pair number and lattice electron number by empirical electron theory of solids and molecules in high‐speed penetration process. The research shows that the adiabatic shearing sensitivity increases with the increase of the covalent electron pair number n_A, decreases with the increase of the lattice electron number n_l. The n_A of each structure unit in 30CrMnMo steel is larger than that in C45E4steel, the n_l of each structure unit in 30CrMnMo steel is smaller than that in C45E4steel. Therefore, the adiabatic shearing sensitivity is higher for 30CrMnMo targets damaged by adiabatic shear failure, and yet C45E4 targets were damaged by ductile fracture without any adiabatic shear band. The basis can be provided for appropriately selecting and designing materials with different adiabatic shearing sensitivity by studying the specific alloy elements on the influence of adiabatic shearing sensitivity in valence electron structure level.     

A coupled BEM and arbitrary Lagrangian–Eulerian FEM model for the solution of two‐dimensional laminar flows in external flow fields

This paper describes a new computational model developed to solve two‐dimensional incompressible viscous flow problems in external flow fields. The model based on the Navier–Stokes equations in primitive variables is able to solve the infinite boundary value problems by extracting the boundary effects on a specified finite computational domain, using the pressure projection method. The external flow field is simulated using the boundary element method by solving a pressure Poisson equation that assumes the pressure as zero at the infinite boundary. The momentum equation of the flow motion is solved using the three‐step finite element method. The arbitrary Lagrangian–Eulerian method is incorporated into the model, to solve the moving boundary problems. The present model is applied to simulate various external flow problems like flow across circular cylinder, acceleration and deceleration of the circular cylinder moving in a still fluid and vibration of the circular cylinder induced by the vortex shedding. The simulation results are found to be very reasonable and satisfactory. Copyright © 2001 John Wiley & Sons, Ltd.     

An integrated,finite element‐based process model for the analysis of flow,heat transfer,and solidification in a continuous slab caster

An integrated, finite element‐based process model is presented for the prediction of full three‐dimensional flow, heat transfer, and solidification occurring in a continuous caster. Described in detail are the basic models for the analysis of turbulent flow and heat transfer in the liquid steel zone, in the zone of mixture of the liquid steel and solidified steel, and in the solidified zone. Then, the models are integrated to form a process model which can take into account the strong interdependence between the heat transfer behaviour and the flow behaviour. The capability of the process model to reveal the detailed aspects of turbulent flow, heat transfer, and solidification occurring in a continuous caster is demonstrated through a series of process simulations. Copyright © 2003 John Wiley & Sons, Ltd.