Seismic response of reduced micropolar elastic half-space

Gade, Maheshreddy; Raghukanth, S. T. G.

doi:10.1007/s10950-016-9557-9

Cited by 9 publications

(7 citation statements)

References 20 publications

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“…These rigid fault blocks rotate around their centroids in a manner dictated by the local geometry of the blocks and their interactions with neighboring blocks. Using this description, permanent effects of rotational motions during seismogenic deformation have been observed and it has been shown that the deformation is better described by the micropolar theory compared to the linear elastic theory (Twiss, 2009;Twiss et al, 1993;Unruh et al, 2003;Lewis et al, 2008;Twiss et al, 1991;Schemmann et al, 2008;Wojtal 2001;Unruh et al, 1996;Gade & Raghukanth, 2016;Teisseyre et al, 2006;Twiss & Unruh, 1998.…”

Section: Introductionmentioning

confidence: 99%

Understanding Micropolar Theory in the Earth Sciences I: The Eigenfrequency $$\omega _r$$

Abreu

Durand

2021

Pure Appl. Geophys.

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Even though micropolar theories are widely applied for engineering applications such as the design of metamaterials, applications in the study of the Earth’s interior still remain limited and in particular in seismology. This is due to the lack of understanding of the required elastic material parameters present in the theory as well as the eigenfrequency $$\omega _r$$ ω r which is not observed in seismic data. By showing that the general dynamic equations of the Timoshenko’s beam is a particular case of the micropolar theory we are able to connect micropolar elastic parameters to physically measurable quantities. We then present an alternative micropolar model that, based on the same physical basis as the original model, circumvents the problem of the original eigenfrequency $$\omega _r$$ ω r laking in seismological data. We finally validate our model with a seismic experiment and show it is relevant to explain observed seismic dispersion curves.

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Section: Introductionmentioning

confidence: 99%

Understanding Micropolar Theory in the Earth Sciences I: The Eigenfrequency $$\omega _r$$

Abreu

Durand

2021

Pure Appl. Geophys.

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“…Until today the main applications of micropolar theory in seismic studies have been related to the modelling the elastic response of granular medium Schwartz and Johnson, 1984;Mouraille et al, 2006;Hiraiwa et al, 2016;Merkel and Luding, 2017;Merkel et al, 2011) or to better describe brittle deformation at crustal scale (Kissel and Laj, 2012;Luyendyk et al, 1980;Wells and Heller, 1988). In particular, it has been shown that it plays a key role in rupture processes at plate tectonics scale (Twiss, 2009;Gade and Raghukanth, 2016;Teisseyre et al, 2006). This comes from the incapability of the linear elastic theory to provide a complete continuum description of distributed brittle deformation .…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…Heterogeneity, such as ultra-low velocity zones (Thorne and Garnero, 2004), which could be due to a certain degree of melt (Hier-Majumder, 2014;Liu et al, 2016), is unlikely to be affected by micropolar motions, as they would not rotate independently of the surrounding mantle. There is hope in the future to compare simulations of wave propagation in micropolar media with seismological data such as rotational records provided by the emerging technology of rotational sensors (Yin et al, 2016;Gade and Raghukanth, 2016;Suryanto et al, 2006;Schreiber et al, 2006;Bernauer et al, 2009;Ferreira and Igel, 2009;Wassermann et al, 2009;Igel et al, 2007Igel et al, , 2005. It has already been shown that in the nearfield, rotational ground motions are much larger compared to what is expected from the classical linear elasticity (Lee et al, 2009).…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

Effect of observed micropolar motions on wave propagation in deep Earth minerals

Abreu

Thomas

Durand

2018

Physics of the Earth and Planetary Interiors

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We provide a method to compute the Cosserat couple modulus for a bridgmanite (MgSiO 3 silicate perovskite) solid from frequency gaps observed in Raman experiments. To this aim, we apply micropolar theory which is a generalization of the classical linear elastic theory, where each particle has an intrinsic rotational degree of freedom, called micro-rotation and/or spin, and which depends on the so-called Cosserat couple modulus l c that characterizes the micropolar medium. We investigate both wave propagation and dispersion. The wave propagation simulations in both potassium nitrate ðKNO 3 Þ and bridgmanite crystal leads to a faster elastic wave propagation as well as to an independent rotational field of motion, called optic mode, which is smaller in amplitude compared to the conventional rotational field. The dispersion analysis predicts that the optic mode only appears above a cutoff frequency, x r , which has been observed in Raman experiments done at high pressures and temperatures on bridgmanite crystal. The comparison of the cutoff frequency observed in experiments and the micropolar theory enables us to compute for the first time the temperature and pressure dependency of the Cosserat couple modulus l c of bridgmanite. This study thus shows that the micropolar theory can explain particle motions observed in laboratory experiments that were before neglected and that can now be used to constrain the micropolar elastic constants of Earth's mantle like material. This pioneer work aims at encouraging the use of micropolar theory in future works on deep Earth's mantle material by providing Cosserat couple modulus that were not available before.

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“…In addition, Poisson's ratio is the ratio of transverse contraction strain to longitudinal extension strain in the direction of the stretching force [4,5]. As has been previously reported, the elastic half space is an 'ideal concept', useful in a wide range of different situations, from nanotechnology [6][7][8][9] and contact mechanics [10,11] to seismics [12][13][14][15] and can provide a useful insight into a significant number of physical phenomena. An interesting phenomenon which will be analyzed in this paper is the conditions under which the motion of a rigid sphere on an elastic half space can be considered as harmonic.…”

Section: Introductionmentioning

confidence: 99%

Small oscillations of a rigid sphere on an elastic half space: a theoretical analysis

Kontomaris

Malamou

2020

Eur. J. Phys.

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Harmonic motion is a significant topic in undergraduate lectures for university physics students. A typical example, presented in lectures around the globe, is the motion of a mass at the end of a spring. It should be emphasized that the harmonic motion in the aforementioned case is just an approximation for small displacements. However, the value of this example for teaching purposes is undeniable, if used properly. Its significance is connected to the adoption of an analytical way of thinking by the students that can help them to not only memorize isolated fragments but to really understand the topic in depth. As a result, the students should be able to apply a similar analysis to new and unsolved problems and explore unknown physical systems using basic theoretical tools. To move in the right direction, a new example is presented in this paper: the motion of a rigid sphere on an elastic half space. This phenomenon is extremely complicated. However, in this paper it is shown that for a specific range of values, this motion can be approximated to harmonic motion. This fact will significantly help students to learn how to resolve unknown problems and tasks using their knowledge. In addition, the analysis provided by this paper can be used as an alternative and simpler solution for data processing in nanoindentation experiments. As a result, it can be used as a valuable tool not only for undergraduate physics students but also for young researchers in the fields of nanotechnology and materials science.

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Seismic response of reduced micropolar elastic half-space

Cited by 9 publications

References 20 publications

Understanding Micropolar Theory in the Earth Sciences I: The Eigenfrequency $$\omega _r$$

Understanding Micropolar Theory in the Earth Sciences I: The Eigenfrequency $$\omega _r$$

Effect of observed micropolar motions on wave propagation in deep Earth minerals

Small oscillations of a rigid sphere on an elastic half space: a theoretical analysis

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