Journal: Computational Mechanics

Abbreviation

Comput. mech.

Publisher

Springer

Journal Volumes

ISSN

0178-7675
1432-0924

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Publications 1 - 10 of 30
  • A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method
    Item type: Journal Article
    De Lorenzis, Laura; Wriggers, Peter; Zavarise, Giorgio (2012)
    Computational Mechanics
  • Multiple crack detection in 3D using a stable XFEM and global optimization
    Item type: Journal Article
    Agathos, Konstantinos; Chatzi, Eleni; Bordas, Stéphane P.A. (2018)
    Computational Mechanics
    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.
  • A mixed-order quasicontinuum approach for beam-based architected materials with application to fracture
    Item type: Journal Article
    Kraschewski, Kevin; Phlipot, Gregory P.; Kochmann, Dennis M. (2024)
    Computational Mechanics
    Predicting the mechanics of large structural networks, such as beam-based architected materials, requires a multiscale computational strategy that preserves information about the discrete structure while being applicable to large assemblies of struts. Especially the fracture properties of such beam lattices necessitate a two-scale modeling strategy, since the fracture toughness depends on discrete beam failure events, while the application of remote loads requires large simulation domains. As classical homogenization techniques fail in the absence of a separation of scales at the crack tip, we present a concurrent multiscale technique: a fully-nonlocal quasicontinuum (QC) multi-lattice formulation for beam networks, based on a conforming mesh. Like the original atomistic QC formulation, we maintain discrete resolution where needed (such as around a crack tip) while efficiently coarse-graining in the remaining simulation domain. A key challenge is a suitable model in the coarse-grained domain, where classical QC uses affine interpolations. This formulation fails in bending-dominated lattices, as it overconstrains the lattice by preventing bending without stretching of beams. Therefore, we here present a beam QC formulation based on mixed-order interpolation in the coarse-grained region—combining the efficiency of linear interpolation where possible with the accuracy advantages of quadratic interpolation where needed. This results in a powerful computational framework, which, as we demonstrate through our validation and benchmark examples, overcomes the deficiencies of previous QC formulations and enables, e.g., the prediction of the fracture toughness and the diverse nature of stress distributions of stretching- and bending-dominated beam lattices in two and three dimensions.
  • A regularized model for impact in explicit dynamics applied to the split Hopkinson pressure bar
    Item type: Journal Article
    Otto, Peter; De Lorenzis, Laura; Unger, Jörg F. (2016)
    Computational Mechanics
  • Stochastic multiscale homogenization analysis of heterogeneous materials under finite deformations with full uncertainty in the microstructure
    Item type: Journal Article
    Ma, Juan; Sahraee, Shahab; Wriggers, Peter; et al. (2015)
    Computational Mechanics
  • A Hu–Washizu variational approach to self-stabilized virtual elements: 2D linear elastostatics
    Item type: Journal Article
    Lamperti, Andrea; Cremonesi, Massimiliano; Perego, Umberto; et al. (2023)
    Computational Mechanics
    An original, variational formulation of the Virtual Element Method (VEM) is proposed, based on a Hu–Washizu mixed variational statement for 2D linear elastostatics. The proposed variational framework appears to be ideal for the formulation of VEs, whereby compatibility is enforced in a weak sense and the strain model can be prescribed a priori, independently of the unknown displacement model. It is shown how the ensuing freedom in the definition of the strain model can be conveniently exploited for the formulation of self-stabilized and possibly locking-free low order VEs. The superior performances of the VEs formulated within this framework has been verified by application to several numerical tests.
  • A segmentation-free isogeometric extended mortar contact method
    Item type: Journal Article
    Duong, Thang X.; De Lorenzis, Laura; Sauer, Roger A. (2019)
    Computational Mechanics
  • Piecewise oblique boundary treatment for the elastic-plastic wave equation on a cartesian grid
    Item type: Journal Article
    Giese, Guido (2009)
    Computational Mechanics
  • An adaptive acceleration scheme for phase-field fatigue computations
    Item type: Journal Article
    Heinzmann, Jonas; Carrara, Pietro; Ambati, Marreddy; et al. (2024)
    Computational Mechanics
    Phase-field models of fatigue are capable of reproducing the main phenomenology of fatigue behavior. However, phase-field computations in the high-cycle fatigue regime are prohibitively expensive due to the need to resolve spatially the small length scale inherent to phase-field models and temporally the loading history for several millions of cycles. As a remedy, we propose a fully adaptive acceleration scheme based on the cycle jump technique, where the cycle-by-cycle resolution of an appropriately determined number of cycles is skipped while predicting the local system evolution during the jump. The novelty of our approach is a cycle-jump criterion to determine the appropriate cycle-jump size based on a target increment of a global variable which monitors the advancement of fatigue. We propose the definition and meaning of this variable for three general stages of the fatigue life. In comparison to existing acceleration techniques, our approach needs no parameters and bounds for the cycle-jump size, and it works independently of the material, specimen or loading conditions. Since one of the monitoring variables is the fatigue crack length, we introduce an accurate, flexible and efficient method for its computation, which overcomes the issues of conventional crack tip tracking algorithms and enables the consideration of several cracks evolving at the same time. The performance of the proposed acceleration scheme is demonstrated with representative numerical examples, which show a speedup reaching up to four orders of magnitude in the high-cycle fatigue regime with consistently high accuracy.
  • Crack nucleation in heterogeneous bars: h- and p-FEM of a phase field model
    Item type: Journal Article
    Levy, Maxime; Vicentini, Francesco; Yosibash, Zohar (2024)
    Computational Mechanics
    Failure initiation and subsequent crack trajectory in heterogeneous materials, such as functionally graded materials and bones, are yet insufficiently addressed. The AT1 phase field model (PFM) is investigated herein in a 1D setting, imposing challenges and opportunities when discretized by h- and p-finite element (FE) methods. We derive explicit PFM solutions to a heterogeneous bar in tension considering heterogeneous E(x) and GIc(x), necessary for verification of the FE approximations. GIc(x) corrections accounting for the element size at the damage zone in h-FEMs are suggested to account for the peak stress underestimation. p-FEMs do not require any such corrections. We also derive and validate penalty coefficient for heterogeneous domains to enforce damage positivity and irreversibility via penalization. Numerical examples are provided, demonstrating that p-FEMs exhibit faster convergence rates comparing to classical h-FEMs. The new insights are encouraging towards p-FEM discretization in a 3D setting to allow an accurate prediction of failure initiation in human bones.
Publications 1 - 10 of 30