A Stochastic Multi-scale Approach for Numerical Modeling of Complex Materials—Application to Uniaxial Cyclic Response of Concrete

Jehel, Pierre

doi:10.1007/978-3-319-27996-1_6

Cited by 1 publication

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References 33 publications

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“…are used for modeling wave propagation through materials [83,86,132,141,194], however, as mentioned previously, determining the parameters of these models sometimes becomes non-feasible because of either very large system size or very complex micro-structure (heterogeneity). In such cases, a statistical treatment of the heterogeneities in the media can assist in overcoming some of these difficulties [4,35,47,75]. Thinking on these lines leads to the proposition of developing stochastic models for various phenomena (dispersion, scattering attenuation, etc.)…”

Section: Stochastic Modelingmentioning

confidence: 99%

Towards stochastic and deterministic modeling of mechanical waves in disordered media

Shrivastava¹

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Samenvatting 159 Acknowledgments 161 Curriculum Vitae 163 • Non-destructive testing of materials for geotechnical investigations (artificial mechanical waves are sent into the material and the received response is studied using piezoelectric devices such as electronic transducers [215] or bender elements [142, 176]). A mechanical wave propagating in a disordered medium has a characteristic signature, whether the media is Earth [4] or Moon [43, 133]. The schematic illustration in Fig. 1.2 depicts the signature in time. The longitudinal mode (Pwave) arrives first, then comes the transverse mode (S-wave) and then arrive the Surface waves. Similar signatures of mechanical waves were also observed in laboratory experiments [76, 77, 93, 148, 214, 215]. However, on zooming over a particular mode of a mechanical wave in a time series profile, the me-1.5 Mesoscopic Wave Phenomena: Diffusion, Coherent Backscattering Effect & Weak Localization The diffusive transport of energy in disordered systems is a well known fact. This fact has been readily exploited to develop a diffusion model for propagation of multiply scattered mechanical waves [4, 67, 68, 147, 148, 204, 212]. However, unusual wave phenomena have been observed at intermediate or higher frequencies such as large variations in acoustic wave speed and suppression of wave propagation due to wave localization (Anderson localization [9], similar to the localization observed in ultracold atoms [23, 32, 157], microwave and light [3, 30, 31, 44, 171, 188, 213]). Amongst many definitions of Anderson localizations, two of them rely on vanishing diffusion and decay of spatially lo-1.6.2 Experimental Investigations Earthquakes are naturally occurring mechanical waves; they have been measured and recorded since a very long time; they have been quintessential in determining the internal structure of Earth, hence, their study is one of the early experimental investigations of mechanical waves in soil [55, 174]. Ultrasound experiments have become instrumental in recent years to study the unique vibrational response of granular materials [102, 103, 104, 147]. For kHz-MHz frequency signals (mechanical waves) that are sent through materials, the received signals are analyzed for identifying the internal structure of Effect of Mass Disorder on Bulk Sound Wave Speed: A Multiscale Spectral Analysis relations for disordered chains; these dispersion relations confirm the decrease in cutoff frequency and thus wave speed with increasing disorder. 1

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Section: Stochastic Modelingmentioning

confidence: 99%

Towards stochastic and deterministic modeling of mechanical waves in disordered media

Shrivastava¹

View full text Add to dashboard Cite

show abstract

A Stochastic Multi-scale Approach for Numerical Modeling of Complex Materials—Application to Uniaxial Cyclic Response of Concrete

Cited by 1 publication

References 33 publications

Towards stochastic and deterministic modeling of mechanical waves in disordered media

Towards stochastic and deterministic modeling of mechanical waves in disordered media

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