pinecone/core-2020-05-10-deduplication huggingface dataset:
An adaptive time integration strategy based on displacement history
  curvature

This work introduces a time-adaptive strategy that uses a refinement
estimator based on the first Frenet curvature. In dynamics, a time-adaptive
strategy is a mechanism that interactively proposes changes to the time step
used in iterative methods of solution. These changes aim to improve the
relation between quality of response and computational cost. The method here
proposed is suitable for a variety of numerical time integration problems,
e.g., in the study of bodies subjected to dynamical loads. The motion equation
in its space-discrete form is used as reference to derive the formulation
presented in this paper. Our method is contrasted with other ones based on
local error estimator and apparent frequencies. We check the performance of our
proposal when employed with the central difference, the explicit
generalized-alpha and the Chung-Lee integration methods. The proposed
refinement estimator demands low computational resources, being easily applied
to several direct integration methods.Comment: 24 pages, 3 tables, 21 figure
New bounding techniques for goal-oriented error estimation applied to
  linear problems

The paper deals with the accuracy of guaranteed error bounds on outputs of
interest computed from approximate methods such as the finite element method. A
considerable improvement is introduced for linear problems thanks to new
bounding techniques based on Saint-Venant's principle. The main breakthrough of
these optimized bounding techniques is the use of properties of homothetic
domains which enables to cleverly derive guaranteed and accurate boundings of
contributions to the global error estimate over a local region of the domain.
Performances of these techniques are illustrated through several numerical
experiments.Comment: 36 page
Total and selective reuse of Krylov subspaces for the resolution of
  sequences of nonlinear structural problems

This paper deals with the definition and optimization of augmentation spaces
for faster convergence of the conjugate gradient method in the resolution of
sequences of linear systems. Using advanced convergence results from the
literature, we present a procedure based on a selection of relevant
approximations of the eigenspaces for extracting, selecting and reusing
information from the Krylov subspaces generated by previous solutions in order
to accelerate the current iteration. Assessments of the method are proposed in
the cases of both linear and nonlinear structural problems.Comment: International Journal for Numerical Methods in Engineering (2013) 24
  page
Second order convex maximum entropy approximants with applications to high order PDE

We present a new approach for second order maximum entropy (max-ent) meshfree approximants that produces positive and smooth basis functions of uniform aspect ratio even for non-uniform node sets, and prescribes robustly feasible constraints for the entropy maximization program defining the approximants. We examine the performance of the proposed approximation scheme in the numerical solution by a direct Galerkin method of a number of partial differential equations (PDEs), including structural vibrations, elliptic second order PDEs, and fourth order PDEs for Kirchhoff-Love thin shells and for a phase field model describing the mechanics of biomembranes. The examples highlight the ability of the method to deal with non-uniform node distributions, and the high accuracy of the solutions. Surprisingly, the first order meshfree max-ent approximants with large supports are competitive when compared to the proposed second order approach in all the tested examples, even in the higher order PDEs.Peer ReviewedPostprint (author's final draft
On the performance of non-conforming finite elements for the upper bound limit analysis of plates

This is a preprint version of an article accepted for publication in International Journal for Numerical Methods in Engineering Copyright © 2012 John Wiley & Sons, Ltd.International audienceIn this paper, the upper bound limit analysis of thin plates in bending is addressed using various types of triangular finite elements for the generation of velocity fields and second order cone programming (SOCP) for the minimization problem. Three different C1-discontinuous finite elements are considered : the quadratic 6 node Lagrange triangle (T6), an enhanced T6 element with a cubic bubble function at centroid (T6b) and the cubic Hermite triangle (H3). Through numerical examples involving Johansen and von Mises yield criteria, it is shown that cubic elements (H3) give far better results in terms of convergence rate and precision than fully conforming elements found in the literature, especially for problems involving clamped boundaries
Automatic solver for non-linear partial differential equations with implicit local laws: Application to unilateral contact

International audienceIn general, non-linear continuum mechanics combine global balance equations and local constitutive laws. In this work, frictionless contact between a rigid tool and a thin elastic shell is considered. This class of boundary value problems involves two non-linear algebraic laws: the first one gives explicitly the stress field as a function of the strain throughout the continuum part, whereas the second one is a non-linear equation relating the contact forces and the displacement at the boundary.Given the fact that classical computational approaches sometimes require significant effort in implementation of complex non-linear problems, a computation technique based on automatic differentiation of constitutive laws is presented in this paper. The procedure enables to compute automatically the higher-order derivatives of these constitutive laws and thereafter to define the Taylor series that are the basis of the continuation technique called asymptotic numerical method. The algorithm is about the same with an explicit or implicit constitutive relation. In the modelling of forming processes, many tool shapes can be encountered. The presented computational technique permits an easy implementation of these complex surfaces, for instance in a finite element code : the user is only required to define the tool geometry and the computer is able to obtain the higher-order derivatives
A wave finite element-based formulation for computing the forced response of structures involving rectangular flat shells

International audienceThe harmonic forced response of structures involving several noncoplanar rectangular flat shells is investigated by using the Wave Finite Element method. Such flat shells are connected along parallel edges where external excitation sources as well as mechanical impedances are likely to occur. Also, they can be connected to one or several coupling elements whose shapes and dynamics can be complex. The dynamic behavior of the connected shells is described by means of numerical wave modes traveling towards and away from the coupling interfaces. Also, the coupling elements are modeled by using the conventional finite element (FE) method. A FE mesh tying procedure between shells having incompatible meshes is considered, which uses Lagrange multipliers for expressing the coupling conditions in wave-based form. A global wave-based matrix formulation is proposed for computing the amplitudes of the wave modes traveling along the shells. The resulting displacement solutions are obtained by using a wave mode expansion procedure. The accuracy of the wave-based matrix formulation is highlighted in comparison with the conventional FE method through three test cases of variable complexities. The relevance of the method for saving large CPU times is emphasized. Its efficiency is also highlighted in comparison with the component mode synthesis technique
A Nested Dissection Approach to Modeling Transport in Nanodevices:
  Algorithms and Applications

Modeling nanoscale devices quantum mechanically is a computationally
challenging problem where new methods to solve the underlying equations are in
a dire need. In this paper, we present an approach to calculate the charge
density in nanoscale devices, within the context of the non equilibrium Greens
function approach. Our approach exploits recent advances in using an
established graph partitioning approach. The developed method has the
capability to handle open boundary conditions that are represented by full self
energy matrices required for realistic modeling of nanoscale devices. Our
method to calculate the electron density has a reduced complexity compared to
the established recursive Greens function approach. As an example, we apply our
algorithm to a quantum well superlattice and a carbon nanotube, which are
represented by a continuum and tight binding Hamiltonian respectively, and
demonstrate significant speed up over the recursive method
Polar decomposition based corotational framework for triangular shell elements with distributed loads

A polar decomposition based corotational formulation for deriving geometrically nonlinear triangular shell elements is proposed. This formulation is novel in two aspects. (1) Original formulas for the projector operator and its variation are presented, leading to simple algorithms for the computation of the nodal residual vector and of the consistent tangent stiffness tensor. (2) For the first time in the context of a corotational kinematic description, a rigorous treatment of distributed dead and follower loads is performed, thoroughly accounting for the various contributions entailed in the residual vector and in the tangent stiffness. Numerical simulations of popular benchmark problems are reported, showing the effectiveness of the proposed approach. An accessible and adaptable MATLAB toolkit implementing the present formulation is provided as supplementary material
Model Order Reduction in Hyperelasticity: A Proper Generalized Decomposition Approach

International audienceThis paper deals with the extension of proper generalized decomposition methods to non-linear problems, in particular, to hyperelasticity. Among the different approaches that can be considered for the linearization of the doubly weak form of the problem, we have implemented a new one that uses asymptotic numerical methods in conjunction with proper generalized decomposition to avoid complex consistent linearization schemes necessary in Newton strategies. This approach results in an approximation of the problem solution in the form of a series expansion. Each term of the series is expressed as a finite sum of separated functions. The advantage of this approach is the presence of only one tangent operator, identical for every term in the series. The resulting approach has proved to render very accurate results that can be stored in the form of a meta-model in a very compact format. This opens the possibility to use these results in real-time, reaching kHz feedback rates, or to be used in deployed, handheld devices such as smartphones and tablets
Subdivision Shell Elements with Anisotropic Growth

A thin shell finite element approach based on Loop's subdivision surfaces is
proposed, capable of dealing with large deformations and anisotropic growth. To
this end, the Kirchhoff-Love theory of thin shells is derived and extended to
allow for arbitrary in-plane growth. The simplicity and computational
efficiency of the subdivision thin shell elements is outstanding, which is
demonstrated on a few standard loading benchmarks. With this powerful tool at
hand, we demonstrate the broad range of possible applications by numerical
solution of several growth scenarios, ranging from the uniform growth of a
sphere, to boundary instabilities induced by large anisotropic growth. Finally,
it is shown that the problem of a slowly and uniformly growing sheet confined
in a fixed hollow sphere is equivalent to the inverse process where a sheet of
fixed size is slowly crumpled in a shrinking hollow sphere in the frictionless,
quasi-static, elastic limit.Comment: 20 pages, 12 figures, 1 tabl
Port reduction in parametrized component static condensation: approximation and a posteriori error estimation

We introduce a port (interface) approximation and a posteriori error bound framework for a general component-based static condensation method in the context of parameter-dependent linear elliptic partial differential equations. The key ingredients are as follows: (i) efficient empirical port approximation spaces—the dimensions of these spaces may be chosen small to reduce the computational cost associated with formation and solution of the static condensation system; and (ii) a computationally tractable a posteriori error bound realized through a non-conforming approximation and associated conditioner—the error in the global system approximation, or in a scalar output quantity, may be bounded relatively sharply with respect to the underlying finite element discretization.
Our approximation and a posteriori error bound framework is of particular computational relevance for the static condensation reduced basis element (SCRBE) method. We provide several numerical examples within the SCRBE context, which serve to demonstrate the convergence rate of our port approximation procedure as well as the efficacy of our port reduction error bounds.Research Council of NorwayUnited States. Office of Naval Research (Grant N00014-11-0713
A stable XFEM formulation for multi-phase problems enforcing the accuracy of the fluxes through Lagrange multipliers

When applied to diffusion problems in a multi-phase setup, the popular extended finite element method (XFEM) strategy suffers from an inaccurate representation of the local fluxes in the vicinity of the interface. The XFEM enrichment improves the global quality of the solution but it is not enforcing any local feature to the fluxes. Thus, the resulting numerical fluxes in the vicinity of the interface are not realistic, in particular when conductivity ratios between the different phases are very high. This paper introduces an additional restriction to the XFEM formulation aiming at properly reproducing the features of the local fluxes in the transition zone. This restriction is implemented through Lagrange multipliers, and the stability of the resulting mixed formulation is tested satisfactorily through the Chapelle–Bathe numerical procedure. Several examples are presented, and the solutions obtained show a spectacular improvement with respect to the standard XFEM.Peer ReviewedPostprint (author’s final draft
Active macro-zone approach for incremental\ud
elastoplastic-contact analysis

The symmetric boundary element method, based on the Galerkin hypotheses, has found an application in\ud
the nonlinear analysis of plasticity and in contact-detachment problems, but both dealt with separately. In\ud
this paper, we want to treat these complex phenomena together as a linear complementarity problem.\ud
A mixed variable multidomain approach is utilized in which the substructures are distinguished into\ud
macroelements, where elastic behavior is assumed, and bem-elements, where it is possible that plastic strains\ud
may occur. Elasticity equations are written for all the substructures, and regularity conditions in weighted\ud
(weak) form on the boundary sides and in the nodes (strong) between contiguous substructures have to be\ud
introduced, in order to attain the solving equation system governing the elastoplastic-contact/detachment\ud
problem. The elastoplasticity is solved by incremental analysis, called for active macro-zones, and uses the\ud
well-known concept of self-equilibrium stress field here shown in a discrete form through the introduction\ud
of the influence matrix (self-stress matrix). The solution of the frictionless contact/detachment problem was\ud
performed using a strategy based on the consistent formulation of the classical Signorini equations rewritten\ud
in discrete form by utilizing boundary nodal quantities as check elements in the zones of potential contact\ud
or detachment
A two-scale failure model for heterogeneous materials: numerical implementation based on the finite element method

This is the accepted version of the following article: Toro, S., Sánchez, P.J., Huespe, A.E., Giusti, S.M., Blanco, P.J. and Feijóo, R.A. (2014), A two-scale failure model for heterogeneous materials: numerical implementation based on the finite element method. Int. J. Numer. Meth. Engng., 97: 313–351. doi: 10.1002/nme.4576, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.4576/abstractIn the first part of this contribution, a brief theoretical revision of the mechanical and variational foundations of a Failure-Oriented Multiscale Formulation (FOMF) devised for modeling failure in heterogeneous\ud
materials is described. The proposed model considers two well separated physical length scales, namely: (i) the “macro” scale where nucleation and evolution of a cohesive surface is considered as a medium to characterize the degradation phenomenon occurring at the lower length scale, and (ii) the “micro” scale where some mechanical processes that lead to the material failure are taking place, such as strain localization, damage, shear band formation, etc. These processes are modeled using the concept of Representative Volume Element (RVE). On the macro scale, the traction separation response, characterizing the mechanical behavior of the cohesive interface, is a result of the failure processes simulated in the micro scale. The traction\ud
separation response is obtained by a particular homogenization technique applied on specific RVE subdomains. Standard, as well as, Non-Standard boundary conditions are consistently derived in order to\ud
preserve “objectivity” of the homogenized response with respect to the micro-cell size. In the second part of the paper, and as an original contribution, the detailed numerical implementation of the two-scale model based on the Finite Element Method is presented. Special attention is devoted to the topics which are distinctive of the FOMF, such as: (i) the finite element technologies adopted in each scale along with their corresponding algorithmic expressions, (ii) the generalized treatment given to the kinematical boundary conditions in the RVE and (iii) how these kinematical restrictions affect the capturing of macroscopic material instability modes and the posterior evolution of failure at the RVE level. Finally, a set of numerical simulations is performed.Peer ReviewedPostprint (author’s final draft
A comparison of techniques for overcoming non-uniqueness of boundary integral equations for the collocation partition of unity method in two dimensional acoustic scattering.

The Partition of Unity Method has become an attractive approach for extending the allowable frequency range for wave simulations beyond that available using piecewise polynomial elements. The non-uniqueness of solution obtained from the conventional boundary integral equation (CBIE) is well known. The CBIE derived through Green's identities suffers from a problem of non-uniqueness at certain characteristic frequencies. Two of the standard methods of overcoming this problem are the so-called Combined Helmholtz Integral Equation Formulation (CHIEF) method and that of Burton and Miller. The latter method introduces a hypersingular integral, which may be treated in various ways. In this paper, we present the collocation partition of unity boundary element method (PUBEM) for the Helmholtz problem and compare the performance of CHIEF against a Burton–Miller formulation regularised using the approach of Li and Huang
Multiscale thermomechanical contact: Computational homogenization with isogeometric analysis

Cataloged from PDF version of article.A computational homogenization framework is developed in the context of the thermomechanical contact of two boundary layers with microscopically rough surfaces. The major goal is to accurately capture the temperature jump across the macroscopic interface in the finite deformation regime with finite deviations from the equilibrium temperature. Motivated by the limit of scale separation, a two-phase thermomechanically decoupled methodology is introduced, wherein a purely mechanical contact problem is followed by a purely thermal one. In order to correctly take into account finite size effects that are inherent to the problem, this algorithmically consistent two-phase framework is cast within a self-consistent iterative scheme that acts as a first-order corrector. For a comparison with alternative coupled homogenization frameworks as well as for numerical validation, a mortar-based thermomechanical contact algorithm is introduced. This algorithm is uniformly applicable to all orders of isogeometric discretizations through non-uniform rational B-spline basis functions. Overall, the two-phase approach combined with the mortar contact algorithm delivers a computational framework of optimal efficiency that can accurately represent the geometry of smooth surface textures. Copyright (c) 2013 John Wiley & Sons, Ltd
Explicit strategies for incompressible fluid-structure interaction problems: Nitsche type mortaring versus Robin-Robin coupling

International audienceWe discuss explicit coupling schemes for fluid-structure interaction problems where the added mass effect is important. In this paper we show the close relation between coupling schemes using Nitsche's method and a Robin-Robin type coupling. In the latter case the method may be implemented either using boundary integrals of the stresses or the more conventional discrete lifting operators. Recalling the explicit method proposed in Comput. Methods Appl. Mech. Engrg. 198(5-8):766-784, 2009 we make the observation that this scheme is stable under a hyperbolic type CFL condition, but that optimal accuracy imposes a parabolic type CFL conditions due to the splitting error. Two strategies to enhance the accuracy of the coupling scheme under the hyperbolic CFL-condition are suggested, one using extrapolation and defect-correction and one using a penalty-free non-symmetric Nitsche method. Finally we illustrate the performance of the proposed schemes on some numerical examples in two and three space dimensions
Comparison of three accelerated FFT-based schemes for computing the mechanical response of composite materials

International audienceSince Moulinec & Suquet (1994, 1998) introduced an iterative method based on Fourier transforms to compute the mechanical properties of heterogeneous materials, improved algorithms have been proposed to increase the convergence rate of the scheme. This paper is devoted to the comparison of the accelerated schemes proposed by Eyre & Milton (1999), by Michel et al (2000) and by Monchiet & Bonnet (2012). It shows that the algorithms by Eyre-Milton and by Michel et al are particular cases of Monchiet-Bonnet algorithm, corresponding to particular choices of parameters of the method. An upper bound of the spectral radius of the schemes is determined, which enables to propose sufficient conditions of convergence of the schemes. Conditions are found for minimizing this upper bound. This study shows that the scheme which minimizes this upper bound is the scheme of Eyre & Milton. The paper discusses the choice of the convergence test used in the schemes