Elastodynamics of Linearized Isotropic State-Based Peridynamic Media
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The peridynamic theory has been used to model and simulate numerically various kinds of mechanical behavior of solids. This work is devoted to analytical solutions of the elastodynamic behavior of linearized isotropic state-based peridynamic materials. First, we present the solutions of the dispersion relations, group velocities, and phase velocities of longitudinal and transverse waves, and examine in detail the effects of the Poisson’s ratio on these properties. It is shown that the elastodynamic behavior of the state-based peridynamic material with a negative Poisson’s ratio is remarkably different from that of the material with a positive Poisson’s ratio. We then derive the general solutions of initial-value problems, and obtain the Green’s function in a closed form. Finally, we study the evolution of a displacement discontinuity in the state-based peridynamic medium, and find that each component of the discontinuity in the three-dimensional theory varies independently according to the same vibrational mode. The results may have implications in investigations of wave propagations, including discontinuities such as phase transitions and kink propagations.
KeywordsElastodynamics Nonlocal continuum theory Dispersion relation Wave propagation Peridynamics Green’s function
Mathematics Subject Classification45A05 74A05 74B99 74J05
The work is supported by the National Natural Science Foundation of China under Grant 11521202. Part of the work was completed when Linjuan Wang was visiting the Department of Mechanical Engineering at Massachusetts Institute of Technology under support of the Chinese Scholarship Council, and Professor Rohan Abeyaratne.
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