References of "Beex, Lars 50000691"
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See detailMultiscale computational mechanics: industrial applications
Bordas, Stéphane UL; Kerfriden, Pierre; Beex, Lars UL et al

Presentation (2014, November 25)

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See detailMultiscale Quasicontinuum Methods for Dissipative Truss Models and Beam Networks
Beex, Lars UL; Peerlings, Ron; Geers, Marc et al

Presentation (2014, November 05)

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See detailCardiff/Luxembourg Computational Mechanics Research Group
Bordas, Stéphane UL; Kerfriden, Pierre; Hale, Jack UL et al

Poster (2014, November)

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See detailDiscrete Multiscale Modelling and Future Research Plans concerning Metals
Beex, Lars UL; Bordas, Stéphane UL; Rappel, Hussein UL et al

Presentation (2014, October 14)

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See detailCentral summation in the quasicontinuum method
Beex, Lars UL; Peerlings, Ron; Geers, Marc

in Journal of the Mechanics & Physics of Solids (2014), 70

The quasicontinuum (QC) method [Tadmor, E.B., Phillips, R., Ortiz, M., 1996. Mixed atomistics and continuum models of deformation in solids. Langmuir 12, 4529–4534] is a multiscale methodology to ... [more ▼]

The quasicontinuum (QC) method [Tadmor, E.B., Phillips, R., Ortiz, M., 1996. Mixed atomistics and continuum models of deformation in solids. Langmuir 12, 4529–4534] is a multiscale methodology to significantly reduce the computational cost of atomistic simulations. The method ensures an accurate incorporation of small-scale atomistic effects in large-scale models. It essentially consists of an interpolation of the displacements of large numbers of atoms between representative atoms (repatoms) and an estimation of the total potential energy of the atomistic lattice by a so-called summation (or sampling) rule. In this paper a novel energy-based summation rule is presented for the QC method that allows for a seamless coupling between coarse domains and fully resolved domains. In the presented summation rule only the repatoms are used in combination with one extra sampling atom in the center of each interpolation triangle. The presented summation rule is therefore straightforward and computationally efficient. The performance of the proposed summation rule is evaluated for a number of two-dimensional and three-dimensional multiscale atomistic test problems. [less ▲]

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See detailUncertainty quantification of dry woven fabrics: A sensitivity analysis on material properties
Akmar, Ilyani; Lahmer, Tom; Beex, Lars UL et al

in Composite Structures (2014), 116

Based on sensitivity analysis, we determine the key meso-scale uncertain input variables that influence the macro-scale mechanical response of a dry textile subjected to uni-axial and biaxial deformation ... [more ▼]

Based on sensitivity analysis, we determine the key meso-scale uncertain input variables that influence the macro-scale mechanical response of a dry textile subjected to uni-axial and biaxial deformation. We assume a transversely isotropic fashion at the macro-scale of dry woven fabric. This paper focuses on global sensitivity analysis; i.e. regression- and variance-based methods. The sensitivity of four meso-scale uncertain input parameters on the macro-scale response are investigated; i.e. the yarn height, the yarn spacing, the yarn width and the friction coefficient. The Pearson coefficients are adopted to measure the effect of each uncertain input variable on the structural response. Due to computational effectiveness, the sensitivity analysis is based on response surface models. The Sobol’s variance-based method which consists of first-order and total-effect sensitivity indices are presented. The sensitivity analysis utilizes linear and quadratic correlation matrices, its corresponding correlation coefficients and the coefficients of determination of the response uncertainty criteria. The correlation analysis, the response surface model and Sobol’s indices are presented and compared by means of uncertainty criteria influences on MataBerkait-dry woven fabric material properties. To anticipate, it is observed that the friction coefficient and yarn height are the most influential factors with respect to the specified macro-scale mechanical responses. [less ▲]

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See detailMULTISCALE QUASICONTINUUM APPROACHES FOR DISCRETE MODELS OF FIBROUS MATERIALS SUCH AS ELECTRONIC TEXTILE AND PAPER MATERIALS
Beex, Lars UL; Peerlings, Ron; Geers, Marc et al

Scientific Conference (2014, July 20)

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See detailMultiscale Quasicontinuum Approaches for Planar Beam Lattices
Beex, Lars UL; Kerfriden, Pierre; Bordas, Stéphane UL

Scientific Conference (2014, July)

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See detailMultiscale quasicontinuum approaches for beam lattices
Beex, Lars UL; Peerlings, Ron; Geers, Marc et al

Scientific Conference (2014, July)

The quasicontinuum (QC) method was originally developed to reduce the computational efforts of large-scale atomistic (conservative) lattice computations. QC approaches have an intrinsically multiscale ... [more ▼]

The quasicontinuum (QC) method was originally developed to reduce the computational efforts of large-scale atomistic (conservative) lattice computations. QC approaches have an intrinsically multiscale character, as they combine fully resolved regions in which discrete lattice events can occur, with coarse-grained regions in which the lattice model is interpolated and integrated (summed in QC terminology). In previous works, virtual-power-based QC approaches were developed for dissipative (i.e. non-conservative) lattice computations which can for instance be used for fibrous materials. The virtual-power-based QC approaches have focused on dissipative spring/truss networks, but numerous fibrous materials can more accurately be described by (planar) beam networks. In this presentation, different QC approaches for planar beam lattices are introduced. In contrast to spring/truss lattices, beam networks include not only displacements but also rotations which need to be incorporated in the QC method, resulting in a mixed formulation. Furthermore, the presentation will show that QC approaches for planar beam lattices require higher-order interpolations to obtain accurate results, which also influences the numerical integration (summation in QC terminology). Results using different interpolations and types of integration will be shown for multiscale examples. [less ▲]

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See detailMultiscale quasicontinuum methods for fibrous materials
Beex, Lars UL; Peerlings, Ron; Geers, Marc et al

Scientific Conference (2014, July)

The QC method was originally proposed for (conservative) atomistic lattice models and is based on energy-minimization. Lattice models for fibrous materials however, are often non-conservative and energy ... [more ▼]

The QC method was originally proposed for (conservative) atomistic lattice models and is based on energy-minimization. Lattice models for fibrous materials however, are often non-conservative and energy-based QC methods can thus not straightforwardly be used. Examples presented here are a lattice model proposed for woven fabrics and a lattice model to describe interfiber bond failure and subsequent frictional fiber slidings. A QC framework is proposed that is based on the virtual-power statement of a non-conservative lattice model. Using the virtual-power statement, dissipative mechanisms can be included in the QC framework while the same summation rules suffice. Its validity is shown for a lattice model with elastoplastic trusses. The virtual-power-based QC method is also adopted to deal with the lattice model for bond failure and subsequent fiber sliding presented. In contrast to elastoplastic interactions that are intrinsically local dissipative mechanisms, bond failure and subsequent fiber sliding entail nonlocal dissipative mechanisms. Therefore, the virtual-power-based QC method is also equipped with a mixed formulation in which not only the displacements are interpolated, but also the internal variables associated with dissipation. [less ▲]

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See detailA multiscale quasicontinuum method for dissipative lattice models and discrete networks
Beex, Lars UL; Peerlings, Ron; Geers, Marc

in Journal of the Mechanics & Physics of Solids (2014), 64

Lattice models and discrete networks naturally describe mechanical phenomena at the mesoscale of fibrous materials. A disadvantage of lattice models is their computational cost. The quasicontinuum (QC ... [more ▼]

Lattice models and discrete networks naturally describe mechanical phenomena at the mesoscale of fibrous materials. A disadvantage of lattice models is their computational cost. The quasicontinuum (QC) method is a suitable multiscale approach that reduces the computational cost of lattice models and allows the incorporation of local lattice defects in large-scale problems. So far, all QC methods are formulated for conservative (mostly atomistic) lattice models. Lattice models of fibrous materials however, often require non-conservative interactions. In this paper, a QC formulation is derived based on the virtual-power of a non-conservative lattice model. By using the virtual-power statement instead of force-equilibrium, errors in the governing equations of the force-based QC formulations are avoided. Nevertheless, the non-conservative interaction forces can still be directly inserted in the virtual-power QC framework. The summation rules for energy-based QC methods can still be used in the proposed framework as shown by two multiscale examples. [less ▲]

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See detailA multiscale quasicontinuum method for lattice models with bond failure and fiber sliding
Beex, Lars UL; Peerlings, Ron; Geers, Marc

in Computer Methods in Applied Mechanics & Engineering (2014), 269

Structural lattice models incorporating trusses and beams are frequently used to mechanically model fibrous materials, because they can capture (local) mesoscale phenomena. Physically relevant lattice ... [more ▼]

Structural lattice models incorporating trusses and beams are frequently used to mechanically model fibrous materials, because they can capture (local) mesoscale phenomena. Physically relevant lattice computations are however computationally expensive. A suitable multiscale approach to reduce the computational cost of large-scale lattice computations is the quasicontinuum (QC) method. This method resolves local mesoscale phenomena in regions of interest and coarse grains elsewhere, using only the lattice model. In previous work, a virtual-power-based QC framework is proposed for lattice models that include local dissipative mechanisms. In this paper, the virtual-power-based QC method is adopted for lattice models in which bond failure and subsequent frictional fiber sliding are incorporated – which are of significant importance for fibrous materials such as paper, cardboard, textile and electronic textile. Bond failure and fiber sliding are nonlocal dissipative mechanisms and to deal with this nonlocality, the virtual-power-based QC method is equipped with a mixed formulation in which the kinematic variables as well as the internal history variables are interpolated. Previously defined summation rules can still be used to sample the governing equations in this QC framework. Illustrative examples are presented. [less ▲]

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See detailQuasicontinuum-based multiscale approaches for plate-like beam lattices experiencing in-plane and out-of-plane deformation
Beex, Lars UL; Kerfriden, Pierre; Rabczuk, Timon et al

in Computer Methods in Applied Mechanics & Engineering (2014), 279

The quasicontinuum (QC) method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations. The method incorporates small-scale local lattice phenomena (e.g. a ... [more ▼]

The quasicontinuum (QC) method is a multiscale approach that aims to reduce the computational cost of discrete lattice computations. The method incorporates small-scale local lattice phenomena (e.g. a single lattice defect) in macroscale simulations. Since the method works directly and only on the beam lattice, QC frameworks do not require the construction and calibration of an accompanying continuum model (e.g. a cosserat/micropolar description). Furthermore, no coupling procedures are required between the regions of interest in which the beam lattice is fully resolved and coarse domains in which the lattice is effectively homogenized. Hence, the method is relatively straightforward to implement and calibrate. In this contribution, four variants of the QC method are investigated for their use for planar beam lattices which can also experience out-of-plane deformation. The different frameworks are compared to the direct lattice computations for three truly multiscale test cases in which a single lattice defect is present in an otherwise perfectly regular beam lattice. [less ▲]

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See detailA discrete network model for bond failure and frictional sliding in fibrous materials
Wilbrink, David; Beex, Lars UL; Peerlings, Ron

in International Journal of Solids and Structures (2013), 50(9), 1354-1363

Discrete network models and lattice models using trusses or beams can be used to mechanically model fibrous materials, since the discrete elements represent the individual fibers or yarns at the mesoscale ... [more ▼]

Discrete network models and lattice models using trusses or beams can be used to mechanically model fibrous materials, since the discrete elements represent the individual fibers or yarns at the mesoscale of these materials. Consequently, local mesoscale phenomena, such as individual fiber failure and interfiber bond failure, can be incorporated. Only a few discrete network models in which bond failure is incorporated include frictional fiber sliding that occurs after bond failure has taken place, although this occurs in the mechanical behaviour of several fibrous materials. In this paper, a spring network model for interfiber bond failure and subsequent frictional fiber sliding is developed, which is formulated in a thermodynamical setting. The thermodynamical basis ensures that performed mechanical work is either stored in the network or dissipated due to bond failure and subsequent sliding. A numerical implementation of the framework is proposed in which the kinematic and internal variables are simultaneously solved, because the internal variables are directly coupled in the framework. Variations in network connectivity, bond strength, fiber length and anisotropy are implemented in the framework. The results show amongst others that the macroscopic yield point scales with the bond strength and that the macroscopic stiffness and the macroscopic yield point scale with the fiber length. The presented results also show that the macroscopic yield point becomes significantly less pronounced for an increase of the fiber length. [less ▲]

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See detailExperimental identification of a lattice model for woven fabrics: Application to electronic textile
Beex, Lars UL; Verberne, Cyriel; Peerlings, Ron

in Composites : Part A, Applied Science & Manufacturing (2013), 48

Lattice models employing trusses and beams are suitable to investigate the mechanical behavior of woven fabrics. The discrete features of the mesostructures of woven fabrics are naturally incorporated by ... [more ▼]

Lattice models employing trusses and beams are suitable to investigate the mechanical behavior of woven fabrics. The discrete features of the mesostructures of woven fabrics are naturally incorporated by the discrete elements of lattice models. In this paper, a lattice model for woven materials is adopted which consists of a network of trusses in warp and weft direction, which represent the response of the yarns. Additional diagonal trusses are included that provide a resistance against relative rotation of the yarns. The parameters of these families of discrete elements can be separately identified from tensile experiments in three in-plane directions which correspond with the orientations of the discrete elements. The lattice model and the identification approach are applied to electronic textile. This is a fabric in which conductive wires are incorporated to allow the embedment of electronic components such as light-emitting diodes. The model parameters are established based on tensile tests on samples of the electronic textile. A comparison between the experimental results of an out-of-plane punch test and the simulation results shows that the lattice model and its characterization procedure are accurate until extensive biaxial tensile deformation occurs. [less ▲]

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See detailOn the influence of delamination on laminated paperboard creasing and folding
Beex, Lars UL; Peerlings, Ron

in Philosophical Transactions of the Royal Society of London. Series A : Mathematical and Physical Sciences (2012), 370

Laminated paperboard is used as a packaging material for a wide range of products. During production of the packaging, the fold lines are first defined in a so-called creasing (or scoring) operation in ... [more ▼]

Laminated paperboard is used as a packaging material for a wide range of products. During production of the packaging, the fold lines are first defined in a so-called creasing (or scoring) operation in order to obtain uncracked folds. During creasing as well as folding, cracking of the board is to be avoided. A mechanical model for a single fold line has been proposed in a previous study (Beex & Peerlings 2009 Int. J. Solids Struct. 46, 4192–4207) to investigate the general mechanics of creasing and folding, as well as which precise mechanisms trigger the breaking of the top layer. In the present study, we employ this modelling to study the influence of delamination on creasing and folding. The results reveal the separate role of the cohesive zone model and the friction model in the description of delamination. They also show how the amount of delamination behaviour should be controlled to obtain the desired high folding stiffness without breaking of the top layer. [less ▲]

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See detailA quasicontinuum methodology for multiscale analyses of discrete microstructural models
Beex, Lars UL; Peerlings, Ron; Geers, Marc

in International Journal for Numerical Methods in Engineering (2011), 87(7), 701-718

Many studies in different research fields use lattice models to investigate the mechanical behavior of materials. Full lattice calculations are often performed to determine the influence of localized ... [more ▼]

Many studies in different research fields use lattice models to investigate the mechanical behavior of materials. Full lattice calculations are often performed to determine the influence of localized microscale phenomena on large-scale responses but they are usually computationally expensive. In this study the quasicontinuum (QC) method (Phil. Mag. A 1996; 73:1529–1563) is extended towards lattice models that employ discrete elements, such as trusses and beams. The QC method is a multiscale approach that uses a triangulation to interpolate the lattice model in regions with small fluctuations in the deformation field, while in regions of high interest the exact lattice model is obtained by refining the triangulation to the internal spacing of the lattice. Interpolation ensures that the number of unknowns is reduced while summation ensures that only a selective part of the underlying lattice model must be visited to construct the governing equations. As the QC method has so far only been applied to atomic lattice models, the existing summation procedures have been revisited for structural lattice models containing discrete elements. This has led to a new QC method that makes use of the characteristic structure of the considered truss network. The proposed QC method is, to the best of the authors’ knowledge, the only QC method that does not need any correction at the interface between the interpolated and the fully resolved region and at the same time gives exact results unlike the cluster QC methods. In its present formulation, the proposed QC method can only be used for lattice models containing nearest neighbor interactions, but with some minor adaptations it can also be used for lattices with next-nearest neighbor interactions such as atomic lattices. [less ▲]

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See detailAn experimental and computational study of laminated paperboard creasing and folding
Beex, Lars UL; Ron, Peerlings

in International Journal of Solids and Structures (2009)

Laminated paperboard is often used as a packaging material for products such as toys, tea and frozenfoods. To make the paperboard packages appealing for consumers, the fold lines must be both neat and ... [more ▼]

Laminated paperboard is often used as a packaging material for products such as toys, tea and frozenfoods. To make the paperboard packages appealing for consumers, the fold lines must be both neat and undamaged. The quality of the folds depends on two converting processes: the manufacture of fold lines (creasing) and the subsequent folding. A good crease contains some delamination, initiated during creasing, to reduce the bending stiffness and to prevent the board from breaking during folding. However, for boards of high grammage breaking of the top layer is nevertheless a frequent problem. The mechanisms that operate in the creasing zone during creasing and folding, and that may thus result in breaking of the top layer, are studied in this contribution on the basis of idealized small-scale creasing and folding experiments. However, since experimental observations are only limited means to study the paperboard’s behavior, a mechanical model is proposed to obtain more detailed insight. Although the material and delamination descriptions used in the mechanical model are both relatively straightforward, comparisons between the model and the experimental data show that the model predicts the paperboard’s response well. The mechanical model shows – in combination with experimental strain fields – that multiple delaminations are initiated in the shear regions. Moreover, only the mechanical model reveals the mechanism that is responsible for the failure of the top layer if a crease is too shallow. Finally, the model also demonstrates that not only delamination but also plastic behavior must occur during creasing if breaking of the top layer is to be avoided. [less ▲]

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See detailBayesian inference for the stochastic identification of elastoplastic material parameters: Introduction, misconceptions and insights
Rappel, Hussein UL; Beex, Lars UL; Hale, Jack UL et al

E-print/Working paper (n.d.)

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material ... [more ▼]

We discuss Bayesian inference (BI) for the probabilistic identification of material parameters. This contribution aims to shed light on the use of BI for the identification of elastoplastic material parameters. For this purpose a single spring is considered, for which the stress-strain curves are artificially created. Besides offering a didactic introduction to BI, this paper proposes an approach to incorporate statistical errors both in the measured stresses, and in the measured strains. It is assumed that the uncertainty is only due to measurement errors and the material is homogeneous. Furthermore, a number of possible misconceptions on BI are highlighted based on the purely elastic case. [less ▲]

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