pinecone/core-2020-05-10-deduplication huggingface dataset:
A generalised method for ratchet analysis of structures undergoing arbitrary thermo-mechanical load histories

A novel approach is presented based upon the Linear Matching Method framework in order to directly calculate the ratchet limit of structures subjected to arbitrary thermo-mechanical load histories. Traditionally, ratchet analysis methods have been based upon the fundamental premise of decomposing the cyclic load history into cyclic and constant components respectively, in order to assess the magnitude of additional constant loading a structure may accommodate before ratcheting occurs. The method proposed in this paper, for the first time, accurately and efficiently calculates the ratchet limit with respect to a proportional variation between the cyclic primary and secondary loads, as opposed to an additional primary load only. The method is a strain based approach and utilises a novel convergence scheme in order to calculate an approximate ratchet boundary based upon a predefined target magnitude of ratchet strain per cycle. The ratcheting failure mechanism evaluated by the method leads to less conservative ratchet boundaries compared to the traditional Bree solution. The method yields the total and plastic strain ranges as well as the ratchet strains for various levels of loading between the ratchet and limit load boundaries. Two example problems have been utilised in order to verify the proposed methodology
Simultaneous-FETI and Block-FETI: robust domain decomposition with multiple search directions.

International audienceDomain Decomposition methods often exhibit very poor performance when applied to engineering problems with large heterogeneities. In particular for heterogeneities along domain interfaces the iterative techniques to solve the interface problem are lacking an efficient preconditioner. Recently a robust approach, named FETI-Geneo, was proposed where troublesome modes are precomputed and deflated from the interface problem. The cost of the FETI-Geneo is however high. We propose in this paper techniques that share similar ideas with FETI-Geneo but where no pre-processing is needed and that can be easily and efficiently implemented as an alternative to standard Domain Decomposition methods. In the block iterative approaches presented in this paper, the search space at every iteration on the interface problem contains as many directions as there are domains in the decomposition. Those search directions originate either from the domain-wise preconditioner (in the Simultaneous FETI method) or from the block structure of the right-hand side of the interface problem (Block FETI). We show on 2D structural examples that both methods are robust and provide good convergence in the presence of high heterogeneities, even when the interface is jagged or when the domains have a bad aspect ratio. The Simultaneous FETI was also efficiently implemented in an optimized parallel code and exhibited excellent performance compared to the regular FETI method
Implementation of a generalized exponential basis functions  method for linear and non-linear problems

This  is  the  accepted  version  of  the  following  article:  Mossaiby, F., Ghaderian, M., Rossi, R. Implementation of a generalized exponential basis functions method for linear and non-linear problems. International Journal for Numerical Methods in Engineering [on line]. Jul 2015, which has been published in final form at http://dx.doi.org/10.1002/nme.4985.In this paper, we address shortcomings of the method of exponential basis functions (EBF) by extending it to general linear and non-linear problems. In linear problems, the solution is approximated using a linear combination of exponential functions. The coefficients are calculated such that the homogenous form of equation is satisfied on some grid. To solve non-linear problems, they are converted to into a succession of linear ones using a Newton-Kantorovich approach. The generalized exponential basis functions method (GEBF) developed can be implemented with greater ease compared to EBF, as all calculations can be performed using real numbers and no characteristic equation is needed. The details of an optimized implementation are described. We compare GEBF on some benchmark problems with methods in the literature, such as variants of the boundary element method, where GEBF shows a good performance. Also in a 3D problem, we report the run time of the proposed method compared to Kratos, a parallel, highly optimized finite element code. The results show that in this example, to obtain the same level of error much less computational effort is needed in the proposed method. Practical limitations might be encountered however for large problems because of dense matrix operations involved.Peer ReviewedPostprint (author’s final draft
Segregated Runge-Kutta methods for the incompressible Navier-Stokes equations

In this work, we propose Runge-Kutta time integration schemes for the incompressible Navier-Stokes equations with two salient properties. First, velocity and pressure computations are segregated at the time integration level, without the need to perform additional fractional step techniques that spoil high orders of accuracy. Second, the proposed methods keep the same order of accuracy for both velocities and pressures. The segregated Runge-Kutta methods are motivated as an implicit-explicit Runge-Kutta time integration of the projected Navier-Stokes system onto the discrete divergence-free space, and its re-statement in a velocity-pressure setting using a discrete pressure Poisson equation. We have analysed the preservation of the discrete divergence constraint for segregated Runge-Kutta methods and their relation (in their fully explicit version) with existing half-explicit methods. We have performed a detailed numerical experimentation for a wide set of schemes (from first to third order), including implicit and IMEX integration of viscous and convective terms, for incompressible laminar and turbulent flows. Further, segregated Runge-Kutta schemes with adaptive time stepping are proposed.Postprint (author's final draft
A generalized finite-strain damage model for quasi-incompressible hyperelasticity using hybrid formulation

This is the accepted version of the following article: [Comellas, E., Bellomo, F. J., and Oller, S. (2015) A generalized finite-strain damage model for quasi-incompressible hyperelasticity using hybrid formulation. Int. J. Numer. Meth. Engng, doi: 10.1002/nme.5118.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5118/abstractA new generalized damage model for quasi-incompressible hyperelasticity in a total Lagrangian finite-strain framework is presented. A Kachanov-like reduction factor (1 - D) is applied on the deviatoric part of the hyperelastic constitutive model. Linear and exponential softening are defined as damage evolution laws, both describable in terms of only two material parameters. The model is formulated following continuum damage mechanics theory such that it can be particularized for any hyperelastic model based on the volumetric–isochoric split of the Helmholtz free energy. However, in the present work, it has been implemented in an in-house finite element code for neo-Hooke and Ogden hyperelasticity. The details of the hybrid formulation used are also described. A couple of three-dimensional examples are presented to illustrate the main characteristics of the damage model. The results obtained reproduce a wide range of softening behaviors, highlighting the versatility of the formulation proposed. The damage formulation has been developed to be used in conjunction with mixing theory in order to model the behavior of fibered biological tissues. As an example, the markedly different behaviors of the fundamental components of the rectus sheath were reproduced using the damage model, obtaining excellent correlation with the experimental results from literature.Peer ReviewedPostprint (author’s final draft
A distortion measure to validate and generate curved high-order meshes on CAD surfaces with independence of parameterization

This is the accepted version of the following article: [Gargallo-Peiró, A., Roca, X., Peraire, J., and Sarrate, J. (2016) A distortion measure to validate and generate curved high-order meshes on CAD surfaces with independence of parameterization. Int. J. Numer. Meth. Engng, 106: 1100–1130. doi: 10.1002/nme.5162], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5162/abstractA framework to validate and generate curved nodal high-order meshes on Computer-Aided Design (CAD) surfaces is presented. The proposed framework is of major interest to generate meshes suitable for thin-shell and 3D finite element analysis with unstructured high-order methods. First, we define a distortion (quality) measure for high-order meshes on parameterized surfaces that we prove to be independent of the surface parameterization. Second, we derive a smoothing and untangling procedure based on the minimization of a regularization of the proposed distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes to enforce that the nodes slide on the surfaces. Moreover, the proposed algorithm repairs invalid curved meshes (untangling), deals with arbitrary polynomial degrees (high-order), and handles with low-quality CAD parameterizations (independence of parameterization). Third, we use the optimization procedure to generate curved nodal high-order surface meshes by means of an a posteriori approach. Given a linear mesh, we increase the polynomial degree of the elements, curve them to match the geometry, and optimize the location of the nodes to ensure mesh validity. Finally, we present several examples to demonstrate the features of the optimization procedure, and to illustrate the surface mesh generation process.Peer ReviewedPostprint (author's final draft
A distortion measure to validate and generate curved high-order meshes on CAD surfaces with independence of parameterization

A framework to validate and generate curved nodal high-order meshes on Computer-Aided Design (CAD) surfaces is presented. The proposed framework is of major interest to generate meshes suitable for thin-shell and 3D finite element analysis with unstructured high-order methods. First, we define a distortion (quality) measure for high-order meshes on parameterized surfaces that we prove to be independent of the surface parameterization. Second, we derive a smoothing and untangling procedure based on the minimization of a regularization of the proposed distortion measure. The minimization is performed in terms of the parametric coordinates of the nodes to enforce that the nodes slide on the surfaces. Moreover, the proposed algorithm repairs invalid curved meshes (untangling), deals with arbitrary polynomial degrees (high-order), and handles with low-quality CAD parameterizations (independence of parameterization). Third, we use the optimization procedure to generate curved nodal high-order surface meshes by means of an a posteriori approach. Given a linear mesh, we increase the polynomial degree of the elements, curve them to match the geometry, and optimize the location of the nodes to ensure mesh validity. Finally, we present several examples to demonstrate the features of the optimization procedure, and to illustrate the surface mesh generation processThe first author was sponsored by CUR from DIUE of the Generalitat de Catalunya\ud
and the European Social Fund (grants FI-DGR’11 and BE-DGR’12), and by the Ferran Sunyer i Balaguer Foundation (grant FSB’13).\ud
The work of the corresponding author was partially supported by the Boeing Co. & US Air Force Office of Scientific Research & European Commission through the Boeing-MIT Alliance & the Computational Math\ud
Program & Marie Skłodowska-Curie Actions (HiPerMeGaFlowS individual fellowship grant).Peer ReviewedPostprint (author's final draft
The particle finite element method (PFEM) in thermo-mechanical problems

This is the accepted version of the following article: [Rodriguez, J. M., Carbonell, J. M., Cante, J. C., and Oliver, J. (2016) The particle finite element method (PFEM) in thermo-mechanical problems. Int. J. Numer. Meth. Engng, doi: 10.1002/nme.5186.], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5186/fullThe aim of this work is to develop a numerical framework for accurately and robustly simulating the different conditions exhibited by thermo-mechanical problems. In particular, the work will focus on the analysis of problems involving large strains, rotations, multiple contacts, large boundary surface changes, and thermal effects.\ud
The framework of the numerical scheme is based on the particle finite element method (PFEM) in which the spatial domain is continuously redefined by a distinct nodal reconnection, generated by a Delaunay triangulation. In contrast to classical PFEM calculations, in which the free boundary is obtained by a geometrical procedure (a - shape method), in this work, the boundary is considered as a material surface, and the boundary nodes are removed or inserted by means of an error function.\ud
The description of the thermo-mechanical constitutive model is based on the concepts of large strains plasticity. The plastic flow condition is assumed nearly incompressible, so a u-p mixed formulation, with a stabilization of the pressure term via the polynomial pressure projection, is proposed.\ud
One of the novelties of this work is the use of a combination between the isothermal split and the so-called IMPL-EX hybrid integration technique to enhance the robustness and reduce the typical iteration number of the fully implicit Newton–Raphson solution algorithm.\ud
The new set of numerical tools implemented in the PFEM algorithm, including new discretization techniques, the use of a projection of the variables between meshes, and the insertion and removal of points allows us to eliminate the negative Jacobians present during large deformation problems, which is one of the drawbacks in the simulation of coupled thermo-mechanical problems.\ud
Finally, two sets of numerical results in 2D are stated. In the first one, the behavior of the proposed locking-free element type and different time integration schemes for thermo-mechanical problems is analyzed. The potential of the method for modeling more complex coupled problems as metal cutting and metal forming processes is explored in the last example.Peer ReviewedPostprint (author's final draft
A quasi-optimal coarse problem and an augmented Krylov solver for the
  Variational Theory of Complex Rays

The Variational Theory of Complex Rays (VTCR) is an indirect Trefftz method
designed to study systems governed by Helmholtz-like equations. It uses wave
functions to represent the solution inside elements, which reduces the
dispersion error compared to classical polynomial approaches but the resulting
system is prone to be ill conditioned. This paper gives a simple and original
presentation of the VTCR using the discontinuous Galerkin framework and it
traces back the ill-conditioning to the accumulation of eigenvalues near zero
for the formulation written in terms of wave amplitude. The core of this paper
presents an efficient solving strategy that overcomes this issue. The key
element is the construction of a search subspace where the condition number is
controlled at the cost of a limited decrease of attainable precision. An
augmented LSQR solver is then proposed to solve efficiently and accurately the
complete system. The approach is successfully applied to different examples.Comment: International Journal for Numerical Methods in Engineering, Wiley,
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Substructured formulations of nonlinear structure problems - influence
  of the interface condition

We investigate the use of non-overlapping domain decomposition (DD) methods
for nonlinear structure problems. The classic techniques would combine a global
Newton solver with a linear DD solver for the tangent systems. We propose a
framework where we can swap Newton and DD, so that we solve independent
nonlinear problems for each substructure and linear condensed interface
problems. The objective is to decrease the number of communications between
subdomains and to improve parallelism. Depending on the interface condition, we
derive several formulations which are not equivalent, contrarily to the linear
case. Primal, dual and mixed variants are described and assessed on a simple
plasticity problem.Comment: in International Journal for Numerical Methods in Engineering, Wiley,
  201
Velocity-based formulations for standard and quasi-incompressible hypoelastic-plastic solids

This is the accepted version of the following article: [Franci, A., Oñate, E., and Carbonell, J. M. (2016) Velocity-based formulations for standard and quasi-incompressible hypoelastic-plastic solids. Int. J. Numer. Meth. Engng, 107: 970–990. doi: 10.1002/nme.5205], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5205/abstractWe present three velocity-based updated Lagrangian formulations for standard and quasi-incompressible hypoelastic-plastic solids. Three low-order finite elements are derived and tested for non-linear solid mechanics problems. The so-called V-element is based on a standard velocity approach, while a mixed velocity–pressure formulation is used for the VP and the VPS elements. The two-field problem is solved via a two-step Gauss–Seidel partitioned iterative scheme. First, the momentum equations are solved in terms of velocity increments, as for the V-element. Then, the constitutive relation for the pressure is solved using the updated velocities obtained at the previous step. For the VPS-element, the formulation is stabilized using the finite calculus method in order to solve problems involving quasi-incompressible materials. All the solid elements are validated by solving two-dimensional and three-dimensional benchmark problems in statics as in dynamics.Peer ReviewedPostprint (author's final draft
Effect of interpolation on noise propagation from images to DIC displacement maps

International audienceThis paper introduces and validates a new prediction of sensor noise propagation from images of randomly marked surfaces to displacement maps obtained by Digital Image Correlation (DIC). Images are indeed often affected by sensor noise, which propagates to DIC output. We consider here the 2D global DIC (G-DIC), for which this output is the in-plane displacement calculated at a set of nodes. Predictive formula for the resolution of the displacement at these nodes is already available in the literature. The contribution of the present paper is to revisit this formula to take into account the interpolation required by sub-pixel displacement. A generalization is also proposed to predict the displacement resolution throughout the field of view. It is then extended to several kinds of DIC. The correlation procedure is thoroughly described in order to emphasize the role of the interpolation. A numerical assessment on synthetic data validates the new prediction and shows the improvement brought about by the proposed formula
Numerical integration of rate-independent BCC single crystal plasticity models: comparative study of two classes of numerical algorithms

In an incremental formulation suitable to numerical implementation, the use of rate-independent theory of crystal plasticity essentially leads to four fundamental problems. The first is to determine the set of potentially active slip systems over a time increment. The second is to select the active slip systems among the potentially active ones. The third is to compute the slip rates (or the slip increments) for the active slip systems. And the last problem is the possible non-uniqueness of slip rates. The purpose of this paper is to propose satisfactory responses to the above-mentioned first three issues by presenting and comparing two novel numerical algorithms. The first algorithm is based on the usual return-mapping integration scheme, while the second follows the so-called ultimate scheme. The latter is shown to be more relevant and efficient than the former. These comparative performances are illustrated through various numerical simulations of the mechanical behavior of single crystals and polycrystalline aggregates subjected to monotonic and complex loadings. Although these algorithms are applied in this paper to Body-Centered-Cubic (BCC) crystal structures, they are quite general and suitable for integrating the constitutive equations for other crystal structures (e.g., FCC and HCP)
Multisurface plasticity for Cosserat materials: plate element implementation and validation

International audienceThe macroscopic behaviour 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 behaviour 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
Strict lower bounds with separation of sources of error in
  non-overlapping domain decomposition methods

This article deals with the computation of guaranteed lower bounds of the
error in the framework of finite element (FE) and domain decomposition (DD)
methods. In addition to a fully parallel computation, the proposed lower bounds
separate the algebraic error (due to the use of a DD iterative solver) from the
discretization error (due to the FE), which enables the steering of the
iterative solver by the discretization error. These lower bounds are also used
to improve the goal-oriented error estimation in a substructured context.
Assessments on 2D static linear mechanic problems illustrate the relevance of
the separation of sources of error and the lower bounds' independence from the
substructuring. We also steer the iterative solver by an objective of precision
on a quantity of interest. This strategy consists in a sequence of solvings and
takes advantage of adaptive remeshing and recycling of search directions.Comment: International Journal for Numerical Methods in Engineering, Wiley,
  201