In this work, a concurrent multiscale approach to dynamic fracture simulation is established to couple Peridynamics (PD) with the Extended Finite Element Method (XFEM). PD is a nonlocal reformulation of the classical continuum mechanics (CCM) based on a spatial-integral temporal-differential formulation. With its unique capability in incorporating material length scale, there is a continuing interest in establishing multiscale computational methods that integrate PD with CCM to achieve both high accuracy and efficiency. In the proposed multiscale approach, the coarse-scale XFEM simulation is performed over the entire problem domain and coexists with a localized fine-scale PD region where material crack pre-exists or is expected to initiate. The concurrent coupling between the XFEM and PD is achieved through two key technical ingredients. First, a bridging-scale projection operator that projects the fine-scale PD solution onto the overlapping coarse-scale FE basis functions. Second, a class of two-way nonlocal matching boundary conditions (NMBC) that transmits waves from the FE domain to the PD region as well as eliminates spurious wave reflections at the artificial numerical interface. The NMBC is cast in the form of a parameterized expression that involves the displacements and their higher-order time derivatives of PD nodes at the numerical interface. The non-reflective and wave-transmitting conditions are realized by minimizing the associated residual and its higher-order derivatives, which are functions of the PD dispersion relation at the particular wavelength of interest. The NMBC is established for bond-based PD, ordinary state-based PD, non-ordinary state-based PD, and its stabilized version. To further accommodate the evolving nature of the dynamic fracture, an adaptive scheme is established so that the PD region is dynamically prescribed to trace the propagating crack. The accuracy and efficiency of the established concurrent multiscale coupling approach are first demonstrated by several elastodynamic wave propagation examples in both 1D and 2D. Its effectiveness and robustness in material dynamic failure simulation are further demonstrated by several dynamic brittle fracture examples in 2D.

References:

\[1\]   D. Qian, G. J. Wagner, W. K. Liu. *A multiscale projection method for the analysis of carbon nanotubes*. Computer Methods in Applied Mechanics and Engineering 193, 2004: 1603-1632.

\[2\]   Y. Yang, S. Chirputkar, D. N. Alpert, T. Eason, S. Spottswood, and D. Qian, *Enriched space-time finite element method: a new paradigm for multiscaling from elastodynamics to molecular dynamics*, International Journal for Numerical Methods in Engineering*,* 92, 2012: 115-140.

\[3\]   C. Nicely, S. Tang, and D. Qian, “*Nonlocal matching boundary conditions for non-ordinary peridynamics with correspondence material model*”, Computer Methods in Applied Mechanics and Engineering 338, 2018: 463-490


Multiscale Dynamic Fracture Simulation Based on Concurrent Coupling of Peridynamics and Extended Finite Element Method

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Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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