scholarly journals Rake rotation introduces ambiguity in the formulation of slip-dependent constitutive models: slip modulus or slip path?

2014 ◽  
Vol 57 (5) ◽  
Author(s):  
Andrea Bizzarri
Keyword(s):  
Seismic Moment ◽  
A Priori ◽  
Constitutive Models ◽  
Stress Release ◽  
Coseismic Slip ◽  
Slip Vector ◽  
Analytical Formulation ◽  
Grid Dispersion ◽  
Governing Law ◽  
Release Processes

<p>The linear slip–weakening (SW) law, predicting that the traction decreases for increasing fault slip, is one of the most widely adopted governing models to describe the traction evolution and the stress release processes occurring during coseismic slip failures. We will show that, contrary to other constitutive models, the SW law inherently poses the problem of considering the Euclidean norm of the slip vector or its cumulative value along its path. In other words, it has the intrinsic problem of its analytical formulation, which does not have a solution a priori. By considering a fully dynamic, spontaneous, 3–D rupture problem, with rake rotation allowed, in this paper we explore whether these two formulations can lead to different results. We prove that, for homogeneous configurations, the two formulations give the same results, with a normalized difference less than 1%, which is comparable to the numerical error due to grid dispersion. In particular, we show that the total slip, the resulting seismic moment, the fracture energy density, the slip–weakening curve and the energy flux at the rupture front are practically identical in the two formulations. These findings contribute to reconcile the results presented in previous papers, where the two formulations have been differently employed. However, this coincidence is not the rule. Indeed, by considering models with a highly heterogeneous initial shear stress distribution, where the rake variation is significant, we have also demonstrated that the overall rupture history is quite different by assuming the two formulations, as well as the fault striations, the traction evolution and the scalar seismic moment. In this case the choice of the analytical formulation of the governing law does really matter.</p>

scholarly journals Earthquake source parameters that display the first digit phenomenon

2015 ◽  
Vol 22 (5) ◽  
pp. 625-632
Author(s):  
P. A. Toledo ◽  
S. R. Riquelme ◽  
J. A. Campos
Keyword(s):  
Seismic Moment ◽  
Waiting Times ◽  
Source Parameters ◽  
Tohoku Earthquake ◽  
Earthquake Source ◽  
Coseismic Slip ◽  
Self Organized ◽  
Earthquake Source Parameters ◽  
Self Organized Criticality

Abstract. We study the main parameters of earthquakes from the perspective of the first digit phenomenon: the nonuniform probability of the lower first digit different from 0 compared to the higher ones. We found that source parameters like coseismic slip distributions at the fault and coseismic inland displacements show first digit anomaly. We also found the tsunami runups measured after the earthquake to display the phenomenon. Other parameters found to obey first digit anomaly are related to the aftershocks: we show that seismic moment liberation and seismic waiting times also display an anomaly. We explain this finding by invoking a self-organized criticality framework. We demonstrate that critically organized automata show the first digit signature and we interpret this as a possible explanation of the behavior of the studied parameters of the Tohoku earthquake.

Explicit formulae for stationary distributions of stress release processes

2000 ◽  
Vol 37 (2) ◽  
pp. 315-321 ◽  
Author(s):  
K. Borovkov ◽  
D. Vere-Jones
Keyword(s):  
Closed Form ◽  
Stationary Distribution ◽  
Exponential Function ◽  
Markov Models ◽  
Risk Process ◽  
Stress Release ◽  
Stationary Distributions ◽  
Explicit Formulae ◽  
Tectonic Forces ◽  
Release Processes

Stress release processes are special Markov models attempting to describe the behaviour of stress and occurrence of earthquakes in seismic zones. The stress is built up linearly by tectonic forces and released spontaneously when earthquakes occur. Assuming that the risk is an exponential function of the stress, we derive closed form expressions for the stationary distribution of such processes, the moments of the risk, and the autocovariance function of the reciprocal risk process.

scholarly journals Earthquake source parameters which display first digit phenomenon

2015 ◽  
Vol 2 (3) ◽  
pp. 811-832
Author(s):  
P. A. Toledo ◽  
S. R. Riquelme ◽  
J. A. Campos
Keyword(s):  
Seismic Moment ◽  
Waiting Times ◽  
Source Parameters ◽  
Tohoku Earthquake ◽  
Earthquake Source ◽  
Coseismic Slip ◽  
Self Organized ◽  
Earthquake Source Parameters ◽  
Self Organized Criticality

Abstract. We study main parameters of earthquakes from the perspective of the first digit phenomenon: the nonuniform probability of the lower first digit different from zero compared to the higher ones. We found that source parameters like coseismic slip distributions at the fault and coseismic inland displacements show first digit anomaly. We also found the tsunami runups measured after the earthquake to display the phenomenon. Other parameters found to obey first digit anomaly are related to the aftershocks: we show that seismic moment liberation and seismic waiting times also display an anomaly. We explain this finding by invoking a self-organized criticality frame. We show that critically organized automata show the first digit signature and we interpret this as a possible explanation of the behavior of the studied parameters of the Tohoku earthquake.

scholarly journals Energy dissipation for hereditary and energy conservation for non-local fractional wave equations

2020 ◽  
Vol 378 (2172) ◽  
pp. 20190295 ◽  
Author(s):  
Dušan Zorica ◽  
Ljubica Oparnica
Keyword(s):  
Energy Dissipation ◽  
Energy Conservation ◽  
Wave Equations ◽  
A Priori ◽  
Constitutive Models ◽  
Equation Of Motion ◽  
Constitutive Law ◽  
Energy Estimates ◽  
Fractional Wave Equations ◽  
Non Local

Using the method of a priori energy estimates, energy dissipation is proved for the class of hereditary fractional wave equations, obtained through the system of equations consisting of equation of motion, strain and fractional order constitutive models, that include the distributed-order constitutive law in which the integration is performed from zero to one generalizing all linear constitutive models of fractional and integer orders, as well as for the thermodynamically consistent fractional Burgers models, where the orders of fractional differentiation are up to the second order. In the case of non-local fractional wave equations, obtained using non-local constitutive models of Hooke- and Eringen-type in addition to the equation of motion and strain, a priori energy estimates yield the energy conservation, with the reinterpreted notion of the potential energy. This article is part of the theme issue ‘Advanced materials modelling via fractional calculus: challenges and perspectives’.

Stick-slip and wear phenomena at the contact interface between an elastic beam and a rigid substrate

2020 ◽  
pp. 108128652097167
Author(s):  
Francesco D’Annibale ◽  
Arnaldo Casalotti ◽  
Angelo Luongo
Keyword(s):  
A Priori ◽  
Constitutive Models ◽  
Elastic Beam ◽  
Longitudinal Direction ◽  
Static Problem ◽  
Rigid Substrate ◽  
Equilibrium Equations ◽  
Stick Slip ◽  
Contact Points ◽  
Nonlinear Constitutive Models

In this paper, the static behavior of an elastic beam resting on a rigid substrate is investigated. The structure lies on a rigid substrate and exchanges with it tangential forces, in correspondence with a finite number of contact points. These actions entail extension of the beam in the longitudinal direction together with a negligible bending, owing to the small eccentricity between the beam’s axis line and the rigid substrate. The beam obeys a linear elastic law, while, at the interface, different nonlinear constitutive models are considered to account for stick-slip phenomena due to friction, as well as wear due to abrasion. It is assumed that the contact points are a-priori known, thus entailing that the structural system can be treated as naturally discrete. The static problem is accordingly shown to be governed by a system of nonlinear ordinary differential equations in time, which rules, in incremental form, the equilibrium at the contact points in the longitudinal direction. A numerical solution for the equilibrium equations is carried out, under different imposed time histories of the longitudinal displacement assigned at the boundary. Numerical results are presented to compare and discuss the in-time evolution of the contact interactions between the beam and the substrate.

scholarly journals Determination of Residual Stress Fields in a Thermally Grown Oxide under Thermal Cycling Loadings, Using XRD and Raman Spectroscopy — Correlations with Microstructural States

2014 ◽  
Vol 996 ◽  
pp. 890-895
Author(s):  
Felaniaina Rakotovao ◽  
Zhao Jun Tao ◽  
Jean Luc Grosseau-Poussard ◽  
Benoit Panicaud ◽  
Gilles Bonnet ◽  
...  
Keyword(s):  
Residual Stress ◽  
Raman Spectroscopy ◽  
Residual Stresses ◽  
Thermally Grown Oxide ◽  
Stress Fields ◽  
Stress Release ◽  
Thermal Oxide ◽  
Long Time ◽  
Release Processes

The presence of residual stresses in thermal oxide layers has been recognized for a long time. In the present work, the mechanical fields for chromia oxide are determined either by XRD or Raman spectroscopy. In addition, the microstructure of the chromia films is investigated ant its influence on the evolution of the stress release processes is analyzed.

Explicit formulae for stationary distributions of stress release processes

2000 ◽  
Vol 37 (02) ◽  
pp. 315-321 ◽  
Author(s):  
K. Borovkov ◽  
D. Vere-Jones
Keyword(s):  
Closed Form ◽  
Stationary Distribution ◽  
Exponential Function ◽  
Markov Models ◽  
Risk Process ◽  
Stress Release ◽  
Stationary Distributions ◽  
Explicit Formulae ◽  
Tectonic Forces ◽  
Release Processes

Stress release processes are special Markov models attempting to describe the behaviour of stress and occurrence of earthquakes in seismic zones. The stress is built up linearly by tectonic forces and released spontaneously when earthquakes occur. Assuming that the risk is an exponential function of the stress, we derive closed form expressions for the stationary distribution of such processes, the moments of the risk, and the autocovariance function of the reciprocal risk process.

scholarly journals NumPy-based Calibration of Basic Hypoplastic Constitutive Models

2019 ◽  
Vol 1 (1) ◽  
pp. 12-16
Author(s):  
Muzaffer Kerem Ertek
Keyword(s):  
Open Source ◽  
A Priori ◽  
Constitutive Models ◽  
Calibration Procedure ◽  
Surface Flow ◽  
Flow Rule ◽  
Software Packages ◽  
Plastic Potential ◽  
Explicit Procedure ◽  
Rate Type

Constitutive modeling of soils is a crucial topic in geotechnics. Several constitutive models for soils can be found in material libraries of open-source or commercial geotechnical software packages, and these models can be based on various theories. Hypoplasticity as a relatively young theory is an alternative to elastoplasticity and consistently attracts new researchers. Contrary to elastoplasticity, hypoplasticity does not involve a priori defined yield surface, flow rule and plastic potential and arises from a simple tensorial function of the rate type. An exhaustive review of literature, however, points to the fact that for the calibration of these models, commercial symbolic mathematics software is mostly referred to and a calibration procedure based upon an open-source software which any individuals can easily make use of is missing. Therefore, an explicit procedure for calibration making use of NumPy, which is the main package for scientific computing with Python, following a concise summary for the theory of hypoplasticity is established. By doing so, it is expected to draw attention to take advantage of open-source packages that almost the majority of the scientific community utilizes increasingly.

Optimization of the fault plane and coseismic slip from tide-gauge data for the 2nd May 2020 Ierapetra, Crete, Earthquake (Mw 6.6) and the associated tsunami

2021 ◽  
Author(s):  
Enrico Baglione ◽  
Alessandro Amato ◽  
Beatriz Brizuela ◽  
Hafize Basak Bayraktar ◽  
Stefano Lorito ◽  
...  
Keyword(s):  
Tide Gauge ◽  
Moment Tensor ◽  
A Priori ◽  
Source Parameters ◽  
Early Warning Systems ◽  
Tsunami Source ◽  
Coseismic Slip ◽  
Moment Tensors ◽  
Tsunami Early Warning ◽  
Oblique Convergence

&lt;p&gt;We present a tsunami source solution for the 2nd May 2020, Mw 6.6 earthquake that occurred about 80 km offshore south of Crete on the shallow portion of the Hellenic Arc Subduction Zone (HASZ). This earthquake generated a small local tsunami recorded by the Ierapetra tide gauge on Crete island's southern coast. We used these single-marigram data to constrain the main features of the causative rupture. We modelled synthetic tsunami waveforms and measured their misfits with the observed data for each set of source parameters, scanned systematically around the values constrained by some of the available moment tensors.&lt;/p&gt;&lt;p&gt;In the attempts to discriminate between the two auxiliary fault planes of the moment tensor solutions, our results identify a shallow highly-dipping back-thrust fault as the source of this earthquake with the lower misfit. However, a rupture on a lower angle fault, possibly a splay fault of the subduction interface, with a sinistral component due to the oblique convergence on this segment of the HASZ, cannot be ruled out.&lt;/p&gt;&lt;p&gt;These results are relevant in the framework of the tsunami hazard assessments and Tsunami Early Warning Systems. In these frameworks, in addition to the subduction interface and possible ruptures on splay faults, other rupture types, such as those on secondary structures of the considered subduction system, cannot be excluded a priori. This circumstance bears important consequences because, as well as splay faulting, back thrust faulting might enhance the tsunamigenic potential where the subduction itself is less tsunamigenic due to the oblique convergence.&lt;/p&gt;

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