A dynamic hybrid local/nonlocal continuum model for wave propagation
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ORIGINAL PAPER
A dynamic hybrid local/nonlocal continuum model for wave propagation Fei Han1 · Shankun Liu1 · Gilles Lubineau2 Received: 28 November 2018 / Accepted: 14 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work, we develop a dynamic hybrid local/nonlocal continuum model to study wave propagations in a linear elastic solid. The developed hybrid model couples, in the dynamic regime, a classical continuum mechanics model with a bond-based peridynamic model using the Morphing coupling method that introduced in a previous study (Lubineau et al., J Mech Phys Solids 60(6):1088–1102, 2012). The classical continuum mechanical model is known as a local continuum model, while the peridynamic model is known as a nonlocal continuum model. This dynamic hybrid model aims to introduce the nonlocal model into the key structural domain, in which the dispersions or crack nucleations may occur due to flaws, while applying the local model to the rest of the structural domain. Both the local and nonlocal continuum domains are overlapped in the coupled subdomain. We study the speeds and angular frequencies of the plane waves, with small and large wavenumbers obtained by the hybrid model and compare them to purely local and purely nonlocal solutions. The error of the hybrid model is discussed by analyzing the ghost forces, and the work done by the ghost forces is considered equivalent to the energy of spurious reflections. One- and two-dimensional numerical examples illustrate the validity and accuracy of the proposed approach. We show that this dynamic hybrid local/nonlocal continuum model can be successfully applied to simulate wave propagations and crack nucleations induced by waves. Keywords Peridynamics · Continuum mechanics · Morphing coupling method · Hybrid model · Wave dispersion · Fracture
1 Introduction Peridynamics is a recently developed nonlocal theory in solid mechanics [1]. The peridynamic model redefines mechanical problems by replacing the partial differential equations with integral equations, which can naturally handle discontinuous solutions generated by spatial discontinuities. In doing so, the peridynamic model is an interesting tool for studying cracks and how they propagate. In a peridynamic model, it is assumed that the equilibrium of a material point is attained by an integral of internal forces exerted by surrounding points
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Gilles Lubineau [email protected]
1
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, International Research Center for Computational Mechanics, Dalian University of Technology, Dalian 116023, People’s Republic of China
2
Physical Science and Engineering Division, COHMAS Laboratory, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia
across a finite distance [2]. An internal force is defined over the connection vector, called the “bond”, between pairs of points. A bond is often set to break irreversibly when it is stretc
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