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An energy‐based isotropic elastoplastic damage model is developed for investigating the elastoplastic damage responses and stress–strain relationships of nano‐silica incorporated concrete. The formulation employs a multiscale micromechanical framework to determine the effective elastic properties of composites at different scales. The stress–strain constitutive relation is derived by splitting the strain tensor into "elastic‐damage" and "plastic‐damage" parts while introducing the homogenized free potential energy function and the undamaged potential energy function. The elastoplastic damage response of the material is further characterized by elastic–plastic‐damage coupling. To construct realistic 3D three‐phase concrete mesostructures in numerical simulations, this paper introduces an encapsulation placement method that avoids particle overlap checking when placing aggregates. This methodology allows adjustments for the aggregate compactness as needed and enhances computational efficiency in concrete mesostructure construction. The numerical results of the modeling show good agreement with the experimental values in the open literature. Further, the influence of nano‐silica addition contents and ITZ (interfacial transition zone) thicknesses on the elastoplastic damage response of nano‐silica incorporated concrete are quantitatively and qualitatively investigated for the optimization of nano‐silica incorporated cementitious composites. The proposed model facilitates simulating and optimizing the mechanical characteristics of nano‐silica incorporated concrete and enhances the computational efficiency of 3D concrete modeling with the introduced encapsulation placement method. [ABSTRACT FROM AUTHOR]

The influence of the dilatancy angle on the safety of a single anchored sheet pile wall Safety factors and utilization ratios can be determined using the Finite Element Method by reducing the shear strength (SRFEM). However, there is an influence of the applied dilatancy angle ψ ${\psi }$. In the investigated example of a single anchored sheet pile wall, in both purely frictional and cohesive soils, deviations of up to 11 % occur between ψ=0 ${\psi = 0}$ and ψ=ϕ ${\psi = \varphi }$. In addition to the SRFEM, safety factors and utilization ratios can also be determined using a Finite Element implementation of the collapse theorems (FELA). The computed upper and lower bounds represent limits for the results of the SRFEM only for an associated flow rule (ψ=ϕ ${\psi = \varphi }$). Nevertheless, a material with a non‐associated flow rule (ψ<ϕ ${\psi \char60 \varphi }$) can be approximately accounted for by using reduced shear strength parameters according to Davis. In the investigated example, deviations of up to 9 % occur between FELA and SRFEM. Moreover, comparisons with currently used conventional methods, referred to as Limit Equilibrium Analyses (LEA), are of interest. In this paper, the verification in the lower failure plane is investigated with three different safety definitions, where reduced shear strength parameters according to Davis are used for ψ<ϕ ${\psi \char60 \varphi }$ , as for the FELA. Safety factors and utilization ratios determined by means of conventional methods are qualitatively comparable to the results of the SRFEM. Quantitatively, however, the deviations in this example are in the order of 10 %, even for mechanically comparable LEA with realistic dilatancy angles. For LEA with a safety definition according to Kranz, these deviations are partially significantly larger. [ABSTRACT FROM AUTHOR]

Copyright of Geotechnik is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we propose to extend the staggered cell‐centered finite element method (SCFEM) on general meshes for the Stokes problems with variable viscosity (possibly discontinuous). The scheme is cell‐centered in the sense that the solution can be computed by cell unknowns of the primal mesh and the dual mesh for the velocity and the pressure, respectively, where the velocity is approximated by piecewise linear functions (ℙ1$$ {\mathrm{\mathbb{P}}}^1 $$) on the triangular dual submesh, and the pressure is approximated by piecewise constant functions (ℙ0$$ {\mathrm{\mathbb{P}}}^0 $$) on the dual mesh. In order to get the local continuity of numerical stresses across the interfaces, the scheme gives the auxiliary edge unknowns interpolated by the multipoint stress approximation technique. Its stability and convergence properties are presented in the rigorous theoretical framework. Numerical results are carried out to highlight accuracy and computational cost. [ABSTRACT FROM AUTHOR]

In this paper, we analyze a divergence‐free finite element method to solve a fluid–structure interaction spectral problem in the three‐dimensional case. The unknowns of the resulting formulation are the fluid and solid displacements and the fluid pressure on the interface separating both media. The resulting mixed eigenvalue problem is approximated by using appropriate basis of the divergence‐free lowest order Raviart–Thomas elements for the fluid, piecewise linear elements for the solid and piecewise constant elements for the interface pressure. It is proved that eigenvalues and eigenfunctions are correctly approximated and some numerical results are reported in order to assess the performance of the method. [ABSTRACT FROM AUTHOR]

Singular stress fields represent a concern during the design of mechanical connections as they could trigger cracks within the joint, under low‐amplitude loads, generating failures and reducing its service life. Appropriate design plans should therefore be implemented to produce more reliable apparatus. This paper explores the effects induced by both the presence and the absence of stress singularities on the very high cycle fatigue (VHCF) performance of adhesively bonded butt joints through analytical, numerical, and experimental methods. Analytical models defined the conditions to design a stress singularity‐free joint, global–local finite element descriptions studied the stress distributions in detail, and then VHCF experiments extracted S–N outcomes. The suitability of this approach is confirmed numerically while a substantial increase of the joint life is experimentally observed if the singularity is removed. Nonetheless, a non‐singular configuration leads to higher scatter data compared to the original specimen configuration. Highlights: Stress singularities trigger cracks within the joint under fatigue loads.The inverse formulation of the Bogy determinant removes the stress singularity.Singularity‐free joints have higher fatigue life with relevant scatter. [ABSTRACT FROM AUTHOR]

Copyright of Geotechnik is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper, we numerically study porosity problems with three different dissipation mechanisms. The root behavior is analyzed for each case. Then, by using the finite element method and the Newmark‐β scheme, fully discrete approximations are introduced and some numerical results are described to show the energy evolution depending on the viscosity coefficient. [ABSTRACT FROM AUTHOR]

The expansion of the Shanghai metro grid leads to a growing demand for underground stations. This paper studies the seismic performance of a typical cross interchange station in soft soil, combining shaking table testing and numerical modeling. The cross interchange station is composed of a three‐storey section, rigidly connected to a perpendicular two‐storey section, leading to an abrupt change of stiffness in the conjunction area. A series of 1 g shaking table tests are conducted, using synthetic model soil (a mixture of sand and sawdust) and granular concrete with galvanized steel wires to model the soil‐structure system. The experimental results are then used as a benchmark, allowing for validation of a 3D finite element (FE) model. The validated FE model is shown to compare adequately well with the shaking table tests and is subsequently used to indirectly extrapolate the results to prototype scale. The combined experimental and numerical study allows deriving insights on the dynamic response of cross interchange stations. A key conclusion is that the abrupt change of stiffness at the conjunction area leads to concentration of racking deformation at the bottom storey. This leads to significant stress concentrations on the station sidewall in the same area, revealing the increased seismic vulnerability due to the induced stiffness discontinuity. Seismic damage can be avoided by increasing the reinforcement ratio in such critical locations or by introducing deformable joints. [ABSTRACT FROM AUTHOR]

Abstract: We consider the elastic wave equation in three dimensions with transparent boundary conditions on a bounded, not necessarily convex domain. This leads to a coupling of the elastic wave equation in the interior domain with time‐dependent boundary integral equations. This coupled system is to be solved numerically. The major theoretical result of this paper shows a coercivity property of a Calderón operator for the elastic Helmholtz equation, which is valid for all complex frequencies in a half‐plane. Combining Laplace transform and energy techniques, this coercivity in the frequency domain is used to prove the stability of the fully discrete numerical method in the time domain. The considered numerical method couples finite elements and explicit leapfrog time‐stepping in the interior with boundary elements and convolution quadrature on the boundary. We present convergent error bounds for the semi‐ and full discretization. [ABSTRACT FROM AUTHOR]

Summary: Hierarchical model reduction is intended to solve efficiently partial differential equations in domains with a geometrically dominant direction. In many engineering applications, these problems are often reduced to 1‐dimensional differential systems. This guarantees computational efficiency yet dumps local accuracy as nonaxial dynamics are dropped. Hierarchical model reduction recovers the secondary components of the dynamics of interest with a combination of different discretization techniques, following up a natural separation of variables. The dominant direction is generally solved by the finite element method or isogeometric analysis to guarantee flexibility, while the transverse components are solved by spectral methods, to guarantee a small number of degrees of freedom. By judiciously selecting the number of transverse modes, the method has been proven to improve significantly the accuracy of purely 1‐dimensional solvers, with great computational efficiency. A Cartesian framework has been used so far both in slab domains and cylindrical pipes (including arteries) mapped to Cartesian reference domains. In this paper, we investigate the alternative use of a polar coordinates system for the transverse dynamics in circular or elliptical pipes. This seems a natural choice for applications like computational hemodynamics. In spite of this, the selection of a basis function set for the transverse dynamics is troublesome. As pointed out in the literature—even for simple elliptical problems—there is no “best” basis available. In this paper, we perform an extensive investigation of hierarchical model reduction in polar coordinates to discuss different possible choices for the transverse basis, pointing out pros and cons of the polar coordinate system. [ABSTRACT FROM AUTHOR]

Summary: We introduce a time stepping technique using the momentum as dependent variable to solve incompressible multiphase problems. The main advantage of this approach is that the mass matrix is time‐independent making this technique suitable for spectral methods. A level set method is applied to reconstruct the fluid properties such as density. We also introduce a stabilization method using an entropy‐viscosity technique and a compression technique to limit the flattening of the level set function. We extend our algorithm to immiscible conducting fluids by coupling the incompressible Navier‐Stokes and the Maxwell equations. We validate the proposed algorithm against analytical and manufactured solutions. Results on test cases such as Newton's bucket problem and a variation thereof are provided. Surface tension effects are tested on benchmark problems involving bubbles. A numerical simulation of a phenomenon related to the industrial production of aluminium is presented at the end of the paper. [ABSTRACT FROM AUTHOR]

In this paper, we give some new properties of the presented asynchronous algorithms of theta scheme combined with finite elements methods (App. Math. Comp., 217 (2011), 6443-6450) for an evolutionary implicit 2-sided obstacle problem to prove the existence and uniqueness of the discrete solution. Furthermore, an error estimate on the uniform norm is given. [ABSTRACT FROM AUTHOR]

The greater arithmetic intensity of high‐order finite element discretizations makes them attractive for implementation on next‐generation hardware, but assembly of high‐order finite element operators as matrices is prohibitively expensive. As a result, the development of general algebraic solvers for such operators has been an open research challenge. Fast matrix‐free application of high‐order operators has received significant attention in the literature in the context of Poisson‐type problems, but preconditioners and solvers for inverting more general operators are not very well‐developed. In this paper, we consider the problem of preconditioning a definite Maxwell operator at high polynomial order without assembling a matrix. We show that given efficient preconditioners for high‐order H1 finite element problems on the same mesh, efficient H(curl) preconditioners can be constructed in an auxiliary space framework. We demonstrate the resulting preconditioners in a practical setting with tensor‐product basis functions on an unstructured mesh of quadrilaterals. Our approach uses a sparsified H1 solver constructed on a low‐order mesh of the nodal points of the underlying high‐order space, and we show that the resulting H(curl) preconditioner is effective at very high polynomial orders for two‐dimensional model problems with complicated geometry, varying piecewise constant coefficients, and curved elements. The resulting preconditioner scales with nearly optimal O(pd + 1) floating point operation count and optimal O(pd) memory transfer requirements, outperforming existing Maxwell preconditioners in the high‐order regime. [ABSTRACT FROM AUTHOR]

One of the reasons for the success of the finite element method in Solid Mechanics, among other Applied Sciences, is its versatility to deal with bodies of arbitrary shape. In case the problem at hand is modeled by second‐order partial differential equations with Dirichlet conditions prescribed on a curvilinear boundary, method's isoparametric version for meshes consisting of curved triangles or tetrahedra has been mostly employed to recover the optimal approximation properties known to hold for polygonal or polyhedral domains and methods of order greater than one based on standard straight‐edged elements. However, besides algebraic and geometric inconveniences, the isoparametric technique is limited in scope, since its extension to degrees of freedom other than function values is not straightforward. In previous work the author introduced a simple alternative, which bypasses the above drawbacks without eroding qualitative approximation properties. Among other advantages, it can do without curved elements and is based only on polynomial Algebra. The purpose of this paper is two‐fold: On the one hand the mathematical foundations of this method are established, in the framework of a model Poisson problem solved with Lagrange elements; in particular optimal‐rate error estimates both in energy norm and in the mean‐square sense are demonstrated and a numerical comparison with the isoparametric technique is carried out. On the other hand this study is extended to Hermite elements with normal‐derivative degrees of freedom for solving the equation modeling the bending of clamped thin plates with a curvilinear edge. [ABSTRACT FROM AUTHOR]

The complex transverse water proton magnetization subject to diffusion‐encoding magnetic field gradient pulses in a heterogeneous medium such as brain tissue can be modeled by the Bloch‐Torrey partial differential equation. The spatial integral of the solution of this equation in realistic geometry provides a gold‐standard reference model for the diffusion MRI signal arising from different tissue micro‐structures of interest. A closed form representation of this reference diffusion MRI signal called matrix formalism, which makes explicit the link between the Laplace eigenvalues and eigenfunctions of the biological cell and its diffusion MRI signal, was derived 20 years ago. In addition, once the Laplace eigendecomposition has been computed and saved, the diffusion MRI signal can be calculated for arbitrary diffusion‐encoding sequences and b‐values at negligible additional cost. Up to now, this representation, though mathematically elegant, has not been often used as a practical model of the diffusion MRI signal, due to the difficulties of calculating the Laplace eigendecomposition in complicated geometries. In this paper, we present a simulation framework that we have implemented inside the MATLAB‐based diffusion MRI simulator SpinDoctor that efficiently computes the matrix formalism representation for realistic neurons using the finite element method. We show that the matrix formalism representation requires a few hundred eigenmodes to match the reference signal computed by solving the Bloch‐Torrey equation when the cell geometry originates from realistic neurons. As expected, the number of eigenmodes required to match the reference signal increases with smaller diffusion time and higher b‐values. We also convert the eigenvalues to a length scale and illustrate the link between the length scale and the oscillation frequency of the eigenmode in the cell geometry. We give the transformation that links the Laplace eigenfunctions to the eigenfunctions of the Bloch‐Torrey operator and compute the Bloch‐Torrey eigenfunctions and eigenvalues. This work is another step in bringing advanced mathematical tools and numerical method development to the simulation and modeling of diffusion MRI. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to analyze the convergence and regularity of our proposed algorithm of the finite element methods coupled with a theta time discretization scheme for evolutionary Hamilton-Jacobi-Bellman equations with linear source terms with respect to the Dirichlet boundary conditions (Appl. Math. Comput., 262 (2015), 42.55 ). Also, an optimal error estimate with an asymptotic behavior in uniform norm is given. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper we present a sufficient and necessary condition to ensure the ellipticity of the bilinear form which is related to the one-equation coupling of finite and boundary element methods to solve a scalar free space transmission problem for a second order uniform elliptic partial differential equation in the case of general Lipschitz interfaces. This condition relates the minimal eigenvalue of the coefficient matrix in the bounded interior domain to the contraction constant of the shifted double layer integral operator which reflects the shape of the interface. This paper extends and improves earlier results [12] on sufficient conditions, but now includes also necessary conditions. Numerical examples confirm the theoretical results on the sharpeness of the presented estimates. [ABSTRACT FROM AUTHOR]

SUMMARY The simulation of the behavior of structures with uncertain properties is a challenging issue, because it requires suitable probabilistic models and adequate numerical tools. Nowadays, it is possible to perform probabilistic investigations of the structural performance, which take into account a space-variant uncertainty characterization of the structures. Given a structural solver and the probabilistic models, the reliability analysis of the structural response depends on the continuous random fields approximation, which is carried out by means of a finite set of random variables. The paper analyzes the main aspects of discretization in the case of 2D problems. The combination of the well-known Karhunen-Loève series expansion, the finite element method and the hierarchical matrices approach is proposed in the paper. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The strain energy density (SED) averaged over a structural volume allows to assess the fracture and fatigue behaviour of cracked components under mixed‐mode loadings. To rapidly estimate the averaged SED, two approaches have been previously proposed: (a) the direct approach; (b) the peak stress method (PSM) and nodal stress (NS) approach. In this paper, the nodal displacement (ND) approach is presented to rapidly estimate the averaged SED from the nodal displacements by FE analyses. This method combines the advantages of all previous approaches, ie, the use of coarse meshes able to capture the contributions of both stress intensity factors (SIFs) and higher order terms, without requiring geometrical modelling of the control volume. To validate the method, cracked plates and cracked bars under mixed‐mode loadings have been analysed. The averaged SED values estimated by the ND approach agree with those calculated by the direct approach, within a range of applicability. [ABSTRACT FROM AUTHOR]

Smart composite materials fabricated through 4D‐printing methods are attracting enormous research attention for their ability to respond (typically deform) under external stimuli. The design process for such smart materials requires iterations of finite‐element simulations that are computationally expensive. Recently, researchers have tried replacing numerical simulations with machine learning (ML) models to predict the output at a much higher speed. However, there exist very few studies that explore the model algorithm's expressive capacity and analyze the physical interpretation based on the problem. This paper focuses on using ML to predict the nonlinear deformation behavior of digital materials. Various problem construction approaches and model performance are compared and discussed. It is shown that clustering the materials helps improve the generalization of training and models that treat material features as an array of numbers still face difficulties to provide accurate predictions. Inspired by modern computer vision technologies, convolutional kernels outperform other methods by recognizing the material distribution patterns. The performance is further enhanced after reconstructing the regression problem into classification. Moreover, high‐level material design information can be extracted from the model through a sensitivity analysis. This framework may greatly improve the response prediction and design process for 4D‐printed smart materials. [ABSTRACT FROM AUTHOR]

In this paper, we numerically analyse a phase‐lag model with two temperatures which arises in the heat conduction theory. The model is written as a linear partial differential equation of third order in time. The variational formulation, written in terms of the thermal acceleration, leads to a linear variational equation, for which we recall an existence and uniqueness result and an energy decay property. Then, using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives, fully discrete approximations are introduced. A discrete stability property is proved, and a priori error estimates are obtained, from which the linear convergence of the approximation is derived. Finally, some one‐dimensional numerical simulations are described to demonstrate the accuracy of the approximation and the behaviour of the solution. [ABSTRACT FROM AUTHOR]

In this paper, we extend the approach developed by the author for the standard finite element method in the L∞‐norm of the noncoercive variational inequalities (VI) (Numer Funct Anal Optim.2015;36:1107‐1121.) to impulse control quasi‐variational inequality (QVI). We derive the optimal error estimate, combining the so‐called Bensoussan‐Lions Algorithm and the concept of subsolutions for VIs. [ABSTRACT FROM AUTHOR]

This paper presents a newly developed extension of the linear Generalised Beam Theory (GBT) formulation for members with circular axis, previously developed by the authors, to the linear stability analysis case. This extension incorporates the classic GBT kinematic assumptions, which ensure efficiency without sacrificing its accuracy. The finite element implementation of the proposed formulation makes it possible to calculate bifurcation loads and associated buckling mode shapes of members with circular axis and arbitrary flat‐walled cross‐sections, undergoing global‐distortional‐local deformation, with great accuracy and computational savings (with respect to refined shell finite element models). Moreover, it is shown that the remarkable GBT modal decomposition features, stemming from the fact that the kinematic description of the beam is based on a superposition of structurally meaningful cross‐section deformation modes, enable an in‐depth insight into the nature of the buckling modes in curved members. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the analysis and implementation of robust finite element approximation methods for mixed formulations of linear elasticity problems where the elastic body is almost incompressible. Several alternative a posteriori error estimators for the energy norm of the finite element error are introduced and analysed. We establish upper and lower bounds for the energy error in terms of these error estimators and show that the constants in the bounds are independent of the Lamé coefficients: The proposed estimators are robust in the incompressible limit. We also consider the requirement for pressure stabilisation when using lowest‐order conforming approximation. Computational results are presented that validate the theoretical estimates. The software used to generate these results is available online. [ABSTRACT FROM AUTHOR]

Summary: This paper presents a computational method able to effectively model both the simultaneous processes typically observed in backward erosion piping, ie, the pipe tip propagation and the conduit cross‐section enlargement. The numerical method is based on the novel formulation of a problem of localized erosion along a line propagating in a multidimensional porous medium. In this line, a conduit with evolving transverse size is embedded, which conveys a multiphase flow. The two systems, porous medium and pipe, are bridged by exchange terms of multiphase fluid mass and by a shared fluid pressure field. On the contrary, different fields are considered to describe flows, which are assumed as Darcian in the porous medium and turbulent in the conduit. These two flows drive pipe propagation and enlargement, respectively, as modeled by means of proper erosion kinetic laws. The corresponding numerical formulation is based on the combination between one‐ and multidimensional finite elements, to model the erosion conduit and the porous medium, respectively. Several simulations are proposed to demonstrate the ability of the proposed approach in reproducing available experimental data of real‐scale tests on levees. Our results point out the crucial role played by the combined influence of pipe propagation and enlargement, as well as of three‐dimensional (3D) effects. We also assess the mesh independence of the proposed numerical solution, particularly as concerns the calculated pipe propagation history. [ABSTRACT FROM AUTHOR]

Fatigue damage in materials is considered to be the effect of material degradation, and the dispersion in fatigue life is attributed to variability in microstructure. This paper presents a numerical model to simulate fatigue damage evolution using continuum damage mechanics to characterize material degradation. An explicit microstructure topology representation is achieved using Voronoi tessellations. Unlike conventional models which use a scalar approximation for damage, this model treats the damage variable as an anisotropic tensor. The model is used to simulate tensile fatigue failure in thin steel specimen. The fatigue life estimations from the model compares well with published experimental results. The results predict a high variability in fatigue life that is characteristic of metals and alloys, as compared with the existing isotropic damage models available in the literature. The model was also used to study the influence of material inhomogeneity on fatigue life dispersion. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we present residual‐based error estimators applied to the Stokes problem. Implicit and explicit error estimators are developed to predict the error of the numerical solution obtained by a stabilized finite element formulation. Both error estimators arise from the variational multiscale framework, in which the variational form is split into coarse scales (finite element method solution) and fine scales (committed error). This leads to a local problem set on each element in which the error and the residuals are involved. The different ways of linking the error to the residuals produce two error estimators. Local and global error estimates measured in the H1‐seminorm are provided for triangles and quadrilaterals. As an application, using the local error estimates, an adaptive mesh refinement strategy is implemented in order to optimize the computational resources. We present implicit and explicit error estimators for the Stokes equations. The aim is to estimate the error in the FEM simulation to assess the quality of the numerical solution. Using the variational multiscale framework, a local problem is set on the elements in which the error is linked to the residuals. The implicit and explicit error estimators emerge from approximations to this problem. An adaptive mesh refinement strategy is carried out taking the local error estimates. [ABSTRACT FROM AUTHOR]

Modern software's allow computers to perform symbolic calculations in addition to simple numerical computations for which they were originally designed. This fact opens new possibilities in numerical simulation. In this paper a finite element implementation using the commercial software Wolfram Mathematica is used to solve a plane stress elasticity problem. The code adaptability from the provided examples to more challenging problems can easily be performed using the present code. Numerical examples with post‐processing illustrates the new tool and its flexibility. It has been proven in this study the feasibility of Wolfram Mathematica in learning and programming finite element methods for the solution of two‐dimensional problems in elasticity. [ABSTRACT FROM AUTHOR]

Monitoring of the Theodor Heuss bridge in Düsseldorf – part 2: modelling and model improvements for a measurement‐based fatigue analysis Due to calculated deficits in the fatigue bearing capacity of the orthotropic deck, a monitoring system was installed at the Theodor Heuss bridge to measure strains at significant locations for one year. Part 1 of this paper describes the monitoring system and findings on the load‐bearing behavior resulting from the measured data. This second part follows with data‐based fatigue evaluations and the lifetime prediction. The basis of the evaluations is a structural model, which is calibrated based on two load tests in summer and winter. From this, transfer factors are derived, taking into account different load positions, which compensate the distance of the measuring points to the decisive design points. In this way, the measured stress range histograms are transformed into representative load spectra, which are finally used for the lifetime prediction. The evaluations show that further load reserves are available for most components and that a significant improvement is achieved compared to the recalculation. Only the corners of the floor beam cut‐out (cross girder tooth) still show significant deficits, which are also confirmed by the existing cracks. A decision on the future of the Theodor Heuss bridge, which depends on further factors, is currently pending. [ABSTRACT FROM AUTHOR]

ABSTRACT This paper presents qualitative elastoplastic simulations and analyses of fretting fatigue. Three hardening constitutive models are considered, and their effects on stick-slip conditions and lifetime prediction are compared. The computational analysis consists of the estimation of the shakedown limit cycle and the fatigue prediction using Dang Van or Crossland criterion. A particular configuration, the interaction of a flat pad with rounded corners in contact with a flat substrate made, respectively, of Inconel In718 and Titanium Ti64 alloys, is studied. The shakedown state is analysed using the cyclic and ratcheting equivalent strain concepts already discussed in the literature. In the paper, different fretting maps, based on slip, shakedown and fatigue regimes, are numerically produced and analysed. A new variable, the global slip percentage, is proposed for the characterization of the stick-slip regimes. Analyses of a series of slip maps show that the different hardening models do not introduce significant changes in the stick-slip conditions. Using finite element method simulations combined with fatigue limit criteria (Dang Van and Crossland), fretting fatigue maps are qualitatively reproduced. The main contribution of this work is a comparative discussion on the influence of the hardening models complexity on such maps. [ABSTRACT FROM AUTHOR]

SUMMARY This paper contains results of the three-dimensional full-vectorial finite element (3D FEM) frequency-domain simulations of microring silicon resonators intended for the add/drop multiplexing, switching, and sensor applications. The second-order edge elements are used, and the computational domain is closed using the standard perfectly matched layer. The calculations are performed for add-drop and all-pass configurations in a wide spectral range covering the first and the second telecommunication windows. Although computationally very demanding, the three-dimensional full-vectorial finite element offers designers a feasible and efficient way to design and simulate complex integrated optical components containing microring resonators, especially in the case when the radii of rings are too small to approximate that theories were valid. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY Buckling plays a fundamental role in the design of steel tanks because of the small thicknesses of the walls of this class of structures. The first part of the paper presents a review of this phenomenon for liquid-containing circular cylindrical steel tanks that are fully anchored at the base, considering the different buckling modes and especially the secondary buckling occurring in the top part of the tank. A case study based on a cylindrical tank is then introduced in order to investigate various aspects of dynamic buckling. The finite element model of the case study tank is set-up using the added mass method for fluid modelling. The influence of pre-stress states caused by hydrostatic pressure and self-weight on the natural periods of the structure is first studied and it is found that this influence is very small as far as the global behaviour of the tanks is considered, while it is important for local, shell-type, vibration modes. In the following, the efficiency and sufficiency of different ground motion intensity measures is analysed by means of cloud analysis with a set of 40 recorded accelerograms. In particular, the peak ground displacement has been found being the most efficient and sufficient intensity measure so far as the maximum relative displacement of the tank walls is concerned. Finally, incremental nonlinear time-history analyses are performed considering the case study structure under recorded earthquake ground motions in order to identify the critical buckling loads and to derive fragility curves for the buckling limit state. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Summary: Embankment slopes composed of spatially variable soils have a variety of different failure modes that are affected by the correlation distances of the material properties and the geometry and total length of the slope. This paper examines the reliability of soil slopes for embankments of different length and uses parallel computing to analyse very long embankments (up to 100 times the embankment height) for a clay soil characterised by a spatially varying undrained shear strength. Based on a series of analyses using the 3D random finite element method (RFEM), it is first shown that the reliability of slopes of various length can be efficiently computed by combining simple probability theory with a detailed 3D RFEM analysis of a representative shorter slope of length 10 times the slope height. RFEM predictions of reliability indices for longer slopes are then compared with results obtained using Vanmarcke's (1977a) simplified 3D method and Calle's (1985) extended 2D approach. It is shown that these methods can give significantly different results, depending on the horizontal scale of fluctuation relative to the slope length, with RFEM predicting a lower slope reliability than the Vanmarcke and Calle solutions in all cases. The differences in the solutions are evaluated and attributed to differences in the assumed and computed failure surface geometries. [ABSTRACT FROM AUTHOR]

Summary: Buried pipelines are often constructed in seismic and other geohazard areas, where severe ground deformations may induce severe strains in the pipeline. Calculation of those strains is essential for assessing pipeline integrity, and therefore, the development of efficient models accounting for soil‐pipe interaction is required. The present paper is aiming at developing efficient tools for calculating ground‐induced deformation on buried pipelines, often triggered by earthquake action, in the form of fault rupture, liquefaction‐induced lateral spreading, soil subsidence, or landslide. Soil‐pipe interaction is investigated by using advanced numerical tools, which employ solid elements for the soil, shell elements for the pipe, and account for soil‐pipe interaction, supported by large‐scale experiments. Soil‐pipe interaction in axial and transverse directions is evaluated first, using results from special‐purpose experiments and finite element simulations. The comparison between experimental and numerical results offers valuable information on key material parameters, necessary for accurate simulation of soil‐pipe interaction. Furthermore, reference is made to relevant provisions of design recommendations. Using the finite element models, calibrated from these experiments, pipeline performance at seismic‐fault crossings is analyzed, emphasizing on soil‐pipe interaction effects in the axial direction. The second part refers to full‐scale experiments, performed on a unique testing device. These experiments are modeled with the finite element tools to verify their efficiency in simulating soil‐pipe response under landslide or strike‐slip fault movement. The large‐scale experimental results compare very well with the numerical predictions, verifying the capability of the finite element models for accurate prediction of pipeline response under permanent earthquake‐induced ground deformations. [ABSTRACT FROM AUTHOR]

Summary: In this paper, conserving time‐stepping algorithms for frictionless and full stick friction dynamic contact problems are presented. Time integration algorithms for frictionless and full stick friction dynamic contact problems have been designed to preserve the conservation of key discrete properties satisfied at the continuum level. Energy and energy‐momentum–preserving algorithms for frictionless and full stick friction dynamic contact problems, respectively, have been designed and implemented within the framework of the direct elimination method, avoiding the drawbacks linked to the use of penalty‐based or Lagrange multipliers methods. An assessment of the performance of the resulting formulation is shown in a number of selected and representative numerical examples, under full stick friction and slip frictionless contact conditions. Conservation of key discrete properties exhibited by the time‐stepping algorithm is shown. [ABSTRACT FROM AUTHOR]

This paper introduces a new approach to model cracking processes in large reinforced concrete structures, like dams or nuclear power plants. For these types of structures it is unreasonable, due to calculation time, to explicitly model rebars and steel-concrete bonds. To solve this problem, we developed, in the framework of the finite element method, a probabilistic macroscopic cracking model based on a multiscale simulation strategy: the probabilistic model for (finite) elements of reinforced concrete (PMERC). The PMERC's identification strategy is case-specific because it holds information about the local behavior, obtained in advance via numerical experimentations. This information is then projected to the macroscopic finite element scale via inverse analysis. The numerical experimentations are performed using a validated cracking model allowing a fine description of the cracking processes. The method used in the inverse analysis is inspired from regression (supervised learning) algorithms: data on the local scale--the training data coupled with working knowledge of the mechanical problem--would shape the macroscopic model. Although the identification phase can be relatively time-consuming, the structural simulation is as a result, very fast, leading to a sensitive reduction of the overall computational time. It is proposed a first validation of this multiscale modeling strategy on a reinforced concrete slab-beam subjected to three-point bending. We achieved promising results in terms of global behavior and macrocracking (mainly crack openings), and an important reduction in calculation time--up to 99% reduction! So we believe this is a promising approach to solve bigger and more complex structures in shorter time. [ABSTRACT FROM AUTHOR]

Performance-based design methodology is based on reaching performance objectives that are associated to certain damage conditions. These performance objectives are related to the seismic hazard and to the performance levels. In actual application, reliable tools are required for capturing the evolution of the damage condition as well as for measuring and locating it. Moreover, it is essential to accurately establish the relationship between the damage and the performance levels. This paper shows the application of damage mechanics to performance-based design. A layered damage mechanics-based finite element program is presented with a discussion on modeling for prediction of the response of normal-strength and high-strength concrete columns subjected to cyclic flexural loading and various axial load levels. The damage indices derived from these analyses were used to elaborate several damage charts expressed as a function of drift and displacement ductility. This makes it possible to establish a relationship between the damage state and the performance levels. Results have demonstrated the ability of the damage mechanics modeling to accurately predict the behavior of the specimens tested. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY This paper presents new three-dimensional finite elements with embedded strong discontinuities in the small strain infinitesimal range. The goal is to model localized surfaces of failure in solids, such as cracks at fracture, through enhancements of the finite elements that capture the propagating discontinuities of the displacement field in the element interiors. In this way, such surfaces of discontinuity can be sharply resolved in general meshes not necessarily related to the detailed geometry of the surface, unknown a priori. An important issue is also the consideration of general finite element formulations in the developments (e.g., basic displacement-based, mixed or enhanced assumed strain finite element formulations), as needed to optimally resolve the continuum problem in the bulk. The actual modeling of the discontinuity effects, including the incorporation of the cohesive law defining the discontinuity constitutive response, is carried out at the element level with the proper enhancement of the discrete strain field of the element. The added elemental degrees of freedom approximate the displacement jumps associated with the discontinuity and are defined independently from element to element, thus allowing their static condensation at the element level without affecting the global mechanical problem in terms of the number and topology of the global degrees of freedom. In fact, this global-local structure of the finite element methods developed in this work arises naturally from a multi-scale characterization of these localized solutions, with the discontinuities understood to appear in the small scales, thus leading directly to these computationally efficient numerical methods for their numerical resolution, easily incorporated to an existing finite element code. The focus in this paper is on the development of finite elements incorporating a linear interpolation of the displacement jumps in the general three-dimensional setting. These interpolations are shown to be necessary for hexahedral elements to avoid the so-called stress locking that occurs with simpler constant approximations of the jumps (namely, a spurious transfer of stresses across the discontinuity not allowing its full release and, hence, resulting in an overstiff or locked numerical solution). The design of the new finite elements is accomplished in this work by a direct identification of the separation modes to be incorporated in the discrete strain field of the element, rather than from an assumed discontinuous interpolation of the displacements, assuring with this approach their locking-free response by design. An additional issue addressed in the paper is the geometric characterization and propagation of the discontinuity surfaces in the general three-dimensional setting of interest here. The paper includes a series of numerical simulations illustrating and evaluating the properties of the new finite elements. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Recently the hp version of the finite element method, in which adaptivity occurs in both the size, h, of the elements and in the order, p, of the approximating piecewise polynomials, has received increasing attention. It is desirable to combine this optimal order discretization method with an optimal order algebraic solution method like multigrid. An intriguing notion is to use the values of p as the levels of a multilevel method. In this paper we present such a method, known as hp-multigrid, for high-order finite elements and hp-adaptive grids. We present a survey of the development of p-multigrid and hp-multigrid, define an hp-multigrid algorithm based on the p-hierarchical basis for the p levels and h-hierarchical basis for an h-multigrid solution of the p=1 ‘coarse grid’ equations, and present numerical convergence results using hp-adaptive grids. The numerical results suggest that the method has a convergence rate of \documentclass{article}\usepackage{amssymb}\usepackage{amsbsy}\usepackage[mathscr]{euscript}\footskip=0pc\pagestyle{empty}\begin{document}$\frac{1}{2}$\end{document} for Poisson's equation. Published in 2010 by John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we discuss uniformly stable discretizations and fast solvers for the steady and semi-discrete time-dependent Stokes equations, which will be called the Stokes-like equations. We study two pairs of conforming finite elements that are uniformly accurate with respect to all relevant parameters in the equations, one of which is the Scott–Vogelius (RAIRO Modél. Math. Anal. Numér. 1985; 19:111–143) element and the other of which is the finite element pair by Austin et al. (Numer. Linear Algebra Appl. 2004; 11:115–140). We prove that the finite element pair by Austin, Manteuffel and McCormick is uniformly accurate and we design and analyze the fast and robust solution techniques for the linear algebraic systems arising from the discretizations of the Stokes-like equations as well. Our method is based on the augmented Lagrangian Uzawa iterative methods (Augmented Lagrangian Methods. North-Holland: Amsterdam, 1983) and the multigrid methods designed by Austin et al. (Numer. Linear Algebra Appl. 2004; 11:115–140) for the linear algebraic equations from the discretizations of the differential operator ρ2I-κ2Δ-µ2∇div. We prove our methods are robust with respect to all relevant parameters that appear in the equations and also the mesh size, thereby, achieve the fast and robust methods for the solutions to the Stokes-like equations. In particular, the convergence analysis for the multigrid methods designed by Austin et al., has been posed as an open question (Numer. Linear Algebra Appl. 2004; 11:115–140), which is resolved in this paper. Copyright © 2009 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The paper presents a global time domain simulation of a microwave rectenna studied for wireless energy transfer. The novelty of the work is to take into account both distributed electromagnetic parts of the antenna and the rectifier circuit including lumped elements. From a 3D finite element time domain electromagnetic modelling of the structure an equivalent circuit of the antenna is deduced: the input impedance is obtained as a function of frequency over a broad band. Then a rational approximation gives a corresponding PSPICE representation. The electromotive force induced between the ports of the antenna during the microwave illumination is directly computed from the 3D transient scattering problem. The resulting equivalent circuit of the antenna is finally incorporated into the electronic simulator PSPICE, together with the lumped components of the rectenna (ideal diodes and load). Thus a global non-linear time domain analysis of the whole structure becomes available. The results obtained with the methods presented in the paper are compared with those resulting from other techniques. The approach developed in the work could efficiently improve the design stage of rectennas devoted to microwave power transfer. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we consider domain decomposition preconditioners for a system of linear algebraic equations arising from the p-version of the FEM. We analyse several multi-level preconditioners for the Dirichlet problems in the sub-domains in two and three dimensions. It is proved that the condition number of the preconditioned system is bounded by a constant independent of the polynomial degree. Relations between the p-version of the FEM and the h-version are helpful in the interpretations of the results. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes computationally efficient frequency domain formulations for two well-known multiaxial fatigue failure criteria, namely Matake’s critical plane criterion and Crossland’s criterion. For that purpose, it is shown how fatigue-related variables involved in both criteria can be estimated from the power spectral density matrix of the local stress vector. The finite element model of an example structure is then used to illustrate the application of the proposed frequency domain approaches. It is observed that both frequency domain formulations produce consistent results when compared with those obtained in the time domain from Monte-Carlo simulations of local stress vectors while offering tremendous computer savings. A frequency domain tool indicating whether the principal stress directions do rotate with time or not during the loading at a given location in the structure is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we study, from a numerical point of view, an osseointegrated model depending on the density of the osteogenic cells and osteoblasts and one generic growth factor. The problem is written as a coupled system of nonlinear partial differential equations and an ordinary differential equation. The variational formulation leads to two coupled parabolic nonlinear variational equations. Then, its numerical approximation is introduced by using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives. A priori error estimates are then proved, from which the linear convergence is obtained under suitable additional regularity conditions. Finally, some numerical simulations are presented to show the accuracy of the approximation and the behaviour of the solution. [ABSTRACT FROM AUTHOR]

Mathematical modeling and simulation of fluid-structure interaction problems are in the focus of research already for a longer period. However, taking into account also chemical reactions, leading to structural changes, including changes of mechanical properties of the solid phase, is rather new but for many applications is highly important area. This paper formulates a model system for reactive flow and transport in a vessel system, the penetration of chemical substances into the solid wall. Inside the wall, reactions take place that lead to changes of volume and of the mechanical properties of the wall. Numerical algorithms are developed and used to simulate the dynamics of such a mechano-chemical fluid-structure interaction problem. As a proof of concept scenario, plaque formation in blood vessels is chosen. The arbitrary Lagrangian Eulerian approach (ALE) is chosen to solve the systems numerically. Temporal discretization of the fully coupled monolithic model is accomplished by backward Euler scheme and spatial discretization by stabilized finite elements. The numerical approach is verified by numerical tests, and effective methods to maintain mesh qualities under large deformations are described. For realistic system parameters, the simulations show that the plaque formation in blood vessel is a long-time effect. The time scale of the formation is in the simulation of comparable order as in reality. [ABSTRACT FROM AUTHOR]

A number of methods have been developed for solving the dynamics of saturated porous media. However, most solutions are based on the finite element method, and only a few employ finite differences (FDM). One problem with the FDM is the difficulty in fulfilling the inf-sup (Ladyženskaja-Babuška-Brezzi) condition. This paper explores solutions with the FDM, including the development of new schemes aiming at stabilised formulations. The efficiency, accuracy and stability of several FDM and finite element method algorithms are thoroughly investigated as well. A combination of primary variables from the theory of porous media is considered, including the so-called up and uvp formulations. Six numerical schemes are produced and quantitatively studied. Simulations of 1D and 2D wave propagation problems are performed in order to reveal the advantages and drawbacks of all schemes. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The macroscopic behavior of materials is affected by their inner micro-structure. Elementary considerations based on the arrangement, and the physical and mechanical features of the micro-structure may lead to the formulation of elastoplastic constitutive laws, involving hardening/softening mechanisms and non-associative properties. In order to model the non-linear behavior of micro-structured materials, the classical theory of time-independent multisurface plasticity is herein extended to Cosserat continua. The account for plastic relative strains and curvatures is made by means of a robust quadratic-convergent projection algorithm, specifically formulated for non-associative and hardening/softening plasticity. Some important limitations of the classical implementation of the algorithm for multisurface plasticity prevent its application for any plastic surfaces and loading conditions. These limitations are addressed in this paper, and a robust solution strategy based on the singular value decomposition technique is proposed. The projection algorithm is then implemented into a finite element formulation for Cosserat continua. A specific finite element is considered, developed for micropolar plates. The element is validated through illustrative examples and applications, showing able performance. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The capability to analyze structures under static and dynamic loads is an essential skill for structural engineers. Structural analysis therefore is a key component in civil and architectural engineering education, where analytical methods are traditionally complemented by the use of (commercial) software packages. The latter are often closed source, which may obscure the links to the underlying matrix structural analysis or finite element formulation. To stimulate active, cooperative, and solution‐oriented learning, we developed Stabil, an electronic learning environment implemented as a Matlab toolbox. Stabil has an open structure to elucidate the links between theory and implementation and is presently used throughout the curricula of Civil and Architectural Engineering at KU Leuven. This paper explains the main principles of Stabil and discusses teaching experiences over the past 15 years. Stabil can be downloaded from http://bwk.kuleuven.be/bwm/stabil. [ABSTRACT FROM AUTHOR]

In this paper we focus on a meshfree formulation for the solution of time‐harmonic acoustic scattering problems and verify the stability of the procedure. The sound waves propagate in nonhomogeneous media, giving rise to discontinuities in the gradients of the pressure field across the interfaces between regions of different material properties. Meshfree methods usually do not reproduce accurately the discontinuities in a numerical solution. We overcome this issue by introducing Lagrange multiplier fields defined at the interfaces in order to treat the discontinuities in the gradients of the pressure field. The method does not depend on any kind of adjustable parameter. We show by a numerical study of the applicable inf‐sup conditions that the resulting mixed formulation leads to well‐posed problems. The use of the proposed method is illustrated in the solution of a number of problems of wave propagation through nonhomogeneous media. [ABSTRACT FROM AUTHOR]