pinecone/core-2020-05-10-deduplication huggingface dataset:
Two-scale computational modelling of water flow in unsaturated soils containing irregular-shaped inclusions

The focus of this paper is two-dimensional computational modelling of water flow in unsaturated soils consisting of weakly conductive disconnected inclusions embedded in a highly conductive connected matrix. When the inclusions are small, a two-scale Richards’ equation-based model has been proposed in the literature taking the form of an equation with effective parameters governing the macroscopic flow coupled with a microscopic equation, defined at each point in the macroscopic domain, governing the flow in the inclusions. This paper is devoted to a number of advances in the numerical implementation of this model. Namely, by treating the micro-scale as a two-dimensional problem, our solution approach based on a control volume finite element method can be applied to irregular inclusion geometries, and, if necessary, modified to account for additional phenomena (e.g. imposing the macroscopic gradient on the micro-scale via a linear approximation of the macroscopic variable along the microscopic boundary). This is achieved with the help of an exponential integrator for advancing the solution in time. This time integration method completely avoids generation of the Jacobian matrix of the system and hence eases the computation when solving the two-scale model in a completely coupled manner. Numerical simulations are presented for a two-dimensional infiltration problem
Nonintrusive coupling of 3D and 2D laminated composite models based on
  finite element 3D recovery

In order to simulate the mechanical behavior of large structures assembled
from thin composite panels, we propose a coupling technique which substitutes
local 3D models for the global plate model in the critical zones where plate
modeling is inadequate. The transition from 3D to 2D is based on stress and
displacement distributions associated with Saint-Venant problems which are
precalculated automatically for a simple 3D cell. The hybrid plate/3D model is
obtained after convergence of a series of iterations between a global plate
model of the structure and localized 3D models of the critical zones. This
technique is nonintrusive because the global calculations can be carried out
using commercial software. Evaluation tests show that convergence is fast and
that the resulting hybrid model is very close to a full 3D model
A sub‒domain smoothed Galerkin method for solid mechanics problems

A sub‒domain smoothed Galerkin method is proposed to integrate the advantages of mesh‒free Galerkin method and FEM. Arbitrarily shaped sub‒domains are predefined in problems domain with mesh‒free nodes. In each sub‒domain, based on mesh‒free Galerkin weak formulation, the local discrete equation can be obtained by using the moving Kriging interpolation, which is similar to the discretization of the high‒order finite elements. Strain smoothing technique is subsequently applied to the nodal integration of sub‒domain by dividing the sub‒domain into several smoothing cells. Moreover, condensation of DOF can also be introduced into the local discrete equations to improve the computational efficiency. The global governing equations of present method are obtained on the basis of the scheme of FEM by assembling all local discrete equations of the sub‒domains. The mesh‒free properties of Galerkin method are retained in each sub‒domain. Several 2D elastic problems have been solved on the basis of this newly proposed method to validate its computational performance. These numerical examples proved that the newly proposed sub‒domain smoothed Galerkin method is a robust technique to solve solid mechanics problems based on its characteristics of high computational efficiency, good accuracy, and convergence
A Fourier-series-based virtual fields method for the identification of 2-D stiffness distributions

This is the peer reviewed version of the  article, which has been published in final form at http://dx.doi.org/10.1002/nme.4665. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The virtual fields method (VFM) is a powerful technique for the calculation of spatial distributions of material properties from experimentally determined displacement fields. A Fourier-series-based extension to the VFM (the F-VFM) is presented here, in which the unknown stiffness distribution is parameterised in the spatial frequency domain rather than in the spatial domain as used in the classical VFM.We present in this paper the theory of the F-VFM for the case of elastic isotropic thin structures with known boundary conditions. An efficient numerical algorithm based on the two-dimensional Fast Fourier Transform (FFT) is presented, which reduces the computation time by three to four orders of magnitude compared with a direct implementation of the F-VFM for typical experimental dataset sizes. Artefacts specific to the F-VFM (ring- ing at the highest spatial frequency near to modulus discontinuities) can be largely removed through the use of appropriate filtering strategies. Reconstruction of stiffness distributions with the F-VFM has been vali- dated on three stiffness distribution scenarios under varying levels of noise in the input displacement fields. Robust reconstructions are achieved even when the displacement noise is higher than in typical experimental field
Efficient uncertainty propagation for network multiphysics systems

We consider a multiphysics system with multiple component models coupled
together through network coupling interfaces, i.e., a handful of scalars. If
each component model contains uncertainties represented by a set of parameters,
a straightfoward uncertainty quantification (UQ) study would collect all
uncertainties into a single set and treat the multiphysics model as a black
box. Such an approach ignores the rich structure of the multiphysics system,
and the combined space of uncertainties can have a large dimension that
prohibits the use of polynomial surrogate models. We propose an intrusive
methodology that exploits the structure of the network coupled multiphysics
system to efficiently construct a polynomial surrogate of the model output as a
function of uncertain inputs. Using a nonlinear elimination strategy, we treat
the solution as a composite function: the model outputs are functions of the
coupling terms which are functions of the uncertain parameters. The composite
structure allows us to construct and employ a reduced polynomial basis that
depends on the coupling terms; the basis can be constructed with many fewer
system solves than the naive approach, which results in substantial
computational savings. We demonstrate the method on an idealized model of a
nuclear reactor
Multi-level Modelling of Plastic Anisotropy of Aluminium Alloys Using Crystal Plasticity Models and Advanced Yield Functions

<p>The hood, doors and other panels of a car can be made by aluminium sheets, through complex forming operations. Design of forming processes requires trustable models and simulations.</p><p>Forming properties are different in different directions. There are two principle ways to describe this plastic anisotropy of metals. The first one is the continuum theories for materials. The flow properties in various directions are described by the yield function. It is a parametric function calibrated by experimental tests. Unfortunately only a few mechanical tests can be directly used.</p><p>The second approach takes into account that metals consist of many small crystals. The properties of each crystal are determined by crystal planes, but crystals are rotated in many directions. The crystal models either resolve all the details of thousands of crystals in a small volume element, requiring huge computer capacity, or simplified statistical models can be applied. In both cases the models are much more demanding than continuum models. In practice these models can be used to perform virtual experiments for calibration of continuum models.</p><p>In his PhD work Kai Zhang (kai.zhang@ntnu.no) implemented and tested both type of models. More efficient numerical algorithms for computer simulations were developed and programmed for the detailed crystal plasticity approach. Three different cases were investigated experimentally. In one of the cases it was found that even for the detailed computer implementation the predictions could not replace experiments for design purposes. A combination of real and virtual experiments was recommended for calibration. For the other two cases the virtual experiments could be trusted.</p><p>It was found that the best statistical models, that are more than thousand times faster, can replace detailed simulations of the crystal structure with high accuracy.</p>PhD i materialteknologiPhD in Materials Science and Engineerin
Classical and all-floating FETI methods for the simulation of arterial
  tissues

High-resolution and anatomically realistic computer models of biological soft
tissues play a significant role in the understanding of the function of
cardiovascular components in health and disease. However, the computational
effort to handle fine grids to resolve the geometries as well as sophisticated
tissue models is very challenging. One possibility to derive a strongly
scalable parallel solution algorithm is to consider finite element tearing and
interconnecting (FETI) methods. In this study we propose and investigate the
application of FETI methods to simulate the elastic behavior of biological soft
tissues. As one particular example we choose the artery which is - as most
other biological tissues - characterized by anisotropic and nonlinear material
properties. We compare two specific approaches of FETI methods, classical and
all-floating, and investigate the numerical behavior of different
preconditioning techniques. In comparison to classical FETI, the all-floating
approach has not only advantages concerning the implementation but in many
cases also concerning the convergence of the global iterative solution method.
This behavior is illustrated with numerical examples. We present results of
linear elastic simulations to show convergence rates, as expected from the
theory, and results from the more sophisticated nonlinear case where we apply a
well-known anisotropic model to the realistic geometry of an artery. Although
the FETI methods have a great applicability on artery simulations we will also
discuss some limitations concerning the dependence on material parameters.Comment: 29 page
An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems

13 pagesInternational audienceInspired by recent analyses of the finite element heterogeneous multiscale method and the reduced basis technique for nonlinear problems, we present a simple and concise finite element algorithm for the reliable and efficient resolution of elliptic or parabolic multiscale problems of nonmonotone type. Solutions of appropriate cell problems on sampling domains are selected by a greedy algorithm in an offline stage and assembled in a reduced basis (RB). This RB is then used in an online stage to solve two-scale problems at a computational cost comparable to the single-scale case. Both the offline and the online cost are independent of the smallest scale in the physical problem. The performance and accuracy of the algorithm are illustrated on 2D and 3D stationary and evolutionary nonlinear multiscale problems
Numerical assessment of the macroscopic strength criterion of reinforced soils using semidefinite programming

International audienceThe macroscopic strength properties of reinforced soils, regarded as periodic composite materials, are investigated by means of a fem-based formulation of both the static and kinematic approaches of yield design applied to the reinforced soil's unit cell. Since the reinforced soil's individual constituents obey a 3D Mohr-Coulomb strength condition, such a numerical problem can be treated trough an optimization procedure using semidefinite programming. The whole numerical procedure is applied to the derivation of both lower bound and upper bound estimates to the macroscopic yield surface of a soil reinforced either by columnar inclusions (stone columns) or a double array of trenches (cross trench reinforcement). The so-obtained results highlight the efficiency of the proposed numerical method
Phase-field modeling and simulation of fracture in brittle materials with strongly anisotropic surface energy

Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations.Peer ReviewedPostprint (author’s final draft
A dissection solver with kernel detection for symmetric finite element matrices on shared memory computers

International audienceA direct solver for symmetric sparse matrices from finite element problems is presented. The solver is supposed to work as a local solver of domain decomposition methods for hybrid parallelization on cluster systems of multi-core CPUs, and then it is required to run on shared memory computers and to have an ability of kernel detection. Symmetric pivoting with a given threshold factorizes a matrix with a decomposition introduced by a nested bisection and selects suspicious null pivots from the threshold. The Schur complement constructed from the suspicious null pivots is examined by a factorization with 1x1 and 2x2 pivoting and by a robust kernel detection algorithm based on measurement of residuals with orthogonal projections onto supposed image spaces. A static data structure from the nested bisection and a block sub-structure for Schur complements at all bisection-levels can use level 3 BLAS routines efficiently. Asynchronous task execution for each block can reduce idle time of processors drastically and as a result, the solver has high parallel efficiency. Competitive performance of the developed solver to Intel Pardiso on shared memory computers is shown by numerical experiments
Cell-centered finite volume discretizations for deformable porous media

The development of cell-centered finite volume discretizations for deformation is motivated by the desire for a compatible approach with the discretization of fluid flow in deformable porous media. We express the conservation of momentum in the finite volume sense, and introduce three approximations methods for the cell-face stresses. The discretization method is developed for general grids in one to three spatial dimensions, and leads to a global discrete system of equations for the displacement vector in each cell, after which the stresses are calculated based on a local expression. The method allows for anisotropic, heterogeneous and discontinuous coefficients.

The novel finite volume discretization is justified through numerical validation tests, designed to investigate classical challenges in discretization of mechanical equations. In particular our examples explore the stability with respect to the Poisson ratio and spatial discontinuities in the material parameters. For applications, logically Cartesian grids are prevailing, and we also explore the performance on perturbations on such grids, as well as on unstructured grids. For reference, comparison is made in all cases with the lowest-order Lagrangian finite elements, and the finite volume methods proposed herein is comparable for approximating displacement, and is superior for approximating stresses
A parameterized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics

We present a parameterized-background data-weak (PBDW) formulation of the variational data assimilation (state estimation) problem for systems modeled by partial differential equations. The main contributions are a constrained optimization weak framework informed by the notion of experimentally observable spaces; a priori and a posteriori error estimates for the field and associated linear-functional outputs; weak greedy construction of prior (background) spaces associated with an underlying potentially high-dimensional parametric manifold; stability-informed choice of observation functionals and related sensor locations; and finally, output prediction from the optimality saddle in O(M[superscript 3) operations, where M is the number of experimental observations. We present results for a synthetic Helmholtz acoustics model problem to illustrate the elements of the methodology and confirm the numerical properties suggested by the theory. To conclude, we consider a physical raised-box acoustic resonator chamber: we integrate the PBDW methodology and a Robotic Observation Platform to achieve real-time in situ state estimation of the time-harmonic pressure field; we demonstrate the considerable improvement in prediction provided by the integration of a best-knowledge model and experimental observations; we extract, even from these results with real data, the numerical trends indicated by the theoretical convergence and stability analyses.Fondation Sciences Mathematiques de ParisUnited States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Grant FA9550-09-1-0613)United States. Office of Naval Research (Grant N00014-11-1-0713)SUTD-MIT International Design Centr
A fast weakly intrusive multiscale method in explicit dynamics

This paper presents new developments on a weakly intrusive approach for the simplified implementation of space and time multiscale methods within an explicit dynamics software. The 'substitution' method proposed in previous works allows to take advantage of a global coarse model, typically used in an industrial context, running separate, refined in space and in time, local analyses only where needed. The proposed technique is iterative, but the explicit character of the method allows to perform the global computation only once per global time step, while a repeated solution is required for the small local problems only. Nevertheless, a desirable goal is to reach convergence with a reduced number of iterations. To this purpose, we propose here a new iterative algorithm based on an improved interface inertia operator. The new operator exploits a combined property of velocity Hermite time interpolation on the interface and of the central difference integration scheme, allowing the consistent upscaling of interface inertia contributions from the lower scale. This property is exploited to construct an improved mass matrix operator for the interface coupling, allowing to significantly enhance the convergence rate. The efficiency and robustness of the procedure are demonstrated through several examples of growing complexity. Copyright {\copyright} 2014 John Wiley \& Sons, Ltd
Multifidelity approaches for optimization under uncertainty

It is important to design robust and reliable systems by accounting for uncertainty and variability in the design process. However, performing optimization in this setting can be computationally expensive, requiring many evaluations of the numerical model to compute statistics of the system performance at every optimization iteration. This paper proposes a multifidelity approach to optimization under uncertainty that makes use of inexpensive, low-fidelity models to provide approximate information about the expensive, high-fidelity model. The multifidelity estimator is developed based on the control variate method to reduce the computational cost of achieving a specified mean square error in the statistic estimate. The method optimally allocates the computational load between the two models based on their relative evaluation cost and the strength of the correlation between them. This paper also develops an information reuse estimator that exploits the autocorrelation structure of the high-fidelity model in the design space to reduce the cost of repeatedly estimating statistics during the course of optimization. Finally, a combined estimator incorporates the features of both the multifidelity estimator and the information reuse estimator. The methods demonstrate 90% computational savings in an acoustic horn robust optimization example and practical design turnaround time in a robust wing optimization problem.United States. Air Force Office of Scientific Research. Multidisciplinary University Research Initiative (Uncertainty Quantification Grant FA9550-09-0613
Lower bound static approach for the yield design of thick plates

International audienceThe present work addresses the lower bound limit analysis (or yield design) of thick plates under shear-bending interaction. Equilibrium finite elements are used to discretize the bending moment and the shear force fields. Different strength criteria, formulated in the five-dimensional space of bending moment and shear force, are considered, one of them taking into account the interaction between bending and shear resistances. The criteria are chosen to be sufficiently simple so that the resulting optimization problem can be formulated as a second-order cone programming problem, which is solved by the dedicated solver MOSEK. The efficiency of the proposed finite element is illustrated by means of numerical examples on different plate geometries, for which the thin plate solutions as well as the pure shear solutions are accurately obtained as two different limit cases of the plate slenderness ratio. In particular, the proposed element exhibits a good behavior in the thin plate limit
Computational homogenization of soft matter friction: Isogeometric framework and elastic boundary layers

Cataloged from PDF version of article.A computational contact homogenization framework is established for the modeling and simulation of soft
matter friction. The main challenges toward the realization of the framework are (1) the establishment of
a frictional contact algorithm that displays an optimal combination of accuracy, efficiency, and robustness
and plays a central role in (2) the construction of a micromechanical contact test within which samples
of arbitrary size may be embedded and which is not restricted to a single deformable body. The former
challenge is addressed through the extension of mixed variational formulations of contact mechanics to
a mortar-based isogeometric setting where the augmented Lagrangian approach serves as the constraint
enforcement method. The latter challenge is addressed through the concept of periodic embedding, with
which a periodically replicated C1-continuous interface topography is realized across which not only pending
but also ensuing contact among simulation cells will be automatically captured. Two-dimensional
and three-dimensional investigations with unilateral/bilateral periodic/random roughness on two elastic
micromechanical samples demonstrate the overall framework and the nature of the macroscopic frictional
response. Copyright © 2014 John Wiley & Sons, Ltd