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Stephen D. Bond


David J. Littlewood, Stewart A. Silling, John A. Mitchell, Pablo D. Seleson, Stephen D. Bond, Michael L. Parks, Daniel Z. Turner, Damon J. Burnett, Jakob Ostien and Max Gunzburger, Strong Local-Nonlocal Coupling for Integrated Fracture Modeling, Sandia National Laboratories Technical Report (2015) 1-100.


Peridynamics, a nonlocal extension of continuum mechanics, is unique in its ability to capture pervasive material failure. Its use in the majority of system-level analyses carried out at Sandia, however, is severely limited, due in large part to computational expense and the challenge posed by the imposition of nonlocal boundary conditions. Combined analyses in which peridynamics is employed only in regions susceptible to material failure are therefore highly desirable, yet available coupling strategies have remained severely limited. This report is a summary of the Laboratory Directed Research and Development (LDRD) project ``Strong Local-Nonlocal Coupling for Integrated Fracture Modeling,'' completed within the Computing and Information Sciences (CIS) Investment Area at Sandia National Laboratories. A number of challenges inherent to coupling local and nonlocal models are addressed. A primary result is the extension of peridynamics to facilitate a variable nonlocal length scale. This approach, termed the peridynamic partial stress, can greatly reduce the mathematical incompatibility between local and nonlocal equations through reduction of the peridynamic horizon in the vicinity of a model interface. A second result is the formulation of a blending-based coupling approach that may be applied either as the primary coupling strategy, or in combination with the peridynamic partial stress. This blending-based approach is distinct from general blending methods, such as the Arlequin approach, in that it is specific to the coupling of peridynamics and classical continuum mechanics. Facilitating the coupling of peridynamics and classical continuum mechanics has also required innovations aimed directly at peridynamic models. Specifically, the properties of peridynamic constitutive models near domain boundaries and shortcomings in available discretization strategies have been addressed. The results are a class of position-aware peridynamic constitutive laws for dramatically improved consistency at domain boundaries, and an enhancement to the meshfree discretization applied to peridynamic models that removes irregularities at the limit of the nonlocal length scale and dramatically improves convergence behavior. Finally, a novel approach for modeling ductile failure has been developed, motivated by the desire to apply coupled local-nonlocal models to a wide variety of materials, including ductile metals, which have received minimal attention in the peridynamic literature. Software implementation of the partial-stress coupling strategy, the position-aware peridynamic constitutive models, and the strategies for improving the convergence behavior of peridynamic models was completed within the Peridigm and Albany codes, developed at Sandia National Laboratories and made publicly available under the open-source 3-clause BSD license.

Full Text:

DOI: 10.2172/1221526

  author  = {David J. Littlewood and Stewart A. Silling and John A. Mitchell
             and Pablo D. Seleson and Stephen D. Bond and Michael L. Parks
             and Daniel Z. Turner and Damon J. Burnett and Jakob Ostien and
             Max Gunzburger},
  title   = {Strong Local-Nonlocal Coupling for Integrated Fracture Modeling},
  journal = {Sandia National Laboratories Technical Report},
  year    = 2015,
  pages   = {1--100},
  doi     = {10.2172/1221526},
  note    = {SAND2015-7998}

Stephen Bond