Continuum Theory for a Laminated Medium

Sun, C. T.; Achenbach, J. D.; Herrmann, G.

doi:10.1115/1.3601237

Cited by 278 publications

(78 citation statements)

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“…When the wavelength of a travelling signal decreases and becomes comparable with the characteristic size of heterogeneities, successive reflections and refractions of the local waves at the component interfaces lead to dispersion and attenuation of the global wave field. In order to give a theoretical description of these phenomena, several higher order continuum models were proposed by , Sun et al (1968), Bedford & Stern (1971, 1972 and Hegemier et al (1973); for a detailed review of the subject, we refer to Ting (1980). Various self-consistent schemes have been adopted for the purposes of dynamic homogenization by Sabina & Willis (1988), Kanaun & Levin (2003 and Kanaun et al (2004).…”

Section: Introductionmentioning

confidence: 99%

Higher order asymptotic homogenization and wave propagation in periodic composite materials

et al. 2008

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We present an application of the higher order asymptotic homogenization method (AHM) to the study of wave dispersion in periodic composite materials. When the wavelength of a travelling signal becomes comparable with the size of heterogeneities, successive reflections and refractions of the waves at the component interfaces lead to the formation of a complicated sequence of the pass and stop frequency bands. Application of the AHM provides a long-wave approximation valid in the low-frequency range. Solution for the high frequencies is obtained on the basis of the Floquet-Bloch approach by expanding spatially varying properties of a composite medium in a Fourier series and representing unknown displacement fields by infinite plane-wave expansions. Steadystate elastic longitudinal waves in a composite rod (one-dimensional problem allowing the exact analytical solution) and transverse anti-plane shear waves in a fibre-reinforced composite with a square lattice of cylindrical inclusions (two-dimensional problem) are considered. The dispersion curves are obtained, the pass and stop frequency bands are identified.

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Section: Introductionmentioning

confidence: 99%

Higher order asymptotic homogenization and wave propagation in periodic composite materials

et al. 2008

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“…For the purpose of validation, an academic example for which analytical solutions exist in the literature [6] was chosen to display some important results. Using the frequency dependent elastic constants allows for modeling the frequency response of the actual heterogeneous material (Fig.…”

Section: Resultsmentioning

confidence: 99%

Acoustic Band Structures and Homogenization of Periodic Elastic Media

Stadler

Schanz

2010

Proc Appl Math and Mech

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Dispersion curves and frequency dependent velocity surfaces of periodic heterogeneous elastic media are determined from unit-cell problems using quasi periodic boundary conditions. Effective material parameters are obtained using a least square optimization of the phase velocities in the heterogeneous and the effective, generally anisotropic, homogeneous medium. For efficiency, a preconditioned iterative eigenvalue solver and a model order reduction scheme are used. This "dynamic" homogenization procedure is validated for frequencies below the first stop band employing FEM calculations on a finite structure consisting of an array of unit-cells and the effective homogeneous material.

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“…Most of the previous research efforts have been focused on the elastic or acoustic wave propagations through layered media (e.g., Sun et al, 1968;Ben-Amoz, 1975;Cetin, 1994;Nayfeh, 1995;Tadi, 2004). As the amplitudes of stress waves increase, materials in the layers start to fail.…”

Section: State-of-the-art Of Layered Glass Structuresmentioning

confidence: 99%

Effects of Surface Treatment and Interfacial Strength on the Damage Propagation in Layered Transparent Armor under Impact

Chen¹

2011

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The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. This research program is to develop a fundamental understanding of the damage propagation through layered transparent armors under impact loading conditions. The effects of surface quality and interfacial bonding strength on the damage propagation or arrest will also be examined. During the funded period of the program, a gas gun has been developed and used to impact layered glass targets. Notched glass specimens having adhesive interfaces are impacted with plastic projectiles. It is found that, an impact-induced crack arrests at an interface ABSTRACTThis research program is to develop a fundamental understanding of the damage propagation through layered transparent armors under impact loading conditions. The effects of surface quality and interfacial bonding strength on the damage propagation or arrest will also be examined. During the funded period of the program, a gas gun has been developed and used to impact layered glass targets. Notched glass specimens having adhesive interfaces are impacted with plastic projectiles. It is found that, an impact-induced crack arrests at an interface perpendocular to the crack path if the interface is not bonded. When the interface is bonded tightly, the crack passes through the interface in its propagation without being affected by the interface. When the bonded interface has a finite thickness, the crack slows down at the interface and then branches to many cracks that form a fan shape. Besides the crack experiments, the effects of surface quality on bending strength of glass are also investigated.(a) Papers published in peer-reviewed journals (N/A for none) The number of undergraduates funded by this agreement who graduated during this period with a degree in science, mathematics, engineering, or technology fields: (d) Manuscripts Number of Peer-Reviewed Conference Proceeding publications (other than abstracts): 2 NumberThe number of undergraduates funded by your agreement who graduated during this period and will continue to pursue a graduate or Ph.D. degree in science, mathematics, engineering, or technology fields:Number of graduating undergraduates who achieved a 3.5 GPA to 4.0 (4.0 max scale): Number of graduating undergraduates funded by a DoD funded Center of Excellence grant for Education, Research and Engineering:The number of undergraduates funded by your agreement who graduated during this period and intend to work for the Department of DefenseThe number of undergraduates funded by your agreement who graduated during this period and will receive scholarships or fellowships for further studies in science, mathematics, engineering or technology fields: Student Metrics This section only applies to graduating undergraduates supported by this agreement in this reporting perio...

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Continuum Theory for a Laminated Medium

Cited by 278 publications

References 0 publications

Higher order asymptotic homogenization and wave propagation in periodic composite materials

Higher order asymptotic homogenization and wave propagation in periodic composite materials

Acoustic Band Structures and Homogenization of Periodic Elastic Media

Effects of Surface Treatment and Interfacial Strength on the Damage Propagation in Layered Transparent Armor under Impact

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