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See detailAn adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order
Nguyen-Xuan, H.; Liu, G. R.; Bordas, Stéphane UL et al

in Computer Methods in Applied Mechanics & Engineering (2013), 253

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded ... [more ▼]

This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. © 2012 Elsevier B.V. [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 detailAdaptive support domain implementation on the Moving Least Squares approximation for Mfree methods applied on elliptic and parabolic PDE problems using strong-form description
Bourantas, Georgios UL; Skouras, Eugene; Nikiforidis, George

in Computer Modeling in Engineering & Sciences (2009), 43

The extent of application of meshfree methods based on point collocation (PC) techniques with adaptive support domain for strong form Partial Differential Equations (PDE) is investigated. The basis ... [more ▼]

The extent of application of meshfree methods based on point collocation (PC) techniques with adaptive support domain for strong form Partial Differential Equations (PDE) is investigated. The basis functions are constructed using the Moving Least Square (MLS) approximation. The weak-form description of PDEs is used in most MLS methods to circumvent problems related to the increased level of resolution necessary near natural (Neumann) boundary conditions (BCs), dislocations, or regions of steep gradients. Alternatively, one can adopt Radial Basis Function (RBF) approximation on the strong-form of PDEs using meshless PC methods, due to the delta function behavior (exact solution on nodes). The present approach is one of the few successful attempts of using MLS approximation [Atluri, Liu, and Han (2006), Han, Liu, Rajendran and Atluri (2006), Atluri and Liu (2006)] instead of RBF approximation for the meshless PC method using strong-form description. To increase the accuracy of the MLS interpolation method and its robustness in problems with natural BCs, a suitable support domain should be chosen in order to ensure an optimized area of coverage for interpolation. To this end, the basis functions are constructed using two different approaches, pertinent to the dimension of the support domain. On one hand, a compact form for the support domain is retained by keeping its radius constant. On the other hand, one can control the number of neighboring nodes as the support domain of each point. The results show that some inaccuracies are present near the boundaries using the first approach, due to the limited number of nodes belonging to the support domain, which results in failed matrix inversion. Instead, the second approach offers capability for fully matrix inversion under many (if not all) circumstances, resulting in basis functions of increased accuracy and robustness. This PC method, applied along with an intelligent adaptive refinement, is demonstrated for elliptic and for parabolic PDEs, related to many flow and mass transfer problems. [less ▲]

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See detailAn adaptive variational Quasicontinuum methodology for lattice networks with localized damage
Rokos, Ondrej; Peerlings, Ron; Zeman, Jan et al

in International Journal for Numerical Methods in Engineering (2017), 112(2),

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 ... [more ▼]

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. [less ▲]

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See detailAdaptive-gain Extended Kalman Filter: Extension to the Continuous-discrete Case
Boizot, Nicolas UL; Busvelle, Eric; Gauthier, Jean-Paul

Scientific Conference (2009)

In the present article we propose a nonlinear observer that merges the behaviors 1) of an extended Kalman filter, mainly designed to smooth off noise , and 2) of high-gain observers devoted to handle ... [more ▼]

In the present article we propose a nonlinear observer that merges the behaviors 1) of an extended Kalman filter, mainly designed to smooth off noise , and 2) of high-gain observers devoted to handle large perturbations in the state estimation. We specifically aim at continuous-discrete systems. The strategy consists in letting the high-gain self adapt according to the innovation. We define innovation computed over a time window and justify its usage via an important lemma. We prove the general convergence of the resulting observer. [less ▲]

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See detailAddressing volumetric locking and instabilities by selective integration in smoothed finite elements
Hung, Nguyen-Xuan; Bordas, Stéphane UL; Hung, Nguyen-Dang

in Communications in Numerical Methods in Engineering (2009), 25(1), 19-34

This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into ... [more ▼]

This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain. This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy, with slightly lower computational cost than the standard FEM. The one-subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi-equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses. The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one-subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency. Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost. [less ▲]

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See detailAdvances in Applied Mechanics
Bordas, Stéphane UL

Book published by Elsevier (2014)

Advances in Applied Mechanics draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review ... [more ▼]

Advances in Applied Mechanics draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review articles on topics in the mechanical sciences, primarily of interest to scientists and engineers working in the various branches of mechanics, but also of interest to the many who use the results of investigations in mechanics in various application areas, such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering. [less ▲]

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See detailAdvances in error estimation for homogenisation
Alves Paladim, Daniel; Kerfriden, Pierre; Moitinho de Almeida, José Paulo et al

in 13th U.S. National Congress on Computational Mechanics (2015, July)

In this paper, the concept of modeling error is extended to the homogenisation of elliptic PDEs. The main difficulty is the lack of a full description of the diffusion coefficients. We overcome this ... [more ▼]

In this paper, the concept of modeling error is extended to the homogenisation of elliptic PDEs. The main difficulty is the lack of a full description of the diffusion coefficients. We overcome this obstacle by representing them as a random a field. Under this framework, it is possible to quantify the accuracy of the surrogate model (the homogenised model) in terms of first moments of the energy norm and quantities of interest. This work builds on the seminal work of [1]. The methodology here presented rely on the Constitutive Relation Error (CRE) which states that a certain measures of the primal and dual surrogate model upper bound the exact error. The surrogate model, in agreement with homogenisation, is deterministic. This property exploited to obtain bounds whose computation is also deterministic. It is also shown that minimising the CRE in the set of homogenisation schemes leads us to an optimal surrogate that is closely related to the classical Voigt and Reuss models. Numerical examples demonstrate that the bounds are easy and affordable to compute, and useful as long as the mismatch between he diffusion coefficients of the microstructure remain small. In the case of high mismatch, extensions are proposed, through the introduction of stochastic surrogate models.. [1]Romkes, Albert, J. Tinsley Oden, and Kumar Vemaganti."Multi-scale goal-oriented adaptive modeling of random heterogeneous materials." Mechanics of materials 38.8(2006): 859-872. [less ▲]

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See detailADVANCES IN GEOMETRY INDEPENDENT APPROXIMATIONS
Anitescu, Cosmin; Atroshchenko, Elena; Bordas, Stéphane UL et al

Scientific Conference (2019, April 11)

We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no ... [more ▼]

We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no-longer has to be identical to the approximation used to describe the geometry of the domain. As such, the geometry can be described using usual CAD representations, e.g. NURBS, which are the most common in the CAD area, whilst local refinement and meshes approximations can be used to describe the field variables, enabling local adaptivity. We show in which cases the approach passes the patch test and present applications to various mechanics, fracture and multi-physics problems. [less ▲]

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See detailAn agenda for establishing the Ecological Footprint as communication instrument and indicator for sustainable development in small countries: Case study Luxembourg
Hild, Paula UL; Schmitt, Bianca; Morgane, Mey et al

Poster (2010, June)

The Ecological Footprint methodology proposed by the Global Footprint Network (GFN) seems to be not entirely appropriate for small countries with less than one million inhabitants [Ewing et al., 2008 ... [more ▼]

The Ecological Footprint methodology proposed by the Global Footprint Network (GFN) seems to be not entirely appropriate for small countries with less than one million inhabitants [Ewing et al., 2008]. This may be a reason why e.g. results for Luxembourg, a country with 470,000 inhabitants, have never been included into official country Footprint comparisons. Therefore, the methodology needs to be adapted to be used for communication purpose in Luxembourg. This contribution presents Luxembourg’s approach for illustrating the national consumption impacts to finally discuss the integration of the Ecological Footprint as an indicator for sustainable development in the national indicator system. [less ▲]

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See detailAggregate and disaggregate dynamic spatial interaction approaches to modelling coins diffusion
Le Texier, Marion UL; Caruso, Geoffrey UL

in Thill, Jean-Claude (Ed.) Spatial Analysis and Location Modeling in Urban and Regional Systems (2018)

With the 2002 introduction of the euro as a common currency in Europe,the possibility has emerged to assess international mobility using this new tracer, given that every coin bears a specific national ... [more ▼]

With the 2002 introduction of the euro as a common currency in Europe,the possibility has emerged to assess international mobility using this new tracer, given that every coin bears a specific national side. Using a simple two-country framework, four dynamic modeling strategies were designed in order to simulate the diffusion of coins and to understand how this diffusion is affected by population size, mobility rates and coin exchange processes. Methodological implications are raised with respect to aggregation, synchronicity and stochasticity issues. Although each model converges to an equilibrium, the time to reach this end stage and the level of coin mixing in each country strongly varies with the modeling strategy. Calibration is undertaken with French data, using mobility rates as adjustment variables. The experiment shows that convergence to a perfect mix of coins can only be obtained if reciprocal exchanges are modeled, with a time horizon around 2064 - while non-reciprocal models indicate an imperfect mix converging in the year 2020 at the latest. [less ▲]

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See detailAn Agile Approach to Validate a Formal Representation of the GDPR
Bartolini, Cesare UL; Lenzini, Gabriele UL; Santos, Cristiana

in New Frontiers in Artificial Intelligence (in press)

Modelling in a knowledge base of logic formulæ the articles of the GDPR enables a semi-automatic reasoning of the Regulation. To be legally substantiated, it requires that the formulæ express validly the ... [more ▼]

Modelling in a knowledge base of logic formulæ the articles of the GDPR enables a semi-automatic reasoning of the Regulation. To be legally substantiated, it requires that the formulæ express validly the legal meaning of the Regulation's articles. But legal experts are usually not familiar with logic, and this calls for an interdisciplinary validation methodology that bridges the communication gap between formal modelers and legal evaluators. We devise such a validation methodology and exemplify it over a knowledge base of articles of the GDPR translated into Reified I/O (RIO) logic and encoded in LegalRuleML. A pivotal element of the methodology is a human-readable intermediate representation of the logic formulæ that preserves the formulæ's meaning, while rendering it in a readable way to non-experts. After being applied over a use case, we prove that it is possible to retrieve feedback from legal experts about the formal representation of Art. 5.1a and Art. 7.1. What emerges is an agile process to build logic knowledge bases of legal texts, and to support their public trust, which we intend to use for a logic model of the GDPR, called DAPRECO knowledge base. [less ▲]

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See detailALGEBRAIC COARSE-GRAINING METHODS IN FRACTURE MECHANICS: TACKLING LOCAL LACK OF CORRELATION USING DOMAIN DECOMPOSITION
Goury, Olivier; Kerfriden, Pierre; Rabczuk, Timon et al

Scientific Conference (2012, March)

In this paper, we propose to couple model order reduction techniques with domain decomposition meth- ods for the solution to parametric problems of fracture. The nonlinear nature of the problems requires ... [more ▼]

In this paper, we propose to couple model order reduction techniques with domain decomposition meth- ods for the solution to parametric problems of fracture. The nonlinear nature of the problems requires the use of a system approximation method to speed-up the assembly of the non-linear opreators. We show that the method efficiently computes a solution faster than a full order model for a given accuracy. The speed-up increases with the problem size. [less ▲]

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See detailAn Algorithm to compute damage from load in composites
Dunant, Cyrille F.; Bordas, Stéphane UL; Kerfriden, Pierre et al

in Frontiers of Architecture and Civil Engineering in China (2011), 5(2), 180-193

We present a new method to model fracture of concrete based on energy minimisation. The concrete is considered on the mesoscale as composite consisting of cement paste, aggregates and micro pores. In this ... [more ▼]

We present a new method to model fracture of concrete based on energy minimisation. The concrete is considered on the mesoscale as composite consisting of cement paste, aggregates and micro pores. In this first step, the alkali-silica reaction is taken into account through damage mechanics though the process is more complex involving thermo-hygro-chemo-mechanical reaction. We use a non-local damage model that ensures the well-posedness of the boundary value problem (BVP). In contrast to existing methods, the interactions between degrees of freedom evolve with the damage evolutions. Numerical results are compared to analytical and experimental results and show good agreement. [less ▲]

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See detailAlleviating the Mesh Burden in Computational Solid Mechanics
Bordas, Stéphane UL; Rabczuk, Timon; Ródenas, Juan-Jo et al

in Proceedings of ECT2010 (2010, December 12)

The goal of this chapter is to review recent avenues of investigation to alleviate meshing difficulties in computational mechanics and give a few exemplar applications. Keywords: meshing; enrichment ... [more ▼]

The goal of this chapter is to review recent avenues of investigation to alleviate meshing difficulties in computational mechanics and give a few exemplar applications. Keywords: meshing; enrichment; meshfree methods; extended finite element methods; isogeometric analysis; advanced remeshing techniques. [less ▲]

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See detailAn alternative alpha finite element method (AαFEM) for free and forced structural vibration using triangular meshes
Nguyen-Thanh, N.; Rabczuk, Timon; Nguyen-Xuan, H. et al

in Journal of Computational and Applied Mathematics (2010), 233(9), 2112-2135

An alternative alpha finite element method (AαFEM) using triangular elements is proposed that significantly improves the accuracy of the standard triangular finite elements and provides a superconvergent ... [more ▼]

An alternative alpha finite element method (AαFEM) using triangular elements is proposed that significantly improves the accuracy of the standard triangular finite elements and provides a superconvergent solution in the energy norm for the static analysis of two-dimensional solid mechanics problems. In the AαFEM, the piecewise constant strain field of linear triangular FEM models is enhanced by additional strain terms with an adjustable parameter α which results in an effectively softer stiffness formulation compared to a linear triangular element. The element is further extended to the free and forced vibration analyses of solids. Several numerical examples show that the AαFEM achieves high reliability compared to other existing elements in the literature. [less ▲]

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See detailAn alternative alpha finite element method with discrete shear gap technique for analysis of isotropic Mindlin-Reissner plates
Nguyen-Thanh, N.; Rabczuk, Timon; Nguyen-Xuan, H. et al

in Finite Elements in Analysis and Design (2011), 47(5), 519-535

An alternative alpha finite element method (AαFEM) coupled with a discrete shear gap technique for triangular elements is presented to significantly improve the accuracy of the standard triangular finite ... [more ▼]

An alternative alpha finite element method (AαFEM) coupled with a discrete shear gap technique for triangular elements is presented to significantly improve the accuracy of the standard triangular finite elements for static, free vibration and buckling analyses of MindlinReissner plates. In the AαFEM, the piecewise constant strain field of linear triangular elements is enhanced by additional strain terms with an adjustable parameter α which results in an effectively softer stiffness formulation compared to the linear triangular element. To avoid the transverse shear locking, the discrete shear gap technique (DSG) is utilized and a novel triangular element, the Aα-DSG3 is obtained. Several numerical examples show that the Aα-DSG3 achieves high reliability compared to other existing elements in the literature. Through selection of α, under or over estimation of the strain energy can be achieved. [less ▲]

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