References of "Beex, Lars 50000691"
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See detailA refinement indicator for adaptive quasicontinuum approaches for structural lattices
Chen, Li UL; Berke, Peter; Massart, Thierry et al

in International Journal for Numerical Methods in Engineering (in press)

The quasicontinuum method is a concurrent multiscale approach in which lattice models are fully resolved in small regions of interest and coarse-grained elsewhere. Since the method was originally proposed ... [more ▼]

The quasicontinuum method is a concurrent multiscale approach in which lattice models are fully resolved in small regions of interest and coarse-grained elsewhere. Since the method was originally proposed to accelerate atomistic lattice simulations, its refinement criteria – that drive refining coarse-grained regions and/or increasing fully-resolved regions – are generally associated with quantities relevant to the atomistic scale. In this contribution, a new refinement indicator is presented, based on the energies of dedicated cells at coarse-grained domain surfaces. This indicator is incorporated in an adaptive scheme of a generalization of the quasicontinuum method able to consider periodic representative volume elements, like the ones employed in most computational homogenization approaches. However, this indicator can also be used for conventional quasicontinuum frameworks. Illustrative numerical examples of elastic indentation and scratch of different lattices demonstrate the capabilities of the refinement indicator and its impact on adaptive quasicontinuum simulations. [less ▲]

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See detailA Bayesian framework to identify random parameter fields based on the copula theorem and Gaussian fields: Application to polycrystalline materials
Rappel, Hussein UL; Wu, Ling; Noels, Ludovic et al

in Journal of Applied Mechanics (in press)

For many models of solids, we frequently assume that the material parameters do not vary in space, nor that they vary from one product realization to another. If the length scale of the application ... [more ▼]

For many models of solids, we frequently assume that the material parameters do not vary in space, nor that they vary from one product realization to another. If the length scale of the application approaches the length scale of the micro-structure however, spatially fluctuating parameter fi elds (which vary from one realization of the fi eld to another) can be incorporated to make the model capture the stochasticity of the underlying micro-structure. Randomly fluctuating parameter fields are often described as Gaussian fields. Gaussian fi elds however assume that the probability density function of a material parameter at a given location is a univariate Gaussian distribution. This entails for instance that negative parameter values can be realized, whereas most material parameters have physical bounds (e.g. the Young's modulus cannot be negative). In this contribution, randomly fluctuating parameter fi elds are therefore described using the copula theorem and Gaussian fi elds, which allow di fferent types of univariate marginal distributions to be incorporated, but with the same correlation structure as Gaussian fields. It is convenient to keep the Gaussian correlation structure, as it allows us to draw samples from Gaussian fi elds and transform them into the new random fields. The bene fit of this approach is that any type of univariate marginal distribution can be incorporated. If the selected univariate marginal distribution has bounds, unphysical material parameter values will never be realized. We then use Bayesian inference to identify the distribution parameters (which govern the random fi eld). Bayesian inference regards the parameters that are to be identi fied as random variables and requires a user-defi ned prior distribution of the parameters to which the observations are inferred. For the homogenized Young's modulus of a columnar polycrystalline material of interest in this study, the results show that with a relatively wide prior (i.e. a prior distribution without strong assumptions), a single specimen is su ciffient to accurately recover the distribution parameter values. [less ▲]

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See detailIntercorrelated random fields with bounds and the Bayesian identification of their parameters: Application to linear elastic struts and fibers
Rappel, Hussein; Girolami, Mark; Beex, Lars UL

in International Journal for Numerical Methods in Engineering (in press)

Many materials and structures consist of numerous slender struts or fibers. Due to the manufacturing processes of different types of struts and the growth processes of natural fibers, their mechanical ... [more ▼]

Many materials and structures consist of numerous slender struts or fibers. Due to the manufacturing processes of different types of struts and the growth processes of natural fibers, their mechanical response frequently fluctuates from strut to strut, as well as locally within each strut. In associated mechanical models each strut is often represented by a string of beam elements, since the use of conventional three-dimensional finite elements renders the simulations computationally inefficient. The parameter input fields of each string of beam elements are ideally such that the local fluctuations and fluctuations between individual strings of beam elements are accurately captured. The goal of this study is to capture these fluctuations in several intercorrelated bounded random fields. Two formulations to describe the intercorrelations between each random field, as well as the case without any intercorrelation, are investigated. As only a few sets of input fields are available (due to time constraints of the supposed experimental techniques), the identification of the random fields’ parameters involves substantial uncertainties. A probabilistic identification approach based on Bayes’ theorem is employed to treat the involved uncertainties. [less ▲]

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See detailA hyper-reduction method using adaptivity to cut the assembly costs of reduced order models
Hale, Jack UL; Schenone, Elisa; Baroli, Davide UL et al

in Computer Methods in Applied Mechanics and Engineering (2021), 380

At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The ... [more ▼]

At every iteration or timestep of the online phase of some reduced-order modelling schemes, large linear systems must be assembled and then projected onto a reduced order basis of small dimension. The projected small linear systems are cheap to solve, but assembly and projection are now the dominant computational cost. In this paper we introduce a new hyper-reduction strategy called reduced assembly (RA) that drastically cuts these costs. RA consists of a triangulation adaptation algorithm that uses a local error indicator to con- struct a reduced assembly triangulation specially suited to the reduced order basis. Crucially, this reduced assembly triangulation has fewer cells than the original one, resulting in lower assembly and projection costs. We demonstrate the efficacy of RA on a Galerkin-POD type reduced order model (RAPOD). We show performance increases of up to five times over the baseline Galerkin-POD method on a non-linear reaction-diffusion problem solved with a semi-implicit time-stepping scheme and up to seven times for a 3D hyperelasticity problem solved with a continuation Newton-Raphson algorithm. The examples are implemented in the DOLFIN finite element solver using PETSc and SLEPc for linear algebra. Full code and data files to produce the results in this paper are provided as supplementary material. [less ▲]

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See detailFrictional interactions for non-localised beam-to-beam and beam-inside-beam contact
Magliulo, Marco; Lengiewicz, Jakub UL; Zilian, Andreas UL et al

in International Journal for Numerical Methods in Engineering (2021), 122(7), 1706-1731

This contribution presents the extensions of beam-to-beam and beam-inside-beam contact schemes of the same authors towards frictional interactions. Since the schemes are based on the beams’ true surfaces ... [more ▼]

This contribution presents the extensions of beam-to-beam and beam-inside-beam contact schemes of the same authors towards frictional interactions. Since the schemes are based on the beams’ true surfaces (instead of surfaces implicitly deduced from the beams’ centroid lines), the presented enhancements are not only able to account for frictional sliding in the beams’ axial directions, but also in the circumferential directions. Both the frictional beam-to-beam approach as well as the frictional beam-inside-beam approach are applicable to shear-deformable and shear-undeformable beams, as well as to beams with both circular and elliptical cross-sections (although the cross-sections must be rigid). A penalty formulation is used to treat unilateral and frictional contact constraints. FE implementation details are discussed, where automatic differentiation techniques are used to derive the implementations. Simulations involving large sliding displacements and large deformations are presented for both beam-to-beam and beam-inside-beam schemes. All simulation results are compared to those of the frictionless schemes. [less ▲]

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See detailDATA DRIVEN SURGICAL SIMULATIONS
Deshpande, Saurabh UL; Bordas, Stéphane UL; Beex, Lars UL et al

Scientific Conference (2020, July)

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See detailContact between shear-deformable beams with elliptical cross-sections
Magliulo, Marco UL; Zilian, Andreas UL; Beex, Lars UL

in Acta Mechanica (2020), 231

Slender constituents are present in many structures and materials. In associated mechanical models, each slender constituent is often described with a beam. Contact between beams is essential to ... [more ▼]

Slender constituents are present in many structures and materials. In associated mechanical models, each slender constituent is often described with a beam. Contact between beams is essential to incorporate in mechanical models, but associated contact frameworks are only demonstrated to work for beams with circular cross-sections. Only two studies have shown the ability to treat contact between beams with elliptical cross-sections, but those frameworks are limited to point-wise contact, which narrows their applicability. This contribution presents initial results of a framework for shear-deformable beams with elliptical cross-sections if contact occurs along a line or at an area (instead of at a point). This is achieved by integrating a penalty potential over one of the beams’ surfaces. Simo-Reissner Geometrically Exact Beam (GEB) elements are employed to discretise each beam. As the surface of an assembly of such beam elements is discontinuous, a smoothed surface is introduced to formulate the contact kinematics. This enables the treatment of contact for large sliding displacements and substantial deformations. [less ▲]

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See detailNon-localised contact between beams with circular and elliptical cross-sections
Magliulo, Marco UL; Lengiewicz, Jakub UL; Zilian, Andreas UL et al

in Computational Mechanics (2020), 65

The key novelty of this contribution is a dedicated technique to e fficiently determine the distance (gap) function between parallel or almost parallel beams with circular and elliptical cross-sections ... [more ▼]

The key novelty of this contribution is a dedicated technique to e fficiently determine the distance (gap) function between parallel or almost parallel beams with circular and elliptical cross-sections. The technique consists of parametrizing the surfaces of the two beams in contact, fixing a point on the centroid line of one of the beams and searching for a constrained minimum distance between the surfaces (two variants are investigated). The resulting unilateral (frictionless) contact condition is then enforced with the Penalty method, which introduces compliance to the, otherwise rigid, beams' cross-sections. Two contact integration schemes are considered: the conventional slave-master approach (which is biased as the contact virtual work is only integrated over the slave surface) and the so-called two-half-pass approach (which is unbiased as the contact virtual work is integrated over the two contacting surfaces). Details of the finite element formulation which is suitably implemented using Automatic Di fferentiation techniques are presented. A set of numerical experiments shows the overall performance of the framework and allows a quantitative comparison of the investigated variants. [less ▲]

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See detailFusing the Seth-Hill strain tensors to fit compressible elastic material responses in the nonlinear regime
Beex, Lars UL

in International Journal of Mechanical Sciences (2019), 163

Strain energy densities based on the Seth-Hill strain tensors are often used to describe the hyperelastic mechanical behaviours of isotropic, transversely isotropic and orthotropic materials for ... [more ▼]

Strain energy densities based on the Seth-Hill strain tensors are often used to describe the hyperelastic mechanical behaviours of isotropic, transversely isotropic and orthotropic materials for relatively large deformations. Since one parameter distinguishes which strain tensor of the Seth-Hill family is used, one has in theory the possibility to t the material response in the nonlinear regime. Most often for compressible deformations however, this parameter is selected such that the Hencky strain tensor is recovered, because it yields rather physical stress-strain responses. Hence, the response in the nonlinear regime is in practise not often tailored to match experimental data. To ensure that elastic responses in the nonlinear regime can more accurately be controlled, this contribution proposes three generalisations that combine several Seth-Hill strain tensors. The generalisations are formulated such that the stress-strain responses for in finitesimal deformations remain unchanged. Consequently, the identifi cation of the Young's moduli, Poisson's ratios and shear moduli is not a ffected. 3D fi nite element simulations are performed for isotropy and orthotropy, with an emphasis on the identifi cation of the new material parameters. [less ▲]

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See detailClustering Based Model Order Reduction For Hyper Elastoplastic Material Models
Vijayaraghavan, Soumianarayanan UL; Beex, Lars UL; Noels, Ludovic et al

Presentation (2019, July 29)

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See detailA stochastic Galerkin cell-based smoothed finite element method (SGCS-FEM)
Mathew, Tittu; Beex, Lars UL; Bordas, Stéphane UL et al

in International Journal of Computational Methods (2019), 17(8),

In this paper, the cell based smoothed finite element method is extended to solve stochastic partial diff erential equations with uncertain input parameters. The spatial field of Young's moduli and the ... [more ▼]

In this paper, the cell based smoothed finite element method is extended to solve stochastic partial diff erential equations with uncertain input parameters. The spatial field of Young's moduli and the corresponding stochastic results are represented by Karhunen-Lo eve expansion and polynomial chaos expansion, respectively. The Young's Modulus of structure is considered to be random for stochastic static as well as free vibration problems. Mathematical expressions and the solution procedure are articulated in detail to evaluate the statistical characteristics of responses in terms of static displacements and free vibration frequencies. The feasibility and eff ectiveness of the proposed SGCS-FEM method in terms of accuracy and lower requirement on the mesh size in the solution domain over that of conventional FEM for stochastic problems are demonstrated by carefully chosen numerical examples. From the numerical study, it is inferred that the proposed framework is computationally less demanding without compromising accuracy. [less ▲]

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See detailEstimating fibres' material parameter distributions from limited data with the help of Bayesian inference
Rappel, Hussein UL; Beex, Lars UL

in European Journal of Mechanics. A, Solids (2019), 75

Numerous materials are essentially structures of discrete fibres, yarns or struts. Considering these materials at their discrete scale, one may distinguish two types of intrinsic randomness that affect ... [more ▼]

Numerous materials are essentially structures of discrete fibres, yarns or struts. Considering these materials at their discrete scale, one may distinguish two types of intrinsic randomness that affect the structural behaviours of these discrete structures: geometrical randomness and material randomness. Identifying the material randomness is an experimentally demanding task, because many small fibres, yarns or struts need to be tested, which are not easy to handle. To avoid the testing of hundreds of constituents, this contribution proposes an identification approach that only requires a few dozen of constituents to be tested (we use twenty to be exact). The identification approach is applied to articially generated measurements, so that the identified values can be compared to the true values. Another question this contribution aims to answer is how precise the material randomness needs to be identified, if the geometrical randomness will also influence the macroscale behaviour of these discrete networks. We therefore also study the effect of the identified material randomness to that of the actual material randomness for three types of structures; each with an increasing level of geometrical randomness. [less ▲]

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See detailA Tutorial on Bayesian Inference to Identify Material Parameters in Solid Mechanics
Rappel, Hussein UL; Beex, Lars UL; Hale, Jack UL et al

in Archives of Computational Methods in Engineering (2019)

The aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already ... [more ▼]

The aim of this contribution is to explain in a straightforward manner how Bayesian inference can be used to identify material parameters of material models for solids. Bayesian approaches have already been used for this purpose, but most of the literature is not necessarily easy to understand for those new to the field. The reason for this is that most literature focuses either on complex statistical and machine learning concepts and/or on relatively complex mechanical models. In order to introduce the approach as gently as possible, we only focus on stress–strain measurements coming from uniaxial tensile tests and we only treat elastic and elastoplastic material models. Furthermore, the stress–strain measurements are created artificially in order to allow a one-to-one comparison between the true parameter values and the identified parameter distributions. [less ▲]

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See detailIdentifying elastoplastic parameters with Bayes' theorem considering double error sources and model uncertainty
Rappel, Hussein UL; Beex, Lars UL; Noels, Ludovic et al

in Probabilistic Engineering Mechanics (2019), 55

We discuss Bayesian inference for the identi cation of elastoplastic material parameters. In addition to errors in the stress measurements, which are commonly considered, we furthermore consider errors in ... [more ▼]

We discuss Bayesian inference for the identi cation of elastoplastic material parameters. In addition to errors in the stress measurements, which are commonly considered, we furthermore consider errors in the strain measurements. Since a difference between the model and the experimental data may still be present if the data is not contaminated by noise, we also incorporate the possible error of the model itself. The three formulations to describe model uncertainty in this contribution are: (1) a random variable which is taken from a normal distribution with constant parameters, (2) a random variable which is taken from a normal distribution with an input-dependent mean, and (3) a Gaussian random process with a stationary covariance function. Our results show that incorporating model uncertainty often, but not always, improves the results. If the error in the strain is considered as well, the results improve even more. [less ▲]

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See detailAdaptive smoothed stable extended finite element method for weak discontinuities for finite elasticity
Jansari, Chintan; Natarajan, Sundararajan; Beex, Lars UL et al

in European Journal of Mechanics. A, Solids (2019), 78

In this paper, we propose a smoothed stable extended finite element method (S2XFEM) by combining the strain smoothing with the stable extended finite element method (SXFEM) to efficiently treat inclusions ... [more ▼]

In this paper, we propose a smoothed stable extended finite element method (S2XFEM) by combining the strain smoothing with the stable extended finite element method (SXFEM) to efficiently treat inclusions and/or voids in hyperelastic matrix materials. The interface geometries are implicitly represented through level sets and a geometry based error indicator is used to resolve the geometry. For the unknown fields, the mesh is refined based on a recovery based error indicator combined with a quadtree decomposition guarantee the method’s accuracy with respect to the computational costs. Elements with hanging nodes (due to the quadtree meshes) are treated as polygonal elements with mean value coordinates as the basis functions. The accuracy and the convergence properties are compared to similar approaches for several numerical examples. The examples indicate that S2XFEM is computationally the most efficient without compromising the accuracy. [less ▲]

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See detailClassification of states and model order reduction of large scale Chemical Vapor Deposition processes with solution multiplicity
Koronaki, E.D.; Gkinis, P.A.; Beex, Lars UL et al

in Computers and Chemical Engineering (2018), 121

This paper presents an equation-free, data-driven approach for reduced order modeling of a Chemical Vapor Deposition (CVD) process. The proposed approach is based on process information provided by ... [more ▼]

This paper presents an equation-free, data-driven approach for reduced order modeling of a Chemical Vapor Deposition (CVD) process. The proposed approach is based on process information provided by detailed, high-fidelity models, but can also use spatio-temporal measurements. The Reduced Order Model (ROM) is built using the method-of-snapshots variant of the Proper Orthogonal Decomposition (POD) method and Artificial Neural Networks (ANN) for the identification of the time-dependent coefficients. The derivation of the model is completely equation-free as it circumvents the projection of the actual equations onto the POD basis. Prior to building the model, the Support Vector Machine (SVM) supervised classification algorithm is used in order to identify clusters of data corresponding to (physically) different states that may develop at the same operating conditions due to the inherent nonlinearity of the process. The different clusters are then used for ANN training and subsequent development of the ROM. The results indicate that the ROM is successful at predicting the dynamic behavior of the system in windows of operating parameters where steady states are not unique. [less ▲]

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See detailAn equation-free, nested, concurrent multiscale approach without scale-separation
Beex, Lars UL; Kerfriden, Pierre

Scientific Conference (2018, September)

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