Journal
NONLINEARITY
Volume 35, Issue 11, Pages 5664-5713Publisher
IOP Publishing Ltd
DOI: 10.1088/1361-6544/ac8fd9
Keywords
peridynamics; nonlocal continuum mechanics; elasticity
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Funding
- Research Project of National Relevance 'Multiscale Innovative Materials and Structures' by the Italian Ministry of Education, University and Research (MIUR Prin 2017) [2017J4EAYB]
- Italian Ministry of Education, University and Research [CUP-D94I18000260001]
- Australian Research Council DECRA [DE180100957]
- FCT [CEECIND/04399/2017/CP1387/CT0026]
- Australian Laureate Fellowship [FL190100081]
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This study analyzes the interplay between nonlocality and dispersion in a linear equation inspired by peridynamics models. Global dispersive estimates and the existence of conserved functionals are proven through the study of low and high frequency asymptotics. A comparison with the classical local scenario is deepened through numerical analysis.
We study the dispersive properties of a linear equation in one spatial dimension which is inspired by models in peridynamics. The interplay between nonlocality and dispersion is analyzed in detail through the study of the asymptotics at low and high frequencies, revealing new features ruling the wave propagation in continua where nonlocal characteristics must be taken into account. Global dispersive estimates and existence of conserved functionals are proved. A comparison between these new effects and the classical local scenario is deepened also through a numerical analysis.
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