An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions

Technical Report · 08 October 2021

DOI:https://doi.org/10.2172/1825041· OSTI ID:1825041

D'Elia, Marta ^[1]; Littlewood, David J. ^[2]; Trageser, Jeremy ^[2]; Perego, Mauro ^[2]; Bochev, Pavel B. ^[2]

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1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

We develop and analyze an optimization-based method for the coupling of a static peridynamic (PD) model and a static classical elasticity model. The approach formulates the coupling as a control problem in which the states are the solutions of the PD and classical equations, the objective is to minimize their mismatch on an overlap of the PD and classical domains, and the controls are virtual volume constraints and boundary conditions applied at the local-nonlocal interface. Our numerical tests performed on three-dimensional geometries illustrate the consistency and accuracy of our method, its numerical convergence, and its applicability to realistic engineering geometries. We demonstrate the coupling strategy as a means to reduce computational expense by confining the nonlocal model to a subdomain of interest, and as a means to transmit local (e.g., traction) boundary conditions applied at a surface to a nonlocal model in the bulk of the domain.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• DOE Contract Number: NA0003525
• OSTI ID: 1825041
• Report Number(s): SAND2021-12618R; 700766
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
boundary conditions
classical elasticity
coupling methods
finite element method
meshfree method
nonlocal models
optimization
peridynamic