pinecone/core-2020-05-10-deduplication huggingface dataset:
Error behaviour in explicit integration algorithms with automatic substepping.

This paper studies the behaviour of the error incurred when numerically integrating the elasto‐plastic mechanical relationships of a constitutive model for soils using an explicit substepping formulation with automatic error control. The correct update of all the variables involved in the numerical integration of the incremental stress–strain relationships is central to the computational performance of the integration scheme, and, although often missed in the literature, all variables (including specific volume) should be explicitly considered in the algorithmic formulation. This is demonstrated in the paper by studying, in the context of the Cam clay formulations for saturated soils, the influence that the updating of the specific volume has on the accuracy of the numerical solution. The fact that the variation of the local error with the size of the integrated strain depends on the order of local accuracy of the numerical method is also used in the paper to propose a simple and powerful strategy to verify the correctness of the implemented mathematical formulation
Overcoming Element Quality Dependence of Finite Elements with Adaptive
  Extended Stencil FEM (AES-FEM)

The finite element methods (FEM) are important techniques in engineering for
solving partial differential equations, but they depend heavily on element
shape quality for stability and good performance. In this paper, we introduce
the Adaptive Extended Stencil Finite Element Method (AES-FEM) as a means for
overcoming this dependence on element shape quality. Our method replaces the
traditional basis functions with a set of generalized Lagrange polynomial (GLP)
basis functions, which we construct using local weighted least-squares
approximations. The method preserves the theoretical framework of FEM, and
allows imposing essential boundary conditions and integrating the stiffness
matrix in the same way as the classical FEM. In addition, AES-FEM can use
higher-degree polynomial basis functions than the classical FEM, while
virtually preserving the sparsity pattern of the stiffness matrix. We describe
the formulation and implementation of AES-FEM, and analyze its consistency and
stability. We present numerical experiments in both 2D and 3D for the Poison
equation and a time-independent convection-diffusion equation. The numerical
results demonstrate that AES-FEM is more accurate than linear FEM, is also more
efficient than linear FEM in terms of error versus runtime, and enables much
better stability and faster convergence of iterative solvers than linear FEM
over poor-quality meshe
Dual-horizon Peridynamics

In this paper we develop a new Peridynamic approach that naturally includes
varying horizon sizes and completely solves the "ghost force" issue. Therefore,
the concept of dual-horizon is introduced to consider the unbalanced
interactions between the particles with different horizon sizes. The present
formulation is proved to fulfill both the balances of linear momentum and
angular momentum. Neither the "partial stress tensor" nor the "`slice"
technique are needed to ameliorate the ghost force issue in \cite{Silling2014}.
The consistency of reaction forces is naturally fulfilled by a unified simple
formulation. The method can be easily implemented to any existing peridynamics
code with minimal changes. A simple adaptive refinement procedure is proposed
minimizing the computational cost. The method is applied here to the three
Peridynamic formulations, namely bond based, ordinary state based and
non-ordinary state based Peridynamics. Both two- and three- dimensional
examples including the Kalthof-Winkler experiment and plate with branching
cracks are tested to demonstrate the capability of the method in solving wave
propagation, fracture and adaptive analysis
Reconstructing displacements from the solution to the periodic Lippmann-Schwinger equation discretized on a uniform grid

International audienceUniform grid solvers of the periodic Lippmann–Schwinger equation have been introduced by Moulinec and Suquet for the numerical homogenization of heterogeneous materials. Based on the fast Fourier transform, these methods use the strain as main unknown and usually do not produce displacement fields. While this is generally not perceived as a restriction for homogenization purposes, some tasks might require kinematically admissible displacement fields. In this paper, we show how the numerical solution to the periodic Lippmann–Schwinger equation can be post-processed to reconstruct a displacement field. Our procedure is general: it applies to any variant of the Moulinec–Suquet solver. The reconstruction is formulated as an auxiliary elastic equilibrium problem of a homogeneous material, which is solved with displacement-based finite elements. Taking advantage of the periodicity, the uniformity of the grid and the homogeneity of the material, the resulting linear system is formulated and solved efficiently in Fourier space. The cost of our procedure is lower than that of one iteration of the Lippmann–Schwinger solver. An application of this post-processing procedure is proposed, in which the reconstructed displacement field is used to compute a rigorous upper bound on the effective shear modulus of some model microstructure. This is the pre-peer reviewed version of the following article: Reconstructing displacements from the solution to the periodic Lippmann–Schwinger equation discretized on a uniform grid, which has been published in final form at 10.1002/nme.5263. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving. Sections 1 (Introduction) and 5 (Numerical results) have been significantly reworked in the published (final) version of this article. The remainder of this article (including Sections 3 and 4 where the method itself is presented) is essentially unchanged
An adaptive cracking particle method for 2D crack propagation.

Computational modelling of fracture has been attempted in the past with a range of numerical approaches including finite element, extended finite element and meshless methods. The cracking particle method (CPM) of Rabczuk is a pragmatic alternative to explicit modelling of crack surfaces in which a crack is represented by a set of cracking particles that can be easily updated when the crack propagates. The change of cracking angle is recorded in discrete segments of broken lines, which makes this methodology suitable to model discontinuous cracks. In this paper, a new CPM is presented that improves on two counts: firstly, crack path curvature modelling is improved by the use of bilinear segments centred at each particle and secondly, efficiency for larger problems is improved via an adaptive process of both refinement and recovery. The system stiffness is calculated and stored in local matrices, so only a small influenced domain should be recalculated for each step while the remainder can be read directly from storage, which greatly reduces the computational expense. The methodology is applied to several 2D crack problems, and good agreement to analytical solutions and previous work is obtained
Hybrid meshing using constrained Delaunay triangulation for viscous flow simulations

In this paper, we present a generalized prismatic hybrid meshing method for viscous flow simulations. One major difficulty in implementing a robust prismatic hybrid meshing tool is to handle boundary layer mesh collisions and normally an extra data structure (e.g. quadtree in 2D and octree in 3D) is required. The proposed method overcomes this difficulty via an heuristic approach and it only relies on Constrained Delaunay Triangulation/Tetrahedralization(CDT). No extra data structures are required. Geometrical reasoning is used to approximate the maximum marching distance of each point by walking through the CDT. This is combined with post-processing of marching vectors and distance and prohibition of multilevel differences to form an automatic and robust mechanism to remove boundary layer mesh collisions. Benefiting from the matureness of CDT techniques, the proposed method is robust, efficient and simple to implement. Its capability is demonstrated by generating quality prismatic hybrid meshes for industrial models with complex geometries. The proposed method is believed to be able considerably reduce the effort to implement a robust hybrid prismatic mesh generator for viscous flow simulations
An interpolation-based fast multipole method for higher order boundary elements on parametric surfaces

In this article, a black-box higher order fast multipole method for solving boundary integral equations on parametric surfaces in three spatial dimensions is proposed. Such piecewise smooth surfaces are the topic of recent studies in isogeometric analysis. Due to the exact surface representation, the rate of convergence of higher order methods is not limited by approximation errors of the surface. An element-wise clustering strategy yields a balanced cluster tree and an efficient numerical integration scheme for the underlying Galerkin method. By performing the interpolation for the fast multipole method directly on the reference domain, the cost complexity in the polynomial degree is reduced by one order. This gain is independent of the application of either (mathcal{H})- or (mathcal{H}^2)-matrices. In fact, several simplifications in the construction of (mathcal{H}^2)-matrices are pointed out, which are a by-product of the surface representation. Extensive numerical examples are provided in order to quantify and qualify the proposed method. In this article, a black-box higher order fast multipole method for solving boundary integral equations on parametric surfaces in three spatial dimensions is proposed. Such piecewise smooth surfaces are the topic of recent studies in isogeometric analysis. Due to the exact surface representation, the rate of convergence of higher order methods is not limited by approximation errors of the surface. An element-wise clustering strategy yields a balanced cluster tree and an efficient numerical integration scheme for the underlying Galerkin method. By performing the interpolation for the fast multipole method directly on the reference domain, the cost complexity in the polynomial degree is reducedby one order. This gain is independent of the application of either H - or H 2- matrices. In fact, several simplificationsin the construction of  H 2 -matrices are pointed out, which are a by-product of the surface representation. Extensive numerical examples are provided in order to quantify and qualify the proposed method
Prediction of apparent properties with uncertain material parameters using high-order fictitious domain methods and PGD model reduction

International audienceThis 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: (i) a high-order fictitious domain method; (ii) an accurate spectral stochastic model and (iii) 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
An extended boundary element method formulation for the direct calculation of the stress intensity factors in fully anisotropic materials.

We propose a formulation for linear elastic fracture mechanics (LEFM) in which the stress intensity factors (SIF) are found directly from the solution vector of an extended boundary element method (XBEM) formulation. The enrichment is embedded in the BEM formulation, rather than adding new degrees of freedom for each enriched node. Therefore, a very limited number of new degrees of freedom is added to the problem, which contributes to preserving the conditioning of the linear system of equations. The Stroh formalism is used to provide BEM fundamental solutions for any degree of anisotropy, and these are used for both conventional and enriched degrees of freedom. Several numerical examples are shown with benchmark solutions to validate the proposed method
A finite element perspective on non-linear FFT-based micromechanical
  simulations

Fourier solvers have become efficient tools to establish structure-property
relations in heterogeneous materials. Introduced as an alternative to the
Finite Element (FE) method, they are based on fixed-point solutions of the
Lippmann-Schwinger type integral equation. Their computational efficiency
results from handling the kernel of this equation by the Fast Fourier Transform
(FFT). However, the kernel is derived from an auxiliary homogeneous linear
problem, which renders the extension of FFT-based schemes to non-linear
problems conceptually difficult. This paper aims to establish a link between
FE- and FFT-based methods, in order to develop a solver applicable to general
history- and time-dependent material models. For this purpose, we follow the
standard steps of the FE method, starting from the weak form, proceeding to the
Galerkin discretization and the numerical quadrature, up to the solution of
non-linear equilibrium equations by an iterative Newton-Krylov solver. No
auxiliary linear problem is thus needed. By analyzing a two-phase laminate with
non-linear elastic, elasto-plastic, and visco-plastic phases, and by
elasto-plastic simulations of a dual-phase steel microstructure, we demonstrate
that the solver exhibits robust convergence. These results are achieved by
re-using the non-linear FE technology, with the potential of further extensions
beyond small-strain inelasticity considered in this paper.Comment: 27 pages, 9 figures, 3 table
Computation of Higher-Order Moments of Generalized Polynomial Chaos
  Expansions

Because of the complexity of fluid flow solvers, non-intrusive uncertainty
quantification techniques have been developed in aerodynamic simulations in
order to compute the quantities of interest required in an optimization
process, for example. The objective function is commonly expressed in terms of
moments of these quantities, such as the mean, standard deviation, or even
higher-order moments. Polynomial surrogate models based on polynomial chaos
expansions have often been implemented in this respect. The original approach
of uncertainty quantification using polynomial chaos is however intrusive. It
is based on a Galerkin-type formulation of the model equations to derive the
governing equations for the polynomial expansion coefficients. Third-order,
indeed fourth-order moments of the polynomials are needed in this analysis.
Besides, both intrusive and non-intrusive approaches call for their computation
provided that higher-order moments of the quantities of interest need be
post-processed. In most applications they are evaluated by Gauss quadratures,
and eventually stored for use throughout the computations. In this paper
analytical formulas are rather considered for the moments of the continuous
polynomials of the Askey scheme, so that they can be evaluated by
quadrature-free procedures instead. Matlab codes have been developed for this
purpose and tested by comparisons with Gauss quadratures
A Flux Conserving Meshfree Method for Conservation Laws

Lack of conservation has been the biggest drawback in meshfree generalized
finite difference methods (GFDMs). In this paper, we present a novel
modification of classical meshfree GFDMs to include local balances which
produce an approximate conservation of numerical fluxes. This numerical flux
conservation is done within the usual moving least squares framework. Unlike
Finite Volume Methods, it is based on locally defined control cells, rather
than a globally defined mesh. We present the application of this method to an
advection diffusion equation and the incompressible Navier - Stokes equations.
Our simulations show that the introduction of flux conservation significantly
reduces the errors in conservation in meshfree GFDMs.Comment: International Journal for Numerical Methods in Engineerin
An adaptive variational Quasicontinuum methodology for lattice networks
  with localized damage

Lattice networks with dissipative interactions can be used to describe the
mechanics of discrete meso-structures of materials such as 3D-printed
structures and foams. This contribution deals with the crack initiation and
propagation in such materials and focuses on an adaptive multiscale approach
that captures the spatially evolving fracture. Lattice networks naturally
incorporate non-locality, large deformations, and dissipative mechanisms taking
place inside fracture zones. Because the physically relevant length scales are
significantly larger than those of individual interactions, discrete models are
computationally expensive. The Quasicontinuum (QC) method is a multiscale
approach specifically constructed for discrete models. This method reduces the
computational cost by fully resolving the underlying lattice only in regions of
interest, while coarsening elsewhere. In this contribution, the (variational)
QC is applied to damageable lattices for engineering-scale predictions. To deal
with the spatially evolving fracture zone, an adaptive scheme is proposed.
Implications induced by the adaptive procedure are discussed from the
energy-consistency point of view, and theoretical considerations are
demonstrated on two examples. The first one serves as a proof of concept,
illustrates the consistency of the adaptive schemes, and presents errors in
energies. The second one demonstrates the performance of the adaptive QC scheme
for a more complex problem.Comment: 39 pages, 17 figures, 1 table, 2 algorithms; small changes after
  revie
Computational material design for acoustic cloaking

A topology optimization technique based on the topological derivative and the level set function is utilized to design/synthesize the micro-structure of a pentamode material for an acoustic cloaking device. The technique provides a micro-structure consisting of a honeycomb lattice composed of needle-like and joint members. The resulting metamaterial shows a highly anisotropic elastic response with effective properties displaying a ratio between bulk and shear moduli of almost 3 orders of magnitude. Furthermore, in accordance with previous works in the literature, it can be asserted that this kind of micro-structure can be realistically fabricated. The adoption of a topology optimization technique as a tool for the inverse design of metamaterials with applications to acoustic cloaking problems is one contribution of this paper. However, the most important achievement refers to the analysis and discussion revealing the key role of the external shape of the prescribed domain where the optimization problem is posed. The efficiency of the designed micro-structure is measured by comparing the scattering wave fields generated by acoustic plane waves impinging on bare and cloaked bodies.Peer ReviewedPostprint (published version
Linear smoothed extended finite element method

The extended finite element method (XFEM) was introduced in 1999 to treat
problems involving discontinuities with no or minimal remeshing through
appropriate enrichment functions. This enables elements to be split by a
discontinuity, strong or weak and hence requires the integration of
discontinuous functions or functions with discontinuous derivatives over
elementary volumes. Moreover, in the case of open surfaces and singularities,
special, usually non-polynomial functions must also be integrated. A variety of
approaches have been proposed to facilitate these special types of numerical
integration, which have been shown to have a large impact on the accuracy and
the convergence of the numerical solution. The smoothed extended finite element
method (SmXFEM) [1], for example, makes numerical integration elegant and
simple by transforming volume integrals into surface integrals. However, it was
reported in [1, 2] that the strain smoothing is inaccurate when non-polynomial
functions are in the basis. This is due to the constant smoothing function used
over the smoothing domains which destroys the effect of the singularity. In
this paper, we investigate the benefits of a recently developed Linear
smoothing procedure [3] which provides better approximation to higher order
polynomial fields in the basis. Some benchmark problems in the context of
linear elastic fracture mechanics (LEFM) are solved to compare the standard
XFEM, the constant-smoothed XFEM (Sm-XFEM) and the linear-smoothed XFEM
(LSm-XFEM). We observe that the convergence rates of all three methods are the
same. The stress intensity factors (SIFs) computed through the proposed
LSm-XFEM are however more accurate than that obtained through Sm-XFEM. To
conclude, compared to the conventional XFEM, the same order of accuracy is
achieved at a relatively low computational effort.Comment: 21 pages, 13 figures, 1 tabl
Imposition of essential boundary conditions in the material point method.

There is increasing interest in the Material Point Method (MPM) as a means of modelling solid mechanics problems in which very large deformations occur, e.g. in the study of landslides and metal forming, however some aspects vital to wider use of the method have to date been ignored, in particular methods for imposing essential boundary conditions in the case where the problem domain boundary does not coincide with the background grid element edges. In this paper we develop a simple procedure originally devised for standard finite elements for the imposition of essential boundary conditions, to the MPM, expanding its capabilities to boundaries of any inclination. To the authors' knowledge this is the first time that a method has been proposed that allows arbitrary Dirichlet boundary conditions (zero and non-zero values at any inclination) to be imposed in the MPM. The method presented in this paper is different from other MPM boundary approximation approaches, in that: (i) the boundaries are independent of the background mesh, (ii) artificially stiff regions of material points are avoided and (iii) the method does not rely on spurious mirroring of the problem domain to imposed symmetry. The main contribution of this work is equally applicable to standard finite elements and the MPM
Model reduction for LPV systems based on approximate modal decomposition

The paper presents a novel model order reduction technique for large-scale linear parameter varying (LPV) systems. The approach is based on decoupling the original dynamics into smaller dimensional LPV subsystems that can be independently reduced by parameter varying reduction methods. The decomposition starts with the construction of a modal transformation that separates the modal subsystems. Hierarchical clustering is applied then to collect the dynamically similar modal subsystems into larger groups. The resulting parameter varying subsystems are then independently reduced. This approach substantially differs from most of the previously proposed LPV model reduction techniques, since it performs manipulations on the LPV model itself, instead of on a set of  linear time-invariant (LTI) models defined at fixed scheduling parameter values.  Therefore the interpolation, which is often a challenging part in reduction techniques, is inherently solved. The applicability of the developed algorithm is thoroughly investigated and demonstrated by numerical case studies