Cnoidal waves in solids

Veveakis, Manolis; Regenauer-Lieb, Klaus

doi:10.1016/j.jmps.2015.02.010

Cited by 54 publications

(85 citation statements)

References 37 publications

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“…This law allows to include more physics into the hardening evolution as in the theory of plasticity for metals 42 . The Arrhenius dependency of the flow law enables to introduce multi-physical couplings such as the effect of heat generation on the frictional strength or more generally interface phenomena between the solid skeleton and the pores 43,44 . In principle, _ ϵ 0 and Q are functions of internal state variables ξ, that are representative of mechanisms like grain size sensitivity (in which case an expression of the average grain size is the internal state variable), fugacity sensitivity, effect of asperities of the contacts etc.…”

Section: Methodsmentioning

confidence: 99%

Weak phases production and heat generation control fault friction during seismic slip

Rattez

Veveakis

2020

Nat Commun

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The triggering and magnitude of earthquakes is determined by the friction evolution along faults. Experimental results have revealed a drastic decrease of the friction coefficient for velocities close to the maximum seismic one, independently of the material studied. Due to the extreme loading conditions during seismic slip, many competing physical phenomena occur (like mineral decomposition, nanoparticle lubrication, melting among others) that are typically thermal in origin and are changing the nature of the material. Here we show that a large set of experimental data for different rocks can be described by such thermallyactivated mechanisms, combined with the production of weak phases. By taking into account the energy balance of all processes during fault movement, we present a framework that reconciles the data, and is capable of explaining the frictional behavior of faults, across the full range of slip velocities (10 −9 to 10 m/s).

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Section: Methodsmentioning

confidence: 99%

Weak phases production and heat generation control fault friction during seismic slip

Rattez

Veveakis

2020

Nat Commun

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“…3. The momentum and mass balance equations for such a configuration have been detailed in [7,1] to be:…”

Section: Mathematical Modeling Of Isotropic Extension Of a Saturated mentioning

confidence: 99%

“…subject to the boundary conditions σ = 1 when x = 0, x = 1. This case has been extensively studied by [1,7,8,9] analytically for m = 3, and its solution is known as a cnoidal wave solution, because of the Jacobi cn−functions that constitute the base of the solution space. These cn−oidal functions, in brief are similar in spirit to trigonometric functions, except that their periodicity is based on elliptical, instead of circular basis.…”

Section: Onset Of Cracks and Pattern Formationmentioning

confidence: 99%

“…Further to these studies, the results are generalized here for any value of m. To do so, Eq. was implemented in the Finite Element simulator REDBACK [10,11] and validated against the analytical solutions provided by [1]. When m = 1 the solution is the usual, diffusive front met for example at Terzaghi's 1D consolidation problem in compression.…”

Section: Onset Of Cracks and Pattern Formationmentioning

confidence: 99%

“…For any non-linearity in the flow law (exponents m > 1) the solution bifurcates for values of λ larger than a critical value λ cr . An example is given in [1,7,8,9] for the case of m = 3, where the solution presented stress singularities for λ ≥ λ cr ≈ 12.7. From that value of λ onward, the number of peaks increases with increasing λ until obtaining a scaling where the number of peaks N p ∼ √ λ [1].…”

Section: Onset Of Cracks and Pattern Formationmentioning

confidence: 99%

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A note on the instability and pattern formation of shrinkage cracks in viscoplastic soils

Veveakis¹,

Poulet²

2019

Preprint

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In this note we present a theoretical study on the conditions for the onset of cracks, as well as the corresponding pattern formation, in saturated viscoplastic soils under isotropic loading (extension). The type of stress applied is left unspecified, to cover a variety of loadings including shrinkage due to dessication, isotropic thermal expansion, mechanical loading and so forth. By treating the saturated soil as rigid viscoplastic, we obtain a 2D extension of the Cnoidal Waves equations [1]. By numerically solving the corresponding boundary value problem, we retrieve conditions for the onset of cracking instability in 2D loading, and identify the characteristic spacing between cracks to be a length scale combining all the hydro-mechanical parameters of the problem. Finally, we show that in a rectangular slab of clay under isotropic extension, patterns of triangular, rectangular and hexagonal cracks can tessellate the domain, with the hexagonal pattern being the energetically favored, as it minimizes the free energy of the system.

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On the Thermo‐poro‐mechanics of Chemically Active Faults

Veveakis

2021

Instabilities Modeling in Geomechanics

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On the thermo-poro-mechanics of chemically active faults Shear zones in outcrops and core drillings on active faults commonly reveal two scales of localization, with centimeter to tens of meters thick deformation zones embedding much narrower zones of mm-to cm-scale. The narrow zones are often attributed to some form of fast instability such as earthquakes or slow slip events. Surprisingly, the double localisation phenomenon seem to be independent of the mode of failure, as it is observed in brittle cataclastic fault zones as well as ductile mylonitic shear zones. In both a very thin layer of chemically altered, ultra fine grained ultracataclasite or ultramylonite is noted. We present an extension to the classical solid mechanical theory where both length scales emerge as part of the same evolutionary process of shearing the host rock. We highlight the important role of any type of solid-fluid phase transitions that govern the second degree localisation process in the core of the shear zone. In both brittle and ductile shear zones chemistry stops the localisation process caused by a multiphysics feedback loop leading to an unstable slip. The microstructural evolutionary processes govern the time-scale of the transition between slow background shear and fast, intermittent instabilities in the fault zone core. The fast cataclastic fragmentation processes are limiting the rates of forming the ultracataclasites in the brittle domain, while the slow dynamic recrystallisation prolongs the transition to ultramylonites into a slow slip instability in the ductile realm.

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Cnoidal waves in solids

Cited by 54 publications

References 37 publications

Weak phases production and heat generation control fault friction during seismic slip

Weak phases production and heat generation control fault friction during seismic slip

A note on the instability and pattern formation of shrinkage cracks in viscoplastic soils

On the Thermo‐poro‐mechanics of Chemically Active Faults

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