Earthquake processes in a micromorphic continuum

Teisseyre, Roman

doi:10.1007/bf00876588

Cited by 59 publications

(30 citation statements)

References 2 publications

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“…With Boltzmann's axiom, which is in sharp contrast to standard micromorphic models, the model would feature symmetric force-stress tensors. Such an assumption has been made, for example, by Teisseyre [84,85] in his model for the description of seismic wave propagation phenomena (for the use of micromorphic models for earthquake modeling see also the discussion in [60]). …”

mentioning

confidence: 99%

Transparent anisotropy for the relaxed micromorphic model: Macroscopic consistency conditions and long wave length asymptotics

Barbagallo

Madeo

d’Agostino

et al. 2017

International Journal of Solids and Structures

106

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In this paper, we study the anisotropy classes of the fourth order elastic tensors of the relaxed micromorphic model, also introducing their second order counterpart by using a Voigt-type vector notation. In strong contrast with the usual micromorphic theories, in our relaxed micromorphic model only classical elasticity-tensors with at most 21 independent components are studied together with rotational coupling tensors with at most 6 independent components. We show that in the limit case Lc → 0 (which corresponds to considering very large specimens of a microstructured metamaterial) the meso-and microcoefficients of the relaxed model can be put in direct relation with the macroscopic stiffness of the medium via a fundamental homogenization formula. We also show that a similar homogenization formula is not possible in the case of the standard Mindlin-Eringen-format of the anisotropic micromorphic model. Our results allow us to forecast the successful short term application of the relaxed micromorphic model to the characterization of anisotropic mechanical metamaterials.

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confidence: 99%

Transparent anisotropy for the relaxed micromorphic model: Macroscopic consistency conditions and long wave length asymptotics

Barbagallo

Madeo

d’Agostino

et al. 2017

International Journal of Solids and Structures

106

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“…In such elastic continua, the real rotation can be accompanied by other kind of axial motionthe twist-bend motion. On above base, it was theoretically proved that so-called the seismic rotation waves could propagate through grained rocks, initially by Teisseyre [7] who initially attributed the appearance of rotation components in seismic wave by coupling the seismic waves with the micromorphic response of the medium characterized by the an internal/ granular structure [7,8]. From this time, this possibility was extended to rocks with micro-structure or defects [9,10] or even without any internal structure [11 -13], due to the asymmetric stresses in the medium.…”

Section: Introductionmentioning

confidence: 99%

Rotational Components of the Seismic Fields Caused by Local Events

Kurzych¹,

Teisseyre

Krajewski³

et al. 2015

Earthquake Engineering - From Engineering Seismology to Optimal Seismic Design of Engineering Structures

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“…Thus, it is reasonable to believe that the notion of continuum with microstructure can be a suitable tool in describing earthquake phenomena. The scale of earth structures with their extremely complicated internal microstructures justifies the use of continuum mechanics (TEISSEYRE, 1973a(TEISSEYRE, ,b, 1982(TEISSEYRE, , 1995a. Particularly the generalized micromorphic continuum is suitable to introduce microstructure ERINGEN and SUHUBI, 1964;ERINGEN, 1968;ERINGEN and CLAUS, 1970).…”

Section: Introductionmentioning

confidence: 99%

“…Particularly the generalized micromorphic continuum is suitable to introduce microstructure ERINGEN and SUHUBI, 1964;ERINGEN, 1968;ERINGEN and CLAUS, 1970). When the deformations imposed on a microstructural element favour its elongation rather than rotation during fracturing, the symmetric micromorphic continuum is suitable to our considerations of the role of microstructure in the region of the earth interior where earthquakes occur (TEISSEYRE, 1973a(TEISSEYRE, ,b, 1974(TEISSEYRE, , 1975(TEISSEYRE, , 1978(TEISSEYRE, , 1982(TEISSEYRE, , 1986(TEISSEYRE, , 1995a.…”

Section: Introductionmentioning

confidence: 99%

Micromorphic Continuum and Fractal Fracturing in the Lithosphere

Nagahama

Teisseyre

2000

Pure appl. geophys.

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It seems that internal structures and discontinuities in the lithosphere essentially influence the lithospheric deformation such as faulting or earthquakes. The micromorphic continuum provides a good framework to study the continuum with microstructure, such as earthquake structures.Here we briefly introduce the relation between the theory of micromorphic continuum and the rotational effects related to the internal microstructure in epicenter zones. Thereafter the equilibrium equation, in terms of the displacements (the Navier equation) in the medium with microstructure, is derived from the theory of the micromorphic continuum. This equation is the generalization of the Laplace equation in terms of displacements and can lead to Laplace equations such as the local diffusion-like conservation equations for strains. These local balance/stationary state of strains under the steady non-equilibrium strain flux through the plate boundaries bear the scale-invariant properties of fracturing in the lithospheric plate with microstructure.

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Earthquake processes in a micromorphic continuum

Cited by 59 publications

References 2 publications

Transparent anisotropy for the relaxed micromorphic model: Macroscopic consistency conditions and long wave length asymptotics

Transparent anisotropy for the relaxed micromorphic model: Macroscopic consistency conditions and long wave length asymptotics

Rotational Components of the Seismic Fields Caused by Local Events

Micromorphic Continuum and Fractal Fracturing in the Lithosphere

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