Bond-Based Peridynamics Does Not Converge to Hyperelasticity as the Horizon Goes to Zero

Bond-based peridynamics is a nonlocal continuum model in Solid Mechanics in which the energy of a deformation is calculated through a double integral involving pairs of points in the reference and deformed configurations. It is known how to calculate the Γ -limit of this model when the horizon (maxi...

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Bibliographic Details
Published inJournal of elasticity Vol. 141; no. 2; pp. 273 - 289
Main Authors Bellido, J. C., Cueto, J., Mora-Corral, C.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.09.2020
Springer Nature B.V
Subjects
Automotive Engineering
Classical Mechanics
Continuum modeling
Isotropy
Physics
Physics and Astronomy
Sobolev space
Solid mechanics
Gamma-convergence as the horizon goes to zero
49J45
74G65
Hiperelasticity
35Q74
74B20
Bond-based peridynamics
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Summary:Bond-based peridynamics is a nonlocal continuum model in Solid Mechanics in which the energy of a deformation is calculated through a double integral involving pairs of points in the reference and deformed configurations. It is known how to calculate the Γ -limit of this model when the horizon (maximum interaction distance between the particles) tends to zero, and the limit turns out to be a (local) vector variational problem defined in a Sobolev space, of the type appearing in (classical) hyperelasticity. In this paper we impose frame-indifference and isotropy in the model and find that very few hyperelastic functionals are Γ -limits of the bond-based peridynamics model. In particular, Mooney-Rivlin materials are not recoverable through this limit procedure.
ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-020-09782-9