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  1. No Access

    Article

    Linear Peridynamics Fourier Multipliers and Eigenvalues

    A characterization for the Fourier multipliers and eigenvalues of linear peridynamic operators is provided. The analysis is presented for state-based peridynamic operators for isotropic homogeneous media in an...

    Bacim Alali, Nathan Albin in Journal of Peridynamics and Nonlocal Modeling (2024)

  2. No Access

    Article

    Fourier Spectral Methods for Nonlocal Models

    Efficient and accurate spectral solvers for nonlocal models in any spatial dimension are presented. The approach we pursue is based on the Fourier multipliers of nonlocal Laplace operators introduced in Alali ...

    Bacim Alali, Nathan Albin in Journal of Peridynamics and Nonlocal Modeling (2020)

  3. No Access

    Article

    A generalized nonlocal vector calculus

    A nonlocal vector calculus was introduced in Du et al. (Math Model Meth Appl Sci 23:493–540, 2013) that has proved useful for the analysis of the peridynamics model of nonlocal mechanics and nonlocal diffusion mo...

    Bacim Alali, Kuo Liu, Max Gunzburger in Zeitschrift für angewandte Mathematik und Physik (2015)

  4. No Access

    Article

    Peridynamics and Material Interfaces

    The convergence of a peridynamic model for solid mechanics inside heterogeneous media in the limit of vanishing nonlocality is analyzed. It is shown that the operator of linear peridynamics for an isotropic he...

    Bacim Alali, Max Gunzburger in Journal of Elasticity (2015)

  5. No Access

    Article

    Multiscale Dynamics of Heterogeneous Media in the Peridynamic Formulation

    A methodology is presented for investigating the dynamics of heterogeneous media using the nonlocal continuum model given by the peridynamic formulation. The approach presented here provides the ability to mod...

    Bacim Alali, Robert Lipton in Journal of Elasticity (2012)