#### DMCA

## Laplace-Domain, High-Order Homogenization for Transient Dynamic Response of Viscoelastic Composites

Citations: | 2 - 2 self |

### Citations

145 | Microstructure in Linear Elasticity,"
- Mindlin
- 1964
(Show Context)
Citation Context ...number of investigations particularly on composites with elastic constituents. The realization and modeling of these phenomenon dates back to the classical works of Cosserat and Cosserat [5], Mindlin =-=[17]-=-, Eringen and Suhubi [9]. Material dispersion in composites has been modeled using a number of approaches including gradient elasticity [7], mathematical homogenization [13], Floquet-Bloch expansions ... |

69 | Photonic Band Structure: The Face-Centered-Cubic Case,”
- Yablonovitch, Gmitter
- 1989
(Show Context)
Citation Context ... passbands and stopbands. Stopbands refer to frequency bands within which the wave propagation is completely blocked. Band structures were found in the electromagnetic range (i.e., photonic bandgaps) =-=[36, 35]-=- as well as in the acoustic range (i.e., phononic bandgaps) [27, 14, 33]. In order to reveal the evanescent wave fields and bandgap structure, both the real and imaginary components of the wavenumber ... |

41 |
A dispersive effective medium for wave propagation in periodic composites.
- Santosa, Symes
- 1991
(Show Context)
Citation Context ..., Eringen and Suhubi [9]. Material dispersion in composites has been modeled using a number of approaches including gradient elasticity [7], mathematical homogenization [13], Floquet-Bloch expansions =-=[26]-=-, scale bridging through Hamilton’s principle [34], and Mindlin’s theory [8, 10]. The dispersion relation between wave frequency and wavenumber in the frequency domain displays a banded structure with... |

16 |
Microstructural Effects in Elastic Composites,”
- Boutin
- 1996
(Show Context)
Citation Context ...radiction is resolved by observing that the coefficients in these terms themselves are size dependent. It can be shown that D1 and 〈ρH〉 are proportional to l̂, and D2 and 〈ρP〉 are proportional to l̂2 =-=[3]-=-: D1 = O(Cl̂); 〈ρH〉 = O(ρl̂) (41a) D2 = O(Cl̂2); 〈ρP〉 = O(ρl̂2) (41b) where l̂ = l/ζ is the characteristic length of the microstructure in the stretched coordinate system, y, and l the characteristic ... |

16 |
Nonlinear Theory of Microelastic Solids—II,"
- Suhubi, Eringen
- 1964
(Show Context)
Citation Context ...particularly on composites with elastic constituents. The realization and modeling of these phenomenon dates back to the classical works of Cosserat and Cosserat [5], Mindlin [17], Eringen and Suhubi =-=[9]-=-. Material dispersion in composites has been modeled using a number of approaches including gradient elasticity [7], mathematical homogenization [13], Floquet-Bloch expansions [26], scale bridging thr... |

13 |
Programs for Fast Numerical Inversion of Laplace Transforms
- Brancik
- 1999
(Show Context)
Citation Context ...nization model includes the computation of response fields in the Laplace domain and the transformation of the Laplace domain response fields to the time domain. A numerical inverse Laplace transform =-=[4]-=- based on the Fast Fourier Transform and the -algorithm [15] is used to transform the solutions from the Laplace domain to the time domain. The transformation is performed through several steps descr... |

9 |
Higher order asymptotic homogenization and wave propagation in periodic composite materials
- Andrianov, Bolshakov, et al.
- 2008
(Show Context)
Citation Context ..., 14, 33]. In order to reveal the evanescent wave fields and bandgap structure, both the real and imaginary components of the wavenumber must be included [28]. Suzuki and Yu [29] and Andrianov et al. =-=[2]-=- employed the Floquet-Bloch theorem to model the appearance of bandgaps in photonics and phononic ranges, respectively. Hui and Oskay [13] proposed a multiscale homogenization model based on asymptoti... |

8 |
Waves in microstructured materials and dispersion.
- Engelbrecht, Berezovski, et al.
- 2005
(Show Context)
Citation Context ...using a number of approaches including gradient elasticity [7], mathematical homogenization [13], Floquet-Bloch expansions [26], scale bridging through Hamilton’s principle [34], and Mindlin’s theory =-=[8, 10]-=-. The dispersion relation between wave frequency and wavenumber in the frequency domain displays a banded structure with alternating passbands and stopbands. Stopbands refer to frequency bands within ... |

8 |
Complete acoustic band gaps in periodic fibre reinforced composite materials: The carbon/epoxy composite and some metallic systems,’’
- Vasseur, Djafari-Rouhani, et al.
- 1994
(Show Context)
Citation Context ...which the wave propagation is completely blocked. Band structures were found in the electromagnetic range (i.e., photonic bandgaps) [36, 35] as well as in the acoustic range (i.e., phononic bandgaps) =-=[27, 14, 33]-=-. In order to reveal the evanescent wave fields and bandgap structure, both the real and imaginary components of the wavenumber must be included [28]. Suzuki and Yu [29] and Andrianov et al. [2] emplo... |

6 |
Elastic waves in plates with periodically placed inclusions
- Sigalas, Economou
- 1994
(Show Context)
Citation Context ...which the wave propagation is completely blocked. Band structures were found in the electromagnetic range (i.e., photonic bandgaps) [36, 35] as well as in the acoustic range (i.e., phononic bandgaps) =-=[27, 14, 33]-=-. In order to reveal the evanescent wave fields and bandgap structure, both the real and imaginary components of the wavenumber must be included [28]. Suzuki and Yu [29] and Andrianov et al. [2] emplo... |

5 |
Accelerated convergence, divergence, iteration, extrapolation, and curve-fitting
- Macdonald
- 1964
(Show Context)
Citation Context ...n the Laplace domain and the transformation of the Laplace domain response fields to the time domain. A numerical inverse Laplace transform [4] based on the Fast Fourier Transform and the -algorithm =-=[15]-=- is used to transform the solutions from the Laplace domain to the time domain. The transformation is performed through several steps described below: 1. A set of discrete time steps (i.e., tβ where β... |

5 |
Modeling micro-inertia in heterogeneous materials under dynamic loading.
- Wang, Sun
- 2002
(Show Context)
Citation Context ...omposites has been modeled using a number of approaches including gradient elasticity [7], mathematical homogenization [13], Floquet-Bloch expansions [26], scale bridging through Hamilton’s principle =-=[34]-=-, and Mindlin’s theory [8, 10]. The dispersion relation between wave frequency and wavenumber in the frequency domain displays a banded structure with alternating passbands and stopbands. Stopbands re... |

4 |
Theorie des Corps Deformables, Hermann
- Cosserat, Cosserat
- 1909
(Show Context)
Citation Context ...subject to a number of investigations particularly on composites with elastic constituents. The realization and modeling of these phenomenon dates back to the classical works of Cosserat and Cosserat =-=[5]-=-, Mindlin [17], Eringen and Suhubi [9]. Material dispersion in composites has been modeled using a number of approaches including gradient elasticity [7], mathematical homogenization [13], Floquet-Blo... |

4 |
Viscoelastic response of sonic band-gap materials,”
- Psarobas
- 2001
(Show Context)
Citation Context ...gated the influence of material loss on the complex band structure of two-dimensional phononic crystals by incorporating viscoelastic constitutive model in the extended plane-wave expansion. Psarobas =-=[24]-=- discussed the effect of viscoelastic losses in a high-density contrast sonic bandgap material of closed packed rubber sphere in air. Merheb et al. [16] provided a theoretical and experimental study o... |

3 | Computational modeling of polyurea-coated composites subjected to blast loads
- Hui, Oskay
(Show Context)
Citation Context ... identical composition to the composite domain studied herein. The one-dimensional wave propagation problem in periodic viscoelastic media has a semi analytical solution as described in Hui and Oskay =-=[11]-=-. 20 ... |

3 |
A High Order Homogenization Model for Transient Dynamics of Heterogeneous Media Including Micro-Inertia Effects,” Comput.
- Hui, Oskay
- 2014
(Show Context)
Citation Context ... and Cosserat [5], Mindlin [17], Eringen and Suhubi [9]. Material dispersion in composites has been modeled using a number of approaches including gradient elasticity [7], mathematical homogenization =-=[13]-=-, Floquet-Bloch expansions [26], scale bridging through Hamilton’s principle [34], and Mindlin’s theory [8, 10]. The dispersion relation between wave frequency and wavenumber in the frequency domain d... |

3 |
Elastic and viscoelastic effects in rubber/air acoustic band gap structures: A theoretical and experimental study,”Journal of
- Merheb, Deymier, et al.
- 2008
(Show Context)
Citation Context ... in the extended plane-wave expansion. Psarobas [24] discussed the effect of viscoelastic losses in a high-density contrast sonic bandgap material of closed packed rubber sphere in air. Merheb et al. =-=[16]-=- provided a theoretical and experimental study of rubber/air acoustic bandgap structures. Oh et al. [21] investigated wave attenuation and dissipation mechanisms in viscoelastic phononic crystals havi... |

3 |
Material loss influence on the complex band structure and group velocity in phononic crystals
- Moiseyenko, Laude
(Show Context)
Citation Context ...c composites is even more limited. Zhao and Wei [37] studied the bandgap of one-dimensional phononic crystal with viscoelastic host material using the BlochFloquet wave solution. Moiseyenko and Laude =-=[18]-=- investigated the influence of material loss on the complex band structure of two-dimensional phononic crystals by incorporating viscoelastic constitutive model in the extended plane-wave expansion. P... |

3 |
Harmonic wave propagation in viscoelastic heterogeneous materials: Part II. Effective complex moduli
- Naciri, Navi, et al.
- 1994
(Show Context)
Citation Context ...elastic composites are relatively scarce compared to elastic problems (see Refs. [23, 31, 25] for some recent investigations). Modeling research has typically focused on layered or lattice structures =-=[30, 19, 1, 32, 20]-=- based on analytical and semi-analytical approaches. The literature on bandgap in viscoelastic composites is even more limited. Zhao and Wei [37] studied the bandgap of one-dimensional phononic crysta... |

3 |
A three dimensional C1 finite element for gradient elasticity
- Papanicolopulos, Zervos, et al.
- 2009
(Show Context)
Citation Context ...ces of error could be separately assessed if the higher order homogenization scheme without the projection approximation is evaluated directly using higher order (i.e., C1-continuous) finite elements =-=[22]-=- or other numerical approaches (e.g, isogeometric analysis [6]). The implementation of such numerical schemes is not straightforward and out of the scope of the current manuscript. Future investigatio... |

3 |
Complex elastic wave band structures in three-dimensional periodic elastic
- Suzuki, Yu
- 1998
(Show Context)
Citation Context ...e., phononic bandgaps) [27, 14, 33]. In order to reveal the evanescent wave fields and bandgap structure, both the real and imaginary components of the wavenumber must be included [28]. Suzuki and Yu =-=[29]-=- and Andrianov et al. [2] employed the Floquet-Bloch theorem to model the appearance of bandgaps in photonics and phononic ranges, respectively. Hui and Oskay [13] proposed a multiscale homogenization... |

2 |
Characterization of heterogeneous solids via wave methods in computational microelasticity
- Gonella, Greene, et al.
- 2011
(Show Context)
Citation Context ...using a number of approaches including gradient elasticity [7], mathematical homogenization [13], Floquet-Bloch expansions [26], scale bridging through Hamilton’s principle [34], and Mindlin’s theory =-=[8, 10]-=-. The dispersion relation between wave frequency and wavenumber in the frequency domain displays a banded structure with alternating passbands and stopbands. Stopbands refer to frequency bands within ... |

2 |
A nonlocal homogenization model for wave dispersion in dissipative composite materials
- Hui, Oskay
(Show Context)
Citation Context ...ndgap structures. Oh et al. [21] investigated wave attenuation and dissipation mechanisms in viscoelastic phononic crystals having different inclusion types in a long-wavelength regime. Hui and Oskay =-=[12]-=- demonstrated the formation of bandgaps in a one-dimensional layered viscoelastic composite using a semi-analytical solution based on the multiscale homogenization theory. This work helps to elucidate... |

2 | Elastic wave band gaps in 3-d periodic polymer matrix composites - Kafesaki, Sigalas, et al. - 1995 |

2 |
Transient Computational Homogenization for Heterogeneous Materials Under Dynamic Excitation,”
- Pham, Kouznetsova, et al.
- 2013
(Show Context)
Citation Context ... wave attenuation could be due to viscous dissipation, dispersive behavior or both. Studies on wave dispersion in viscoelastic composites are relatively scarce compared to elastic problems (see Refs. =-=[23, 31, 25]-=- for some recent investigations). Modeling research has typically focused on layered or lattice structures [30, 19, 1, 32, 20] based on analytical and semi-analytical approaches. The literature on ban... |

2 |
Tunneling in photonic band structures
- Suzuki, Yu
- 1995
(Show Context)
Citation Context ...e acoustic range (i.e., phononic bandgaps) [27, 14, 33]. In order to reveal the evanescent wave fields and bandgap structure, both the real and imaginary components of the wavenumber must be included =-=[28]-=-. Suzuki and Yu [29] and Andrianov et al. [2] employed the Floquet-Bloch theorem to model the appearance of bandgaps in photonics and phononic ranges, respectively. Hui and Oskay [13] proposed a multi... |

2 |
The effects of dispersion and dissipation on wave propagation in viscoelastic layered composities
- Ting
- 1980
(Show Context)
Citation Context ...elastic composites are relatively scarce compared to elastic problems (see Refs. [23, 31, 25] for some recent investigations). Modeling research has typically focused on layered or lattice structures =-=[30, 19, 1, 32, 20]-=- based on analytical and semi-analytical approaches. The literature on bandgap in viscoelastic composites is even more limited. Zhao and Wei [37] studied the bandgap of one-dimensional phononic crysta... |

2 |
A simple computational homogenization method for structures made of heterogeneous linear viscoelastic materials
- Tran, Yvonnet, et al.
- 2011
(Show Context)
Citation Context ... wave attenuation could be due to viscous dissipation, dispersive behavior or both. Studies on wave dispersion in viscoelastic composites are relatively scarce compared to elastic problems (see Refs. =-=[23, 31, 25]-=- for some recent investigations). Modeling research has typically focused on layered or lattice structures [30, 19, 1, 32, 20] based on analytical and semi-analytical approaches. The literature on ban... |

2 |
The Band Gap of 1D Viscoelastic Phononic Crystal,”
- Zhao, Wei
- 2009
(Show Context)
Citation Context ...ocused on layered or lattice structures [30, 19, 1, 32, 20] based on analytical and semi-analytical approaches. The literature on bandgap in viscoelastic composites is even more limited. Zhao and Wei =-=[37]-=- studied the bandgap of one-dimensional phononic crystal with viscoelastic host material using the BlochFloquet wave solution. Moiseyenko and Laude [18] investigated the influence of material loss on ... |

1 |
Propagation of transient out-of-plane shear waves in viscoelastic layered
- Abu-Alshaikh, Turhan, et al.
(Show Context)
Citation Context ...elastic composites are relatively scarce compared to elastic problems (see Refs. [23, 31, 25] for some recent investigations). Modeling research has typically focused on layered or lattice structures =-=[30, 19, 1, 32, 20]-=- based on analytical and semi-analytical approaches. The literature on bandgap in viscoelastic composites is even more limited. Zhao and Wei [37] studied the bandgap of one-dimensional phononic crysta... |

1 |
Isogeometric discretizations in structural dynamics and wave propagation
- Cottrell, Hughes, et al.
- 2007
(Show Context)
Citation Context ...omogenization scheme without the projection approximation is evaluated directly using higher order (i.e., C1-continuous) finite elements [22] or other numerical approaches (e.g, isogeometric analysis =-=[6]-=-). The implementation of such numerical schemes is not straightforward and out of the scope of the current manuscript. Future investigations will focus on implementation of such numerical schemes with... |

1 |
A physical perspective of the length scales in gradient elasticity through the prism of wave dispersion
- Dontsov, Tokmashev, et al.
(Show Context)
Citation Context ...o the classical works of Cosserat and Cosserat [5], Mindlin [17], Eringen and Suhubi [9]. Material dispersion in composites has been modeled using a number of approaches including gradient elasticity =-=[7]-=-, mathematical homogenization [13], Floquet-Bloch expansions [26], scale bridging through Hamilton’s principle [34], and Mindlin’s theory [8, 10]. The dispersion relation between wave frequency and wa... |

1 |
Discrete lattice simulation of transient motions in elastic and viscoelastic composites
- Nayfeh
- 1974
(Show Context)
Citation Context |

1 |
Wave attenuation and dissipation mechanisms in viscoelastic phononic crystals
- Oh, Kim, et al.
(Show Context)
Citation Context ...gh-density contrast sonic bandgap material of closed packed rubber sphere in air. Merheb et al. [16] provided a theoretical and experimental study of rubber/air acoustic bandgap structures. Oh et al. =-=[21]-=- investigated wave attenuation and dissipation mechanisms in viscoelastic phononic crystals having different inclusion types in a long-wavelength regime. Hui and Oskay [12] demonstrated the formation ... |

1 |
Effective behaviour of ageing linear viscoelastic composites: Homogenization approach
- Sanahuja
(Show Context)
Citation Context ... wave attenuation could be due to viscous dissipation, dispersive behavior or both. Studies on wave dispersion in viscoelastic composites are relatively scarce compared to elastic problems (see Refs. =-=[23, 31, 25]-=- for some recent investigations). Modeling research has typically focused on layered or lattice structures [30, 19, 1, 32, 20] based on analytical and semi-analytical approaches. The literature on ban... |

1 |
Structure of weak shock waves in 2-d layered material systems
- Tsai, Prakash
- 2005
(Show Context)
Citation Context |

1 |
Photonic band structure: Non-spherical atoms in the face-centered-cubic case
- Yablonovitch, Leung
- 1991
(Show Context)
Citation Context ... passbands and stopbands. Stopbands refer to frequency bands within which the wave propagation is completely blocked. Band structures were found in the electromagnetic range (i.e., photonic bandgaps) =-=[36, 35]-=- as well as in the acoustic range (i.e., phononic bandgaps) [27, 14, 33]. In order to reveal the evanescent wave fields and bandgap structure, both the real and imaginary components of the wavenumber ... |