References of "Computational Mechanics"
     in
Bookmark and Share    
Full Text
Peer Reviewed
See detailNitsche’s method for two and three dimensional NURBS patch coupling
Nguyen, Vinh-Phu; Kerfriden, Pierre; Brino, Marco et al

in Computational Mechanics (in press)

We present a Nitche’s method to couple non-conforming two and three-dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for linear ... [more ▼]

We present a Nitche’s method to couple non-conforming two and three-dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for linear elastostatics in two and and three-dimensions. The method can deal with surface-surface or volume-volume coupling, and we show how it can be used to handle heterogeneities such as inclusions. We also present preliminary results on modal analysis. This simple coupling method has the potential to increase the applicability of NURBS-based isogeometric analysis for practical applications. [less ▲]

Detailed reference viewed: 813 (61 UL)
Full Text
Peer Reviewed
See detailMultiple crack detection in 3D using a stable XFEM and global optimization
Agathos, Konstantinos; Chatzi, Eleni; Bordas, Stéphane UL

in Computational Mechanics (2018)

A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid ... [more ▼]

A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid optimizer solution. The proposed XFEM variant is particularly well-suited for the simulation of 3D fracture problems, and as such serves as an efficient solution to the so-called forward problem. A set of heuristic optimization algorithms are recombined into a multiscale optimization scheme. The introduced approach proves effective in tackling the complex inverse problem involved, where identification of multiple flaws is sought on the basis of sparse measurements collected near the structural boundary. The potential of the scheme is demonstrated through a set of numerical case studies of varying complexity. [less ▲]

Detailed reference viewed: 108 (7 UL)
Full Text
Peer Reviewed
See detailMulti-phase-field modeling of anisotropic crack propagation for polycrystalline materials
Nguyen, Thanh Tung UL; Réthoré, J.; Yvonnet, J. et al

in Computational Mechanics (2017), 60

Detailed reference viewed: 29 (0 UL)
Full Text
Peer Reviewed
See detailGradient plasticity crack tip characterization by means of the extended finite element method
Martínez-Pañeda, Emilio; Natarajan, Sundar; Bordas, Stéphane UL

in Computational Mechanics (2017)

Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary ... [more ▼]

Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary dislocations. Characterizing the behavior at the small scales involved in crack tip deformation requires, however, the use of a very refined mesh within microns to the crack. In this work a novel and efficient gradient-enhanced numerical framework is developed by means of the extended finite element method (X-FEM). A mechanism-based gradient plasticity model is employed and the approximation of the displacement field is enriched with the stress singularity of the gradient-dominated solution. Results reveal that the proposed numerical methodology largely outperforms the standard finite element approach. The present work could have important implications on the use of microstructurally-motivated models in large scale applications. The non-linear X-FEM code developed in MATLAB can be downloaded from www.empaneda.com/codes. [less ▲]

Detailed reference viewed: 139 (2 UL)
Full Text
Peer Reviewed
See detailAutomatised selection of load paths to construct reduced-order models in computational damage micromechanics: from dissipation-driven random selection to Bayesian optimization
Goury, Olivier; Amsallem, David; Bordas, Stéphane UL et al

in Computational Mechanics (2016)

In this paper, we present new reliable model order reduction strategies for computational micromechanics. The difficulties rely mainly upon the high dimensionality of the parameter space represented by ... [more ▼]

In this paper, we present new reliable model order reduction strategies for computational micromechanics. The difficulties rely mainly upon the high dimensionality of the parameter space represented by any load path applied onto the representative volume element. We take special care of the challenge of selecting an exhaustive snapshot set. This is treated by first using a random sampling of energy dissipating load paths and then in a more advanced way using Bayesian optimization associated with an interlocked division of the parameter space. Results show that we can insure the selection of an exhaustive snapshot set from which a reliable reduced-order model can be built. [less ▲]

Detailed reference viewed: 254 (31 UL)
Full Text
Peer Reviewed
See detailModelling interfacial cracking with non-matching cohesive interface elements
Nguyen, Viet Ha UL; Nguyen, Chi Thanh; Bordas, Stéphane UL et al

in Computational Mechanics (2016), 58(5), 731-746

Interfacial cracking occurs in many engineering problems such as delamination in composite laminates, matrix/interface debonding in fibre reinforced composites etc. Computational modelling of these ... [more ▼]

Interfacial cracking occurs in many engineering problems such as delamination in composite laminates, matrix/interface debonding in fibre reinforced composites etc. Computational modelling of these interfacial cracks usually employs compatible or matching cohesive interface elements. In this paper, incompatible or non-matching cohesive interface elements are proposed for interfacial fracture mechanics problems. They allow non-matching finite element discretisations of the opposite crack faces thus lifting the constraint on the compatible discretisation of the domains sharing the interface. The formulation is based on a discontinuous Galerkin method and works with both initially elastic and rigid cohesive laws. The proposed formulation has the following advantages compared to classical interface elements: (i) non-matching discretisations of the domains and (ii) no high dummy stiffness. Two and three dimensional quasi-static fracture simulations are conducted to demonstrate the method. Our method not only simplifies the meshing process but also it requires less computational demands, compared with standard interface elements, for problems that involve materials/solids having a large mismatch in stiffnesses. [less ▲]

Detailed reference viewed: 39 (1 UL)
Full Text
Peer Reviewed
See detailNitsche’s method for two and three dimensional NURBS patch coupling
Nguyen, VP; Kerfriden, Pierre; Brino, Marco et al

in Computational Mechanics (2014), 53(6), 1163-1182

We present a Nitche’s method to couple non-conforming two and three-dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for linear ... [more ▼]

We present a Nitche’s method to couple non-conforming two and three-dimensional NURBS (Non Uniform Rational B-splines) patches in the context of isogeometric analysis (IGA). We present results for linear elastostatics in two and and three-dimensions. The method can deal with surface-surface or volume-volume coupling, and we show how it can be used to handle heterogeneities such as inclusions. We also present preliminary results on modal analysis. This simple coupling method has the potential to increase the applicability of NURBS-based isogeometric analysis for practical applications. [less ▲]

Detailed reference viewed: 675 (16 UL)
Full Text
Peer Reviewed
See detailOn efficient and reliable stochastic generation of RVEs for analysis of composites within the framework of homogenization
Salnikov, Vladimir UL; Karamian, Philippe; Choi, Daniel

in Computational Mechanics (2014)

Detailed reference viewed: 26 (0 UL)
Full Text
Peer Reviewed
See detailMesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery
González-Estrada, O. A.; Nadal, E.; Ródenas, J. J. et al

in Computational Mechanics (2013)

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for ... [more ▼]

Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for design purposes (e.g. the mean stress or mean displacement in a particular area, the stress intensity factor for fracture problems). These GOEE are one of the key unsolved problems of advanced engineering applications in, for example, the aerospace industry. This work presents a simple recovery-based error estimation technique for QoIs whose main characteristic is the use of an enhanced version of the Superconvergent Patch Recovery (SPR) technique previously used for error estimation in the energy norm. This enhanced SPR technique is used to recover both the primal and dual solutions. It provides a nearly statically admissible stress field that results in accurate estimations of the local contributions to the discretisation error in the QoI and, therefore, in an accurate estimation of this magnitude. This approach leads to a technique with a reasonable computational cost that could easily be implemented into already available finite element codes, or as an independent postprocessing tool. © 2013 Springer-Verlag Berlin Heidelberg. [less ▲]

Detailed reference viewed: 110 (2 UL)
Full Text
Peer Reviewed
See detailEfficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity
González-Estrada, O. A.; Natarajan, S.; Ródenas, J. J. et al

in Computational Mechanics (2013), 52(1), 37-52

An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown ... [more ▼]

An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a "smooth + singular" decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features. © 2012 Springer-Verlag. [less ▲]

Detailed reference viewed: 232 (4 UL)
Full Text
Peer Reviewed
See detailAn Adaptive Multiscale Method for Quasi-static Crack Growth
Pattabhi, Budarapu; Robert, Gracie; Bordas, Stéphane UL et al

in Computational Mechanics (2013)

This paper proposes an adaptive atomistic-continuum numerical method for quasi-static <br />crack growth. The phantom node method is used to model the crack in the continuum region <br />and a molecular ... [more ▼]

This paper proposes an adaptive atomistic-continuum numerical method for quasi-static <br />crack growth. The phantom node method is used to model the crack in the continuum region <br />and a molecular statics model is used near the crack tip. To ensure self-consistency in the bulk, <br />a virtual atom cluster is used to model the material of the coarse scale. The coupling between <br />the coarse scale and ne scale is realized through ghost atoms. The ghost atom positions are <br />interpolated from the coarse scale solution and enforced as boundary conditions on the ne <br />scale. The ne scale region is adaptively enlarged as the crack propagates and the region behind <br />the crack tip is adaptively coarsened. An energy criterion is used to detect the crack tip loca- <br />tion. The triangular lattice in the ne scale region corresponds to the lattice structure of the <br />(111) plane of an FCC crystal. The Lennard-Jones potential is used to model the atom-atom <br />interactions. The method is implemented in two dimensions. The results are compared to pure <br />atomistic simulations; they show excellent agreement. [less ▲]

Detailed reference viewed: 345 (12 UL)
Full Text
Peer Reviewed
See detailA hybrid smoothed extended finite element/level set method for modeling equilibrium shapes of nano-inhomogeneities
Zhao, X.; Bordas, Stéphane UL; Qu, J.

in Computational Mechanics (2013)

Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does ... [more ▼]

Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does in conventional mechanics analysis. When designing nanodevices and to understand the behavior of materials at the nano-scale, this interfacial energy must therefore be taken into account. The present work develops an effective numerical approach by means of a hybrid smoothed extended finite element/level set method to model nanoscale inhomogeneities with interfacial energy effect, in which the finite element mesh can be completely independent of the interface geometry. The Gurtin-Murdoch surface elasticity model is used to account for the interface stress effect and the Wachspress interpolants are used for the first time to construct the shape functions in the smoothed extended finite element method. Selected numerical results are presented to study the accuracy and efficiency of the proposed method as well as the equilibrium shapes of misfit particles in elastic solids. The presented results compare very well with those obtained from theoretical solutions and experimental observations, and the computational efficiency of the method is shown to be superior to that of its most advanced competitor. © 2013 Springer-Verlag Berlin Heidelberg. [less ▲]

Detailed reference viewed: 282 (7 UL)
Full Text
Peer Reviewed
See detailXLME interpolants, a seamless bridge between XFEM and enriched meshless methods
Amiri, F.; Anitescu, C.; Arroyo, M. et al

in Computational Mechanics (2013)

In this paper, we develop a method based on local maximum entropy shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture ... [more ▼]

In this paper, we develop a method based on local maximum entropy shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics. We obtain improved accuracy relative to the standard extended finite element method at a comparable computational cost. In addition, we keep the advantages of the LME shape functions, such as smoothness and non-negativity. We show numerically that optimal convergence (same as in FEM) for energy norm and stress intensity factors can be obtained through the use of geometric (fixed area) enrichment with no special treatment of the nodes near the crack such as blending or shifting. © 2013 Springer-Verlag Berlin Heidelberg. [less ▲]

Detailed reference viewed: 256 (1 UL)
Full Text
Peer Reviewed
See detailA computational library for multiscale modeling of material failure
Talebi, H.; Silani, M.; Bordas, Stéphane UL et al

in Computational Mechanics (2013)

We present an open-source software framework called PERMIX for multiscale modeling and simulation of fracture in solids. The framework is an object oriented open-source effort written primarily in Fortran ... [more ▼]

We present an open-source software framework called PERMIX for multiscale modeling and simulation of fracture in solids. The framework is an object oriented open-source effort written primarily in Fortran 2003 standard with Fortran/C++ interfaces to a number of other libraries such as LAMMPS, ABAQUS, LS-DYNA and GMSH. Fracture on the continuum level is modeled by the extended finite element method (XFEM). Using several novel or state of the art methods, the piece software handles semi-concurrent multiscale methods as well as concurrent multiscale methods for fracture, coupling two continuum domains or atomistic domains to continuum domains, respectively. The efficiency of our open-source software is shown through several simulations including a 3D crack modeling in clay nanocomposites, a semi-concurrent FE-FE coupling, a 3D Arlequin multiscale example and an MD-XFEM coupling for dynamic crack propagation. © 2013 Springer-Verlag Berlin Heidelberg. [less ▲]

Detailed reference viewed: 471 (4 UL)
Full Text
Peer Reviewed
See detailEnriched residual free bubbles for semiconductor device simulation
Simpson, R. N.; Bordas, Stéphane UL; Asenov, A. et al

in Computational Mechanics (2012), 50(1), 119-133

This article outlines a method for stabilising the current continuity equations which are used for semiconductor device simulation. Residual-free bubble functions (RfBF) are incorporated into a finite ... [more ▼]

This article outlines a method for stabilising the current continuity equations which are used for semiconductor device simulation. Residual-free bubble functions (RfBF) are incorporated into a finite element (FE) implementation that are able to prevent oscillations which are seen when using the conventional Bubnov-Galerkin FE implementation. In addition, it is shown that the RfBF are able to provide stabilisation with very distorted meshes and curved interface boundaries. Comparison with the commonly used SUPG scheme is made throughout, showing that in the case of 2D problems the RfBF allow faster convergence of the coupled semiconductor device equations, especially in the case of distorted meshes. [less ▲]

Detailed reference viewed: 25 (0 UL)
Full Text
Peer Reviewed
See detailLocalized meshless point collocation method for time-dependent magnetohydrodynamics flow through pipes under a variety of wall conductivity conditions
Loukopoulos, Vasilis; Bourantas, Georgios UL; Skouras, Eugene

in Computational Mechanics (2011), 47(2), 137-159

In this article a numerical solution of the time dependent, coupled system equations of magnetohydrody- namics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method ... [more ▼]

In this article a numerical solution of the time dependent, coupled system equations of magnetohydrody- namics (MHD) flow is obtained, using the strong-form local meshless point collocation (LMPC) method. The approxima- tion of the field variables is obtained with the moving least squares (MLS) approximation. Regular and irregular nodal distributions are used. Thus, a numerical solver is developed for the unsteady coupled MHD problems, using the collo- cation formulation, for regular and irregular cross sections, as are the rectangular, triangular and circular. Arbitrary wall conductivity conditions are applied when a uniform mag- netic field is imposed at characteristic directions relative to the flow one. Velocity and induced magnetic field across the section have been evaluated at various time intervals for sev- eral Hartmann numbers (up to 105) and wall conductivities. The numerical results of the strong-form MPC method are compared with those obtained using two weak-form mesh- less methods, that is, the local boundary integral equation (LBIE) meshless method and the meshless local Petrov– Galerkin (MLPG) method, and with the analytical solutions, where they are available. Furthermore, the accuracy of the method is assessed in terms of the error norms L 2 and L ∞ , the number of nodes in the domain of influence and the time step length depicting the convergence rate of the method. Run time results are also presented demonstrating the efficiency and the applicability of the method for real world problems. [less ▲]

Detailed reference viewed: 52 (0 UL)
Full Text
Peer Reviewed
See detailA node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates
Nguyen-Xuan, H.; Rabczuk, T.; Nguyen-Thanh, N. et al

in Computational Mechanics (2010), 46(5), 679-701

In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates. The discrete ... [more ▼]

In this paper, a node-based smoothed finite element method (NS-FEM) using 3-node triangular elements is formulated for static, free vibration and buckling analyses of Reissner-Mindlin plates. The discrete weak form of the NS-FEM is obtained based on the strain smoothing technique over smoothing domains associated with the nodes of the elements. The discrete shear gap (DSG) method together with a stabilization technique is incorporated into the NS-FEM to eliminate transverse shear locking and to maintain stability of the present formulation.Aso-called node-based smoothed stabilized discrete shear gap method (NS-DSG) is then proposed. Several numerical examples are used to illustrate the accuracy and effectiveness of the present method. [less ▲]

Detailed reference viewed: 38 (0 UL)
Full Text
Peer Reviewed
See detailA three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics
Rabczuk, Timon; Bordas, Stéphane UL; Zi, Goangseup

in Computational Mechanics (2007), 40(3), 473-495

This paper proposes a three-dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is ... [more ▼]

This paper proposes a three-dimensional meshfree method for arbitrary crack initiation and propagation that ensures crack path continuity for non-linear material models and cohesive laws. The method is based on a local partition of unity. An extrinsic enrichment of the meshfree shape functions is used with discontinuous and near-front branch functions to close the crack front and improve accuracy. The crack is hereby modeled as a jump in the displacement field. The initiation and propagation of a crack is determined by the loss of hyperbolicity or the loss of material stability criterion. The method is applied to several static, quasi-static and dynamic crack problems. The numerical results very precisely replicate available experimental and analytical results. [less ▲]

Detailed reference viewed: 31 (0 UL)