The Experts below are selected from a list of 46110 Experts worldwide ranked by ideXlab platform

Qiong Meng - One of the best experts on this subject based on the ideXlab platform.

Fredrik Larsson - One of the best experts on this subject based on the ideXlab platform.

  • Localization aligned weakly Periodic Boundary Conditions
    International Journal for Numerical Methods in Engineering, 2017
    Co-Authors: Erik Svenning, Martin Fagerström, Fredrik Larsson
    Abstract:

    When computing the homogenized response of a representative volume element (RVE), a popular choice is to impose Periodic Boundary Conditions on the RVE. Despite their popularity, it is well known that standard Periodic Boundary Conditions lead to inaccurate results if cracks or localization bands in the RVE are not aligned with the Periodicity directions. A previously proposed remedy is to use modified strong Periodic Boundary Conditions that are aligned with the dominating localization direction in the RVE. In the present work, we show that alignment of Periodic Boundary Conditions can also conveniently be performed on weak form. Starting from a previously proposed format for weak micro-Periodicity that does not require a Periodic mesh, we show that aligned weakly Periodic Boundary Conditions may be constructed by only modifying the mapping (mirror function) between the associated parts of the RVE Boundary. In particular, we propose a modified mirror function that allows alignment with an identified localization direction. This modified mirror function corresponds to a shifted stacking of RVEs, and thereby ensures compatibility of the dominating discontinuity over the RVE boundaries. The proposed method leads to more accurate results compared to using unaligned Periodic Boundary Conditions, as demonstrated by the numerical examples.

  • computational homogenization of microfractured continua using weakly Periodic Boundary Conditions
    Computer Methods in Applied Mechanics and Engineering, 2016
    Co-Authors: Erik Svenning, Martin Fagerström, Fredrik Larsson
    Abstract:

    Computational homogenization of elastic media with stationary cracks is considered, whereby the macroscale stress is obtained by solving a Boundary value problem on a Statistical Volume Element (SVE) and the cracks are represented by means of the eXtended Finite Element Method (XFEM). With the presence of cracks on the microscale, conventional BCs (Dirichlet, Neumann, strong Periodic) perform poorly, in particular when cracks intersect the SVE Boundary. As a remedy, we herein propose to use a mixed variational format to impose Periodic Boundary Conditions in a weak sense on the SVE. Within this framework, we develop a novel traction approximation that is suitable when cracks intersect the SVE Boundary. Our main result is the proposition of a stable traction approximation that is piecewise constant between crack-Boundary intersections. In particular, we prove analytically that the proposed approximation is stable in terms of the LBB (inf-sup) condition and illustrate the stability properties with a numerical example. We emphasize that the stability analysis is carried out within the setting of weakly Periodic Boundary Conditions, but it also applies to other mixed problems with similar structure, e.g. contact problems. The numerical examples show that the proposed traction approximation is more efficient than conventional Boundary Conditions (Dirichlet, Neumann, strong Periodic) in terms of convergence with increasing SVE size.

Xianhua Tang - One of the best experts on this subject based on the ideXlab platform.

Frans P. Van Der Meer - One of the best experts on this subject based on the ideXlab platform.

  • Stress‐controlled weakly Periodic Boundary Conditions: Axial stress under varying orientations
    International Journal for Numerical Methods in Engineering, 2020
    Co-Authors: Erik Giesen Loo, Frans P. Van Der Meer
    Abstract:

    The accuracy of multiscale modeling approaches for the analysis of heterogeneous materials hinges on the representativeness of the micromodel. One of the issues that affects this representativeness is the application of appropriate Boundary Conditions. Periodic Boundary Conditions are the most common choice. However, when localization takes place, Periodic Boundary Conditions tend to overconstrain the microscopic problem. Weakly Periodic Boundary Conditions have been proposed to overcome this effect. In this study, the effectiveness of weakly Periodic Boundary Conditions in restoring transverse isotropy of representative volume elements (RVE) for a fiber-reinforced composite with elastoplastic matrix is investigated. The formulation of weakly Periodic Boundary Conditions is extended to allow for force-controlled simulations where a uniaxial stress can be applied. A series of simulations is performed where the orientation of applied stress is gradually varied and the influence of this orientation on the averaged response is examined. An original method is presented to test the correlation between the ultimate principal stress and average localization angle of shear bands within an RVE. It is concluded that weakly Periodic Boundary Conditions alleviate anisotropy in the RVE response but do not remove it.

Billy D. Todd - One of the best experts on this subject based on the ideXlab platform.

  • On the Arnold cat map and Periodic Boundary Conditions for planar elongational flow
    Molecular Physics, 2003
    Co-Authors: Thomas A. Hunt, Billy D. Todd
    Abstract:

    In this paper we show that the Periodic Boundary Conditions used to simulate planar elongational flow are closely related to the Arnold cat map. In particular the relationship between the Arnold cat map and the Periodic Boundary Conditions devised by Kraynik and Reinelt [1992, Int. J. multiphase Flow, 18, 1045], the so-called K-R map, is demonstrated. It is shown that the family of lattices found by Kraynik and Reinelt corresponds to a subset of hyperbolic toral automorphisms. These lattices were previously found to be sufficient to enable molecular dynamics simulations of steady-state planar elongational flow of unrestricted duration. Within the frame of the cat map we provide a re-derivation for the set of eigenvalues, eigenvectors and orientation angles of the K-R map and find it to be considerably simpler than the original derivation provided by Kraynik and Reinel

  • NONEQUILIBRIUM MOLECULAR DYNAMICS SIMULATIONS OF PLANAR ELONGATIONAL FLOW WITH SPATIALLY AND TEMPORALLY Periodic Boundary Conditions
    Physical Review Letters, 1998
    Co-Authors: Billy D. Todd, Peter J. Daivis
    Abstract:

    We apply the spatially and temporally Periodic Boundary Conditions devised by Kraynik and Reinelt [Int. J. Multiphase Flow 18, 1045 (1992)] to an atomic fluid undergoing planar elongational flow. The Periodic Boundary Conditions guarantee theoretically infinite simulation times, and thus provide the most promising method yet developed to simulate molecular fluids undergoing steady planar extension using nonequilibrium molecular dynamics techniques. [S0031-9007(98)06571-5]