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.

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.

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.

Stress Concentrations in Three-Dimensional Electrostriction

1967 ◽  
Vol 34 (2) ◽  
pp. 431-436 ◽  
Author(s):  
T. E. Smith
Keyword(s):  
Displacement Vector ◽  
Spherical Inclusion ◽  
Crack Problem ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Uniform Electric Field ◽  
Inclusion Problem ◽  
Stress Concentrations ◽  
Displacement Potential ◽  
Penny Shaped Crack

Using the techniques employed in developing a Papkovich-Neuber representation for the displacement vector in classical elasticity, a particular integral of the kinematical equations of equilibrium for the uncoupled theory of electrostriction is developed. The particular integral is utilized in conjunction with the displacement potential function approach to problems of the theory of elasticity to obtain closed-form solutions of several stress concentration problems for elastic dielectrics. Under a prescribed uniform electric field at infinity, the problems of an infinite elastic dielectric having first a spherical cavity and then a rigid spherical inclusion are solved. The rigid spheroidal inclusion problem and the penny-shaped crack problem are also solved for the case where the prescribed field is parallel to their axes of revolution.

scholarly journals Modeling nonlinear compressional waves in marine sediments

2009 ◽  
Vol 16 (1) ◽  
pp. 151-157 ◽  
Author(s):  
B. E. McDonald
Keyword(s):  
Marine Sediments ◽  
Plane Waves ◽  
High Stress ◽  
Nonlinear Behavior ◽  
Analytic Solutions ◽  
Compressional Waves ◽  
Series Of Experiments ◽  
Model Equations ◽  
The Time Domain ◽  
Water Saturated

Abstract. A computational model is presented which will help guide and interpret an upcoming series of experiments on nonlinear compressional waves in marine sediments. The model includes propagation physics of nonlinear acoustics augmented with granular Hertzian stress of order 3/2 in the strain rate. The model is a variant of the time domain NPE (McDonald and Kuperman, 1987) supplemented with a causal algorithm for frequency-linear attenuation. When attenuation is absent, the model equations are used to construct analytic solutions for nonlinear plane waves. The results imply that Hertzian stress causes a unique nonlinear behavior near zero stress. A fluid, in contrast, exhibits nonlinear behavior under high stress. A numerical experiment with nominal values for attenuation coefficient implies that in a water saturated Hertzian chain, the nonlinearity near zero stress may be experimentally observable.

Effect of the Interphase Zone on the Bulk Modulus of a Particulate Composite

1996 ◽  
Vol 63 (4) ◽  
pp. 855-861 ◽  
Author(s):  
M. P. Lutz ◽  
R. W. Zimmerman
Keyword(s):  
Exact Solution ◽  
Bulk Modulus ◽  
Spherical Inclusion ◽  
Particulate Composite ◽  
Constant Term ◽  
Stress Concentrations ◽  
Infinite Body ◽  
Effective Bulk Modulus ◽  
Random Dispersion ◽  
Frobenius Series

An exact solution is found for the problem of hydrostatic compression of an infinite body containing a spherical inclusion, with the elastic moduli varying with radius outside of the inclusion. This may represent an interphase zone in a composite, or the transition zone around an aggregate particle in concrete, for example. Both the shear and the bulk moduli are assumed to be equal to a constant term plus a power-law term that decays away from the inclusion. The method of Frobenius series is used to generate an exact solution for the displacements and stresses. The solution is then used to estimate the effective bulk modulus of a material containing a random dispersion of these inclusions. The results demonstrate the manner in which a localized interphase zone around an inclusion may markedly affect both the stress concentrations at the interface, and the overall bulk modulus of the material.

Diffraction of Plane Compressional Waves by an Array of Nanosized Cylindrical Holes

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Q. F. Zhang ◽  
G. F. Wang ◽  
P. Schiavone
Keyword(s):  
Surface Energy ◽  
Dynamic Stress ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Stress Concentrations ◽  
Compressional Waves ◽  
Circular Holes ◽  
Cylindrical Holes ◽  
Effect Of Surface ◽  
Dynamic Stress Concentrations

When the radius of a hole reduces to nanometers, the influence of surface energy becomes prominent in its mechanical behavior. In the present paper, we consider the diffraction of plane compressional waves by an array of nanosized circular holes in an elastic medium. The effect of surface energy is taken into account through surface elasticity theory. Using the wave expansion method, we derive the corresponding elastic diffraction fields. Dynamic stress concentrations around the holes and the scattering cross section are calculated to address the surface effects on the diffraction phenomena.

scholarly journals Analysis of Fracture Behavior of Large Steel Beam-Column Connections

2018 ◽  
Author(s):  
Roberto Leon ◽  
Liangjie Qi ◽  
Jonathan Paquette ◽  
Matthew Eatherton ◽  
Teodora Bogdan ◽  
...  
Keyword(s):  
Scale Effects ◽  
Tall Buildings ◽  
The United States ◽  
Steel Beam ◽  
Moment Frames ◽  
Steel Moment Frames ◽  
Stress Concentrations ◽  
Reduced Beam Section ◽  
Design Qualification ◽  
Beam Section

Recently completed experimental steel beam-column connection tests on the largest specimens of reduced-beam section specimens ever tested have shown that such connections can meet current seismic design qualification protocols, allowing to further extend the current AISC Seismic Provisions and the AISC Provisions for Prequalified Connections for Special and Intermediate Steel Moment Frames. However, the results indicate that geometrical and material effects need to be carefully considered when designing welded connections between very heavy shapes. Understanding of this behavior will ease the use of heavier structural shapes in seismic active areas of the United States, extending the use of heavy steel sections beyond their current use in ultra-tall buildings. To better interpret the experimental test results, extensive detailed finite element analyses are being conducted on the entire series of tests, which comprised four specimens with beams of four very different sizes. The analyses intend to clarify what scale effects, at both the material and geometric level, influence the performance of these connections. The emphasis is on modeling of the connection to understand the balance in deformation between the column panel zones and the reduced beam section, the stress concentrations near the welds, the effects of initial imperfections and residual stresses and the validity of several damage accumulation models. The models developed so far for all four specimens have been able to accurately reproduce the overall load-deformation and moment-rotation time histories.  

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