期刊论文详细信息
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES 卷:49
Analytical solutions of peristatic and peridynamic problems for a 1D infinite rod
Article
Mikata, Yozo
关键词: Peridynamics;    Peristatics;    Continuum mechanics;    Analytical solution;    1D infinite rod;    Dispersion relation;    Anomalous dispersion;    Group velocity;    Special relativity;   
DOI  :  10.1016/j.ijsolstr.2012.02.012
来源: Elsevier
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【 摘 要 】

Peridynamics is a nonlocal theory of continuum mechanics, which was developed by Silling (2000). Since then peridynamics has been applied to a variety of solid mechanics problems ranging from fracture, damage, failure to wave propagation, buckling, and detonation physics. Since the governing equation of peridynamics is an integro-differential equation, most of the treatment in the literature is often numerical. However, the analytical treatment is very important for the development of the peridynamic theory, which is continually developing at the present time. In this paper, peristatic and peridynamic problems for a 1D infinite rod are analytically investigated. We have developed a method to obtain a valid analytical solution starting from a formal analytical solution, which may be divergent. The primary contribution of the present paper is a systematic analytical treatment of peristatic and peridynamic problems for a 10 infinite rod. Additionally, dispersion curves and group velocities for the materials with three different micromoduli are also studied. It is found from the study that some peridynamic: materials can have negative group velocities in certain regions of wavenumber. This indicates that perdynamics can be used for modeling certain types of dispersive media with anomalous dispersion such as the one discussed by Mobley (2007). (C) 2012 Elsevier Ltd. All rights reserved.

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