A unified first-order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones

Earthquake fault zones are more complex, both geometrically and rheologically, than an idealized infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities and multi-physics coupling within and outside of fault zones, here we present a first-order hyperbolic and thermodynamically compatible mathematical model for a continuum in a gravitational field which provides a unified description of nonlinear elasto-plasticity, material damage and of viscous Newtonian flows with phase transition between solid and liquid phases. The fault geometry and secondary cracks are described via a scalar function ξ ∈ [0, 1] that indicates the local level of material damage. The model also permits the representation of arbitrarily complex geometries via a diffuse interface approach based on the solid volume fraction function α ∈ [0, 1]. Neither of the two scalar fields ξ and α needs to be mesh-aligned, allowing thus faults and cracks with complex topology and the use of adaptive Cartesian meshes (AMR). The model shares common features with phase-field approaches, but substantially extends them. We show a wide range of numerical applications that are relevant for dynamic earthquake rupture in fault zones, including the co-seismic generation of secondary off-fault shear cracks, tensile rock fracture in the Brazilian disc test, as well as a natural convection problem in molten rock-like material. This article is part of the theme issue ‘Fracture dynamics of solid materials: from particles to the globe’.

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A unified first order hyperbolic model for nonlinear dynamic rupture processes in diffuse fracture zones

10.5194/egusphere-egu21-15237 ◽

2021 ◽

Author(s):

Alice-Agnes Gabriel ◽

Duo Li ◽

Simone Chiocchetti ◽

Maurizio Tavelli ◽

Ilya Peshkov ◽

...

Keyword(s):

Fault Zone ◽

Scalar Fields ◽

Fault Zones ◽

Diffuse Interface ◽

Material Damage ◽

Earthquake Rupture ◽

Shear Cracks ◽

Dynamic Rupture ◽

First Order ◽

Cartesian Meshes

Earthquake fault zones are more complex, both geometrically and rheologically, than an idealised infinitely thin plane embedded in linear elastic material. &#160;Field and laboratory measurements reveal complex fault zone structure involving tensile and shear fractures spanning a wide spectrum of length scales (e.g., Mitchell & Faulkner, 2009), dense seismic and geodetic recording of small and large earthquakes show hierarchical volumetric faulting patterns (e.g., Cheng et al., 2018, Ross et al., 2019) and 2D numerical models explicitly accounting for off-fault fractures demonstrate important feedback with rupture dynamics and ground motions (e.g., Thomas & Bhat 2018, Okubo et al., 2019).Here (Gabriel et al., 2021) we adopt a diffuse crack representation to incorporate finite strain nonlinear material behaviour, natural complexities and multi-physics coupling within and outside of fault zones into dynamic earthquake rupture modeling. We use a first-order hyperbolic and thermodynamically compatible mathematical model, namely the GPR model (Godunov & Romenski, 1972; Romenski, 1988), &#160;to describe a continuum in a gravitational field which provides a unified description of nonlinear elasto-plasticity, material damage and of viscous Newtonian flows with phase transition between solid and liquid phases.The model shares common features with phase-field approaches but substantially extends them. Pre-damaged faults as well as dynamically induced secondary cracks are therein described via a scalar function indicating the local level of material damage (Tavelli et al., 2020); arbitrarily complex geometries are represented via a diffuse interface approach based on a solid volume fraction function (Tavelli et al., 2019). Neither of the two scalar fields needs to be mesh-aligned, allowing thus faults and cracks with complex topology and the use of adaptive Cartesian meshes (AMR). High-order accuracy and adaptive Cartesian meshes are enabled in 2D and 3D by using the extreme scale hyperbolic PDE solver ExaHyPE (Reinarz et al., 2019).We show a wide range of numerical applications that are relevant for dynamic earthquake rupture in fault zones, including the co-seismic generation of secondary off-fault shear cracks, tensile rock fracture in the Brazilian disc test, as well as a natural convection problem in molten rock-like material. We compare diffuse interface fault models of kinematic cracks, spontaneous dynamic rupture and dynamically generated off-fault shear cracks to sharp interface reference models. To this end, we calibrate the GPR model to resemble empirical tensile and shear crack formation and friction laws. We find that the continuum model can resemble and extend classical solutions, while introducing dynamic differences (i) on the scale of pre-damaged/low-rigidity fault zone, such as out-of- plane rupture rotation; and (ii) on the scale of the intact host rock, such as conjugate shear cracking in tensile lobes.&#160;Our approach is part of the TEAR ERC project (www.tear-erc.eu) and will potentially allow to fully model volumetric fault zone shearing during earthquake rupture, which includes spontaneous partition of fault slip into intensely localized shear deformation within weaker (possibly cohesionless/ultracataclastic) fault-core gouge and more distributed damage within fault rocks and foliated gouges.

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Factors Affecting Acoustic Properties of Natural-Fiber-Based Materials and Composites: A Review

Textiles ◽

10.3390/textiles1010005 ◽

2021 ◽

Vol 1 (1) ◽

pp. 55-85

Author(s):

Tufail Hassan ◽

Hafsa Jamshaid ◽

Rajesh Mishra ◽

Muhammad Qamar Khan ◽

Michal Petru ◽

...

Keyword(s):

Sound Absorption ◽

Natural Fiber ◽

Volume Fraction ◽

Fiber Type ◽

Alkali Treatment ◽

Acoustic Properties ◽

Synthetic Fiber ◽

Sound Insulation ◽

Factors Affecting ◽

Wide Range

Recently, very rapid growth has been observed in the innovations and use of natural-fiber-based materials and composites for acoustic applications due to their environmentally friendly nature, low cost, and good acoustic absorption capability. However, there are still challenges for researchers to improve the mechanical and acoustic properties of natural fiber composites. In contrast, synthetic fiber-based composites have good mechanical properties and can be used in a wide range of structural and automotive applications. This review aims to provide a short overview of the different factors that affect the acoustic properties of natural-fiber-based materials and composites. The various factors that influence acoustic performance are fiber type, fineness, length, orientation, density, volume fraction in the composite, thickness, level of compression, and design. The details of various factors affecting the acoustic behavior of the fiber-based composites are described. Natural-fiber-based composites exhibit relatively good sound absorption capability due to their porous structure. Surface modification by alkali treatment can enhance the sound absorption performance. These materials can be used in buildings and interiors for efficient sound insulation.

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Conduction and convection heat transfer characteristics of water-based au nanofluids in a square cavity with differentially heated side walls subjected to constant temperatures

Thermal Science ◽

10.2298/tsci130604082t ◽

2014 ◽

Vol 18 (suppl.1) ◽

pp. 189-200 ◽

Cited By ~ 4

Author(s):

Primoz Ternik ◽

Rebeka Rudolf

Keyword(s):

Heat Transfer ◽

Rayleigh Number ◽

Base Fluid ◽

Volume Fraction ◽

Heat Transfer Characteristics ◽

Square Cavity ◽

Onset Of Convection ◽

Transfer Characteristics ◽

Wide Range ◽

Water Based

The present work deals with the natural convection in a square cavity filled with the water-based Au nanofluid. The cavity is heated on the vertical and cooled from the adjacent wall, while the other two horizontal walls are adiabatic. The governing differential equations have been solved by the standard finite volume method and the hydrodynamic and thermal fields were coupled together using the Boussinesq approximation. The main objective of this study is to investigate the influence of the nanoparticles? volume fraction on the heat transfer characteristics of Au nanofluids at the given base fluid?s (i.e. water) Rayleigh number. Accurate results are presented over a wide range of the base fluid Rayleigh number and the volume fraction of Au nanoparticles. It is shown that adding nanoparticles in a base fluid delays the onset of convection. Contrary to what is argued by many authors, we show by numerical simulations that the use of nanofluids can reduce the heat transfer rate instead of increasing it.

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Microstructure and magnetic properties of Nd-Fe-B-(Re, Ti) alloys

Nukleonika ◽

10.1515/nuka-2015-0008 ◽

2015 ◽

Vol 60 (1) ◽

pp. 29-33

Author(s):

Mariusz Hasiak

Keyword(s):

Magnetic Properties ◽

Phase Composition ◽

Volume Fraction ◽

Magnetic Characteristics ◽

Ti Alloys ◽

Wide Range ◽

Magnetically Hard ◽

Ti Addition ◽

Microstructure And Magnetic Properties

Abstract The microstructure and magnetic properties of nanocomposite hard magnetic Nd-Fe-B-(Re, Ti) materials with different Nd and Fe contents are studied. The role of Re and Ti addition in phase composition and volume fraction of the Nd-Fe-B phase is determined. All samples are annealed at the same temperature of 993 K for 10 min. Mössbauer spectroscopy shows that the addition of 4 at.% of Re to the Nd8Fe78B14 alloy leads to creation of an ineligible amount of the magnetically hard Nd2Fe14B phase. Moreover, the microstructure and magnetic characteristics recorded in a wide range of temperatures for the Nd8Fe79−xB13Mx (x = 4; M = Re or Ti) alloys are also analyzed.

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First-order formalism for twinlike models with several real scalar fields

The European Physical Journal C ◽

10.1140/epjc/s10052-014-2755-0 ◽

2014 ◽

Vol 74 (2) ◽

Cited By ~ 18

Author(s):

D. Bazeia ◽

A. S. Lobão ◽

L. Losano ◽

R. Menezes

Keyword(s):

Scalar Fields ◽

First Order ◽

Real Scalar

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Laser-Induced Pretransitional Ordering And Nonlinear Optical Properties Of Rigid-Rod Polymer Suspensions

MRS Proceedings ◽

10.1557/proc-328-619 ◽

1993 ◽

Vol 328 ◽

Author(s):

Boris E. Vugmeister ◽

Michelle S. Malcuit ◽

John C. Kralik ◽

Colleen Stevens

Keyword(s):

Phase Transition ◽

Colloidal Particles ◽

Volume Fraction ◽

Orientational Order ◽

Critical Value ◽

Orientational Relaxation ◽

First Order ◽

First Order Phase Transition ◽

Rigid Rod ◽

First Order Phase

ABSTRACTWe investigate the pretransitional behavior in laser-induced alignment of rigid rod-like polytetraflouroethylene (PTFE) suspensions. Using a laser-induced birefringence experiment, we measure both the orientational order parameter and the orientational relaxation time. We find that both increase as the volume fraction of colloidal particles approaches the critical value for the isotropic-nematic phase transition. Experimental results are compared with theory which takes into account the possibility of a first-order phase transition induced by a laser electric field.

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Critical examination of various approaches used for analysing helical cables

The Journal of Strain Analysis for Engineering Design ◽

10.1243/03093247v291043 ◽

1994 ◽

Vol 29 (1) ◽

pp. 43-55 ◽

Cited By ~ 28

Author(s):

M Raoof ◽

I Kraincanic

Keyword(s):

Large Diameter ◽

Numerical Results ◽

Hertzian Contact ◽

Critical Examination ◽

First Order ◽

Wide Range ◽

End Conditions ◽

Parametric Studies ◽

The Individual ◽

Fixed End

Using theoretical parametric studies covering a wide range of cable (and wire) diameters and lay angles, the range of validity of various approaches used for analysing helical cables are critically examined. Numerical results strongly suggest that for multi-layered steel strands with small wire/cable diameter ratios, the bending and torsional stiffnesses of the individual wires may safely be ignored when calculating the 2 × 2 matrix for strand axial/torsional stiffnesses. However, such bending and torsional wire stiffnesses are shown to be first order parameters in analysing the overall axial and torsional stiffnesses of, say, seven wire stands, especially under free-fixed end conditions with respect to torsional movements. Interwire contact deformations are shown to be of great importance in evaluating the axial and torsional stiffnesses of large diameter multi-layered steel strands. Their importance diminishes as the number of wires associated with smaller diameter cables decreases. Using a modified version of a previously reported theoretical model for analysing multilayered instrumentation cables, the importance of allowing for the influence of contact deformations in compliant layers on cable overall characteristics such as axial or torsional stiffnesses is demonstrated by theoretical numerical results. In particular, non-Hertzian contact formulations are used to obtain the interlayer compliances in instrumentation cables in preference to a previously reported model employing Hertzian theory with its associated limitations.

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Nanoemulsions: A Versatile Technology for Oil and Gas Applications

10.2118/204722-ms ◽

2021 ◽

Author(s):

Nouf AlJabri ◽

Nan Shi

Keyword(s):

Droplet Size ◽

Large Scale ◽

Oil And Gas ◽

Volume Fraction ◽

Oil Industry ◽

Oil And Gas Industry ◽

High Energy ◽

Small Droplet ◽

Gas Industry ◽

Wide Range

Abstract Nanoemulsions (NEs) are kinetically stable emulsions with droplet size on the order of 100 nm. Many unique properties of NEs, such as stability and rheology, have attracted considerable attention in the oil industry. Here, we review applications and studies of NEs for major upstream operations, highlighting useful properties of NEs, synthesis to render these properties, and techniques to characterize them. We identify specific challenges associated with large-scale applications of NEs and directions for future studies. We first summarize useful and unique properties of NEs, mostly arising from the small droplet size. Then, we compare different methods to prepare NEs based on the magnitude of input energy, i.e., low-energy and high-energy methods. In addition, we review techniques to characterize properties of NEs, such as droplet size, volume fraction of the dispersed phase, and viscosity. Furthermore, we discuss specific applications of NEs in four areas of upstream operations, i.e., enhanced oil recovery, drilling/completion, flow assurance, and stimulation. Finally, we identify challenges to economically tailor NEs with desired properties for large-scale upstream applications and propose possible solutions to some of these challenges. NEs are kinetically stable due to their small droplet size (submicron to 100 nm). Within this size range, the rate of major destabilizing mechanisms, such as coalescence, flocculation, and Ostwald ripening, is considerably slowed down. In addition, small droplet size yields large surface-to-volume ratio, optical transparency, high diffusivity, and controllable rheology. Similar to applications in other fields (food industry, pharmaceuticals, cosmetics, etc.), the oil and gas industry can also benefit from these useful properties of NEs. Proposed functions of NEs include delivering chemicals, conditioning wellbore/reservoir conditions, and improve chemical compatibility. Therefore, we envision NEs as a versatile technology that can be applied in a variety of upstream operations. Upstream operations often target a wide range of physical and chemical conditions and are operated at different time scales. More importantly, these operations typically consume a large amount of materials. These facts not only suggest efforts to rationally engineer properties of NEs in upstream applications, but also manifest the importance to economically optimize such efforts for large-scale operations. We summarize studies and applications of NEs in upstream operations in the oil and gas industry. We review useful properties of NEs that benefit upstream applications as well as techniques to synthesize and characterize NEs. More importantly, we identify challenges and opportunities in engineering NEs for large-scale operations in different upstream applications. This work not only focuses on scientific aspects of synthesizing NEs with desired properties but also emphasizes engineering and economic consideration that is important in the oil industry.

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A Percolation Equation for Modeling Experimental Results for Continuum Percolation Systems

MRS Proceedings ◽

10.1557/proc-699-r9.4 ◽

2001 ◽

Vol 699 ◽

Author(s):

D.S. McLachlan ◽

C. Chiteme ◽

W.D. Heiss ◽

Junjie Wu

Keyword(s):

Experimental Data ◽

Ac Conductivity ◽

Volume Fraction ◽

Power Laws ◽

Second Order ◽

Experimental Results ◽

Analytical Equation ◽

Scaling Properties ◽

First Order ◽

Dc And Ac Conductivity

AbstractThe standard percolation equations or power laws, for dc and ac conductivity (dielectric constant) are based on scaling ansatz, and predict the behaviour of the first and second order terms, above and below the percolation or critical volume fraction (øc), and in the crossoverregion. Recent experimental results on ac conductivity are presented, which show that these equations, with the exception of real σm above øc and the first order terms in the crossover region, are only valid in the limit σi/σc = 0, where for an ideal dielectric σi=ωε0εr.A single analytical equation, which has the same parameters as the standard percolation equations, and which, for ac conductivity, reduces to the standard percolation power laws in the limit σi(ωε0εr)/σc = 0 for all but one case, is presented. The exception is the expression for real σm below øc, where the standard power law is always incorrect. The equation is then shown to quantitatively fit both first and second order dc and ac experimental data over the entire frequency and composition range. This phenomenological equation is also continuous, has the scaling properties required at a second order metal-insulator and fits scaled first order dc and ac experimental data. Unfortunately, the s and t exponents that are necessary to fit the data to the above analytical equation are usually not the simple dimensionally determined universal ones and depend on a number of factors.

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First-order autoregressive gamma sequences and point processes

Advances in Applied Probability ◽

10.2307/1426429 ◽

1980 ◽

Vol 12 (3) ◽

pp. 727-745 ◽

Cited By ~ 196

Author(s):

D. P. Gaver ◽

P. A. W. Lewis

Keyword(s):

Parameter Estimation ◽

Point Processes ◽

Random Variables ◽

Innovation Process ◽

Sums Of Random Variables ◽

First Order ◽

Wide Range ◽

Serial Correlations ◽

Generating Sequences ◽

Stieltjes Transforms

It is shown that there is an innovation process {∊n} such that the sequence of random variables {Xn} generated by the linear, additive first-order autoregressive scheme Xn = pXn-1 + ∊n are marginally distributed as gamma (λ, k) variables if 0 ≦p ≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.

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