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International Journal for Multiscale Computational Engineering

Impact factor: 1.103

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2011002527
pages 689-706

ON THE ROLE OF THE INFLUENCE FUNCTION IN THE PERIDYNAMIC THEORY

Pablo Seleson
Department of Scientific Computing, Florida State University, Tallahassee, Florida 32306-4120, USA
Michael Parks
Applied Mathematics and Applications, Sandia National Laboratories, Albuquerque, New Mexico 87185-1320, USA

ABSTRACT

The influence function in the peridynamic theory is used to weight the contribution of all the bonds participating in the computation of volume-dependent properties. In this work, we use influence functions to establish relationships between bond-based and state-based peridynamic models. We also demonstrate how influence functions can be used to modulate nonlocal effects within a peridynamic model independently of the peridynamic horizon. We numerically explore the effects of influence functions by studying wave propagation in simple one-dimensional models and brittle fracture in three-dimensional models.

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