The motion of a rigid spherical inclusion in an elastic medium under the action of plane waves

1994 ◽  
Vol 70 (5) ◽  
pp. 1978-1984 ◽  
Author(s):  
I. V. Lebedeva
Keyword(s):  
Elastic Medium ◽  
Spherical Inclusion ◽  
Plane Waves

scholarly journals Localized Heating Near a Rigid Spherical Inclusion in a Viscoelastic Binder Material Under Compressional Plane Wave Excitation

2017 ◽  
Vol 84 (4) ◽  
Author(s):  
Jesus O. Mares ◽  
Daniel C. Woods ◽  
Caroline E. Baker ◽  
Steven F. Son ◽  
Jeffrey F. Rhoads ◽  
...  
Keyword(s):  
Energetic Materials ◽  
Scale Effects ◽  
Spherical Inclusion ◽  
Plane Waves ◽  
Thermal Response ◽  
Resonant Scattering ◽  
Compressional Waves ◽  
Dynamic Events ◽  
Bulk Heating ◽  
Viscoelastic Effects

High-frequency mechanical excitation has been shown to generate heat within composite energetic materials and even induce reactions in single energetic crystals embedded within an elastic binder. To further the understanding of how wave scattering effects attributable to the presence of an energetic crystal can result in concentrated heating near the inclusion, an analytical model is developed. The stress and displacement solutions associated with the scattering of compressional plane waves by a spherical obstacle (Pao and Mow, 1963, “Scattering of Plane Compressional Waves by a Spherical Obstacle,” J. Appl. Phys., 34(3), pp. 493–499) are modified to account for the viscoelastic effects of the lossy media surrounding the inclusion (Gaunaurd and Uberall, 1978, “Theory of Resonant Scattering From Spherical Cavities in Elastic and Viscoelastic Media,” J. Acoust. Soc. Am., 63(6), pp. 1699–1712). The results from this solution are then utilized to estimate the spatial heat generation due to the harmonic straining of the material, and the temperature field of the system is predicted for a given duration of time. It is shown that for certain excitation and sample configurations, the elicited thermal response near the inclusion may approach, or even exceed, the decomposition temperatures of various energetic materials. Although this prediction indicates that viscoelastic heating of the binder may initiate decomposition of the crystal even in the absence of defects such as initial voids or debonding between the crystal and binder, the thermal response resulting from this bulk heating phenomenon may be a precursor to dynamic events associated with such crystal-scale effects.

Transient Response of a Rigid Spherical Inclusion in an Elastic Medium

1965 ◽  
Vol 32 (3) ◽  
pp. 637-642 ◽  
Author(s):  
C. C. Mow
Keyword(s):  
Exact Solution ◽  
Elastic Medium ◽  
Transient Response ◽  
Integral Method ◽  
Spherical Inclusion ◽  
Time History ◽  
Fourier Integral ◽  
Incident Pulse ◽  
History Of

The transient response of a rigid spherical inclusion of arbitrary density embedded in an elastic medium owing to an incident pulse is examined in this paper. The Fourier-integral method is used, and an exact solution of the response is obtained. It is found that the acceleration and velocity of the inclusion are substantially different from those of the medium. A slight difference in the time history of the displacement between the inclusion and the medium is also noted.

scholarly journals Plane Waves Scattered by a Spherical Inclusion in a Half Space of Poroelastic Material

2020 ◽  
Vol 03 (02) ◽  
pp. 1-1
Author(s):  
Doo-Sung Lee ◽  
Keyword(s):  
Half Space ◽  
Existence And Uniqueness ◽  
Spherical Inclusion ◽  
Plane Waves ◽  
Spherical Wave ◽  
Wave Functions ◽  
Successive Approximations ◽  
Compressional Waves ◽  
Poroelastic Material ◽  
The Given

This paper concerns a poroelastic half-space in which plane compressional waves are scattered by a spherical inclusion. Addition theorems for the spherical wave functions are utilized to meet the boundary conditions on the plane, and the satisfaction of the given conditions on the boundary of the sphere leads to three infinite series equations, whose solution can be acquired by successive approximations. Further, its existence and uniqueness are discussed.

Localized Heating due to Stress Concentrations Induced in a Lossy Elastic Medium via the Scattering of Compressional Waves by a Rigid Spherical Inclusion

2016 ◽  
Author(s):  
Jesus O. Mares ◽  
Daniel C. Woods ◽  
Caroline E. Baker ◽  
Steven F. Son ◽  
Jeffrey F. Rhoads ◽  
...  
Keyword(s):  
Energetic Materials ◽  
Scale Effects ◽  
Spherical Inclusion ◽  
Plane Waves ◽  
Thermal Response ◽  
Stress Concentrations ◽  
Compressional Waves ◽  
Dynamic Events ◽  
Bulk Heating ◽  
Viscoelastic Effects

High-frequency mechanical excitation has been shown to generate heat within composite energetic materials and even induce reactions in single energetic crystals embedded within an elastic binder. To further the understanding of how wave scattering effects attributable to the presence of an energetic crystal can result in concentrated heating near the inclusion, an analytical model is presented. The stress and displacement solutions associated with the scattering of compressional plane waves by a spherical obstacle (Pao and Mow, 1963) are modified to account for the viscoelastic effects of the lossy media surrounding the inclusion (Gaunaurd and Uberall, 1978). The results from this solution are then utilized to estimate the spatial heat generation due to the harmonic straining of the material, and the temperature field of the system is predicted for a given duration of time. It is shown that for certain excitation and sample configurations, the elicited thermal response near the inclusion may approach, or even exceed, realistic decomposition temperatures of various energetic materials. Although this prediction indicates that viscoelastic heating of the binder may initiate the decomposition of the crystal even in the absence of defects such as initial voids or debonding between the crystal and binder, the thermal response resulting from this bulk heating phenomenon may be a precursor to dynamic events associated with such crystal-scale effects.

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