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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 detailMultiscale Modelling of Damage and Fracture in Discrete Materials Using a Variational Quasicontinuum Method
Rokos, Ondrej; Peerlings, Ron; Beex, Lars UL et al

Scientific Conference (2017, September 05)

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See detaileXtended Variational Quasicontinuum Methodology for Modelling of Crack Propagation in Discrete Lattice Systems
Rokos, Ondrej; Peerlings, Ron; Zeman, Jan et al

Scientific Conference (2017, July 17)

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See detailAn Enriched Quasi-Continuum Approach to Crack Propagation in Discrete Lattices
Rokos, Ondrej; Peerlings, Ron; Zeman, Jan et al

Scientific Conference (2017, June 14)

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See detailA variational formulation of dissipative quasicontinuum methods
Rokos, Ondrej; Beex, Lars UL; Peerlings, Ron et al

in International Journal of Solids and Structures (2016), 102-103

Lattice systems and discrete networks with dissipative interactions are successfully employed as meso-scale models of heterogeneous solids. As the application scale generally is much larger than that of ... [more ▼]

Lattice systems and discrete networks with dissipative interactions are successfully employed as meso-scale models of heterogeneous solids. As the application scale generally is much larger than that of the discrete links, physically relevant simulations are computationally expensive. The QuasiContinuum (QC) method is a multiscale approach that reduces the computational cost of direct numerical simulations by fully resolving complex phenomena only in regions of interest while coarsening elsewhere. In previous work (Beex et al., J. Mech. Phys. Solids 64, 154-169, 2014), the originally conservative QC methodology was generalized to a virtual-power-based QC approach that includes local dissipative mechanisms. In this contribution, the virtual-power-based QC method is reformulated from a variational point of view, by employing the energy-based variational framework for rate-independent processes (Mielke and Roub cek, Rate-Independent Systems: Theory and Application, Springer-Verlag, 2015). By construction it is shown that the QC method with dissipative interactions can be expressed as a minimization problem of a properly built energy potential, providing solutions equivalent to those of the virtual-power-based QC formulation. The theoretical considerations are demonstrated on three simple examples. For them we verify energy consistency, quantify relative errors in energies, and discuss errors in internal variables obtained for different meshes and two summation rules. [less ▲]

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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 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 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 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 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 & 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 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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