### Abstract

Features of the propagation of longitudinal and transverse plane waves along the layers of nanocomposites with process-induced initial stresses are studied. The composite has a periodic structure: it is made by repeating two highly dissimilar layers. The layers exhibit nonlinear elastic behavior in the range of loads under consideration. A Murnaghan-type elastic potential dependent on the three invariants of the strain tensor is used to describe the mechanical behavior of the composite constituents. To simulate the propagation of waves, finite-strain theory is used for developing a problem statement within the framework of the three-dimensional linearized theory of elasticity assuming finite initial strains. The dependence of the relative velocities of longitudinal and transverse waves on two components of small initial stresses in each layer and on the volume fraction of the constituents is studied. It is established that there are thickness ratios of layers in some nanocomposites such that the wave velocities are independent of the initial stresses and equal to the respective wave velocities in composites without initial stresses.

Original language | English |
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Pages (from-to) | 361-379 |

Number of pages | 19 |

Journal | International Applied Mechanics |

Volume | 43 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2007 |

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### Keywords

- composite materials
- nanocomposites
- three-dimensional linearized theory of elasticity
- initial stresses
- longitudinal and transverse wave propagation
- wave velocities
- elastic-constants
- carbon nanotubes
- mechanics
- stability
- element
- matrix

### Cite this

**Features of plane wave propagation along the layers of a prestrained nanocomposite.** / Zhuk, Ya. A.; Guz, I. A.

Research output: Contribution to journal › Article

*International Applied Mechanics*, vol. 43, no. 4, pp. 361-379. https://doi.org/10.1007/s10778-007-0032-8

}

TY - JOUR

T1 - Features of plane wave propagation along the layers of a prestrained nanocomposite

AU - Zhuk, Ya. A.

AU - Guz, I. A.

PY - 2007/4

Y1 - 2007/4

N2 - Features of the propagation of longitudinal and transverse plane waves along the layers of nanocomposites with process-induced initial stresses are studied. The composite has a periodic structure: it is made by repeating two highly dissimilar layers. The layers exhibit nonlinear elastic behavior in the range of loads under consideration. A Murnaghan-type elastic potential dependent on the three invariants of the strain tensor is used to describe the mechanical behavior of the composite constituents. To simulate the propagation of waves, finite-strain theory is used for developing a problem statement within the framework of the three-dimensional linearized theory of elasticity assuming finite initial strains. The dependence of the relative velocities of longitudinal and transverse waves on two components of small initial stresses in each layer and on the volume fraction of the constituents is studied. It is established that there are thickness ratios of layers in some nanocomposites such that the wave velocities are independent of the initial stresses and equal to the respective wave velocities in composites without initial stresses.

AB - Features of the propagation of longitudinal and transverse plane waves along the layers of nanocomposites with process-induced initial stresses are studied. The composite has a periodic structure: it is made by repeating two highly dissimilar layers. The layers exhibit nonlinear elastic behavior in the range of loads under consideration. A Murnaghan-type elastic potential dependent on the three invariants of the strain tensor is used to describe the mechanical behavior of the composite constituents. To simulate the propagation of waves, finite-strain theory is used for developing a problem statement within the framework of the three-dimensional linearized theory of elasticity assuming finite initial strains. The dependence of the relative velocities of longitudinal and transverse waves on two components of small initial stresses in each layer and on the volume fraction of the constituents is studied. It is established that there are thickness ratios of layers in some nanocomposites such that the wave velocities are independent of the initial stresses and equal to the respective wave velocities in composites without initial stresses.

KW - composite materials

KW - nanocomposites

KW - three-dimensional linearized theory of elasticity

KW - initial stresses

KW - longitudinal and transverse wave propagation

KW - wave velocities

KW - elastic-constants

KW - carbon nanotubes

KW - mechanics

KW - stability

KW - element

KW - matrix

U2 - 10.1007/s10778-007-0032-8

DO - 10.1007/s10778-007-0032-8

M3 - Article

VL - 43

SP - 361

EP - 379

JO - International Applied Mechanics

JF - International Applied Mechanics

SN - 1063-7095

IS - 4

ER -