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Title: Nonlocal and Mixed-Locality Multiscale Finite Element Methods

Journal Article · · Multiscale Modeling & Simulation
DOI:https://doi.org/10.1137/16M1090351· OSTI ID:1429643
 [1];  [2];  [2]
  1. Oregon State Univ., Corvallis, OR (United States). Department of Mathematics; Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research
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In many applications the resolution of small-scale heterogeneities remains a significant hurdle to robust and reliable predictive simulations. In particular, while material variability at the mesoscale plays a fundamental role in processes such as material failure, the resolution required to capture mechanisms at this scale is often computationally intractable. Multiscale methods aim to overcome this difficulty through judicious choice of a subscale problem and a robust manner of passing information between scales. One promising approach is the multiscale finite element method, which increases the fidelity of macroscale simulations by solving lower-scale problems that produce enriched multiscale basis functions. Here, in this study, we present the first work toward application of the multiscale finite element method to the nonlocal peridynamic theory of solid mechanics. This is achieved within the context of a discontinuous Galerkin framework that facilitates the description of material discontinuities and does not assume the existence of spatial derivatives. Analysis of the resulting nonlocal multiscale finite element method is achieved using the ambulant Galerkin method, developed here with sufficient generality to allow for application to multiscale finite element methods for both local and nonlocal models that satisfy minimal assumptions. Finally, we conclude with preliminary results on a mixed-locality multiscale finite element method in which a nonlocal model is applied at the fine scale and a local model at the coarse scale.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000; NA0003525
OSTI ID:
1429643
Report Number(s):
SAND-2017-10571J; 657420
Journal Information:
Multiscale Modeling & Simulation, Vol. 16, Issue 1; ISSN 1540-3459
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

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Cited By (1)

Decoupling Strength and Grid Resolution in Peridynamic Theory journal April 2019

Figures / Tables (9)

Fig. 1.(p. 5)figure Fig. 1.
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Table 1(p. 20)table Table 1
Fig. 5.(p. 21)figure Fig. 5.
Fig. 6.(p. 22)figure Fig. 6.
Fig. 7.(p. 23)figure Fig. 7.
Fig. 8.(p. 23)figure Fig. 8.

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97 MATHEMATICS AND COMPUTING
multiscale
fi nite elements method
nonlocal
mixed locality
peridynamics