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See detailHigher-order quasicontinuum methods for elastic and dissipative lattice models: uniaxial deformation and pure bending
Beex, Lars UL; Rokos, Ondrej; Zeman, Jan et al

in GAMM Mitteilungen (2015), 38(2), 344-368

The quasicontinuum (QC) method is a numerical strategy to reduce the computational cost of direct lattice computations - in this study we achieve a speed up of a factor of 40. It has successfully been ... [more ▼]

The quasicontinuum (QC) method is a numerical strategy to reduce the computational cost of direct lattice computations - in this study we achieve a speed up of a factor of 40. It has successfully been applied to (conservative) atomistic lattices in the past, but using a virtual-power-statement it was recently shown that QC approaches can also be used for spring and beam lattice models that include dissipation. Recent results have shown that QC approaches for planar beam lattices experiencing in-plane and out-of-plane deformation require higher-order interpolation. Higher-order QC frameworks are scarce nevertheless. In this contribution, the possibilities of a second-order and third-order QC framework are investigated for an elastoplastic spring lattice. The higher-order QC frameworks are compared to the results of the direct lattice computations and to those of a linear QC scheme. Examples are chosen so that both a macroscale and a microscale quantity influences the results. The two multiscale examples focused on are (i) macroscopically prescribed uniaxial deformation and (ii) macroscopically prescribed pure bending. Furthermore, the examples include an individual inclusion in a large lattice and hence, are concurrent in nature. [less ▲]

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See detailOpen-Cell Aluminium Foams with Graded Coatings as Passively Controllable Energy Absorbers
Jung, Anne; Beex, Lars UL; Diebels, Stefan et al

in Materials & Design (2015), 87

Compared to most bulk materials, open-cell aluminium (Al) foams (OCAFs) are light-weight and can absorb a significant amount of energy in compression, e.g. during impact.When coatedwith nickel (Ni), OCAFs ... [more ▼]

Compared to most bulk materials, open-cell aluminium (Al) foams (OCAFs) are light-weight and can absorb a significant amount of energy in compression, e.g. during impact.When coatedwith nickel (Ni), OCAFs can absorb even more energy, making them more appropriate for impacts at higher velocities than uncoated OCAFs. When Ni-coated OCAFs experience low-velocity impact however, the stopping distance during the impact is small compared to that of uncoated OCAFs and hence, deceleration occurs fast. This exposes devices (and possibly human beings) protected by OCAFs to large internal forces leading to internal damage. An OCAF that combines the properties of uncoated and coated OCAFs can absorb energy during both low-velocity and high-velocity impact scenarios. This contribution introduces two of such OCAFs which are created by partially and gradually coating OCAFs. The general mechanics of the two OCAFs are revealed using experimental and numerical observation methods. [less ▲]

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See detailQuasicontinuum methods for planar beam lattices (abstract)
Beex, Lars UL; Kerfriden, Pierre; Heaney, Claire et al

Scientific Conference (2015, July)

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See detailMulti-scale fracture, model reduction, CAD and image as a model
Bordas, Stéphane UL; Kerfriden, Pierre; Beex, Lars UL et al

Scientific Conference (2015, June 24)

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See detailReduced order methods
Schenone, Elisa UL; Hale, Jack UL; Beex, Lars UL et al

Presentation (2015, April 16)

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See detailThe mechanical reliability of an electronic textile investigated using the virtual-power-based quasicontinuum method
Beex, Lars UL; Peerlings, Ron; Van Os, Koen et al

in Mechanics of Materials (2015), 80

The quasicontinuum (QC) method is a multiscale method for the solution of lattice models that combines coarse-grained regions and fully resolved regions with individual lattice events. QC methodologies ... [more ▼]

The quasicontinuum (QC) method is a multiscale method for the solution of lattice models that combines coarse-grained regions and fully resolved regions with individual lattice events. QC methodologies are mainly used to reduce the computational costs of conservative atomistic lattice computations. Recently, a virtual-power-based variant has been proposed that enables its use for non-conservative lattice computations. In this contribution the virtual-power-based QC approach is adopted in combination with a recently proposed mesostructural lattice model for electronic textile in order to investigate its mechanical behaviour. The interactions of the lattice model for electronic textile are modelled elastoplastically and hence, regular conservative QC approaches are not adequate. This article incorporates a modification of a previously defined exact summation rule for QC methods –by sampling the lattice interactions directly instead of via the lattice nodes. This leads to a significant reduction of the computational cost, whereas the accuracy of the summation rule remains unaffected. The presented methodology is used to efficiently investigate the failure envelope of an electronic textile – a woven fabric with embedded electronic components and conductive wires. The dependence of the failure envelope on the locations of the conductive wires and the stiffness of the weft yarns is investigated as well. [less ▲]

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

in Journal of the Mechanics and 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 and 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 and 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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