References of "Zeman, Jan"
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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 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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