Multiscale coupling and multiphysics approaches in earth sciences : applications

Geoscientists are confronted with the challenge of assessing nonlinear phenomena that result from multiphysics coupling across multiple scales from the quantum level to the scale of the earth and from femtoseconds to the 4.5 Ga of history of our planet. We neglect in this review electromagnetic modelling of the processes in the Earth’s core, and focus on four types of couplings that underpin fundamental instabilities in the Earth. These are thermal (T), hydraulic (H), mechanical (M) and chemical (C) processes which are driven and controlled by the transfer of heat to the Earth’s surface. Instabilities appear as faults, folds, compaction bands, shear/fault zones, plate boundaries and convective patterns. Convective patterns emerge from buoyancy overcoming viscous drag at a critical Rayleigh number. All other processes emerge from non-conservative thermodynamic forces with a critical critical dissipative source term, which can be characterised by the modified Gruntfest number Gr. These dissipative processes reach a quasi-steady state when, at maximum dissipation, THMC diffusion (Fourier, Darcy, Biot, Fick) balance the source term. The emerging steady state dissipative patterns are defined by the respective diffusion length scales. These length scales provide a fundamental thermodynamic yardstick for measuring instabilities in the Earth. The implementation of a fully coupled THMC multiscale theoretical framework into an applied workflow is still in its early stages. This is largely owing to the four fundamentally different lengths of the THMC diffusion yardsticks spanning micro-metre to tens of kilometres compounded by the additional necessity to consider microstructure information in the formulation of enriched continua for THMC feedback simulations (i.e., micro-structure enriched continuum formulation). Another challenge is to consider the important factor time which implies that the geomaterial often is very far away from initial yield and flowing on a time scale that cannot be accessed in the laboratory. This leads to the requirement of adopting a thermodynamic framework in conjunction with flow theories of plasticity. This framework allows, unlike consistency plasticity, the description of both solid mechanical and fluid dynamic instabilities. In the applications we show the similarity of THMC feedback patterns across scales such as brittle and ductile folds and faults. A particular interesting case is discussed in detail, where out of the fluid dynamic solution, ductile compaction bands appear which are akin and can be confused with their brittle siblings. The main difference is that they require the factor time and also a much lower driving forces to emerge. These low stress solutions cannot be obtained on short laboratory time scales and they are therefore much more likely to appear in nature than in the laboratory. We finish with a multiscale description of a seminal structure in the Swiss Alps, the Glarus thrust, which puzzled geologists for more than 100 years. Along the Glarus thrust, a km-scale package of rocks (nappe) has been pushed 40 km over its footwall as a solid rock body. The thrust itself is a m-wide ductile shear zone, while in turn the centre of the thrust shows a mm-cm wide central slip zone experiencing periodic extreme deformation akin to a stick-slip event. The m-wide creeping zone is consistent with the THM feedback length scale of solid mechanics, while the ultralocalised central slip zones is most likely a fluid dynamic instability.

Interplay of martensitic phase transformation and plastic slip in polycrystals

Inspired by key experimental and analytical results regarding Shape Memory Alloys (SMAs), we propose a modelling framework to explore the interplay between martensitic phase transformations and plastic slip in polycrystalline materials, with an eye towards computational efficiency. The resulting framework uses a convexified potential for the internal energy density to capture the stored energy associated with transformation at the meso-scale, and introduces kinetic potentials to govern the evolution of transformation and plastic slip. The framework is novel in the way it treats plasticity on par with transformation.

We implement the framework in the setting of anti-plane shear, using a staggered implicit/explict update: we first use a Fast-Fourier Transform (FFT) solver based on an Augmented Lagrangian formulation to implicitly solve for the full-field displacements of a simulated polycrystal, then explicitly update the volume fraction of martensite and plastic slip using their respective stick-slip type kinetic laws. We observe that, even in this simple setting with an idealized material comprising four martensitic variants and four slip systems, the model recovers a rich variety of SMA type behaviors. We use this model to gain insight into the isothermal behavior of stress-stabilized martensite, looking at the effects of the relative plastic yield strength, the memory of deformation history under non-proportional loading, and several others.

We extend the framework to the generalized 3-D setting, for which the convexified potential is a lower bound on the actual internal energy, and show that the fully implicit discrete time formulation of the framework is governed by a variational principle for mechanical equilibrium. We further propose an extension of the method to finite deformations via an exponential mapping. We implement the generalized framework using an existing Optimal Transport Mesh-free (OTM) solver. We then model the $\alpha$--$\gamma$ and $\alpha$--$\varepsilon$ transformations in pure iron, with an initial attempt in the latter to account for twinning in the parent phase. We demonstrate the scalability of the framework to large scale computing by simulating Taylor impact experiments, observing nearly linear (ideal) speed-up through 256 MPI tasks. Finally, we present preliminary results of a simulated Split-Hopkinson Pressure Bar (SHPB) experiment using the $\alpha$--$\varepsilon$ model.

Correlazioni tra proprietá reologiche, struttura e processabilitá di blend di LLDPE/LDPE

Polymer blends constitute a valuable way to produce relatively low cost new materials. A still open question concerns the miscibility of polyethylene blends. Deviations from the log-additivity rule of the newtonian viscosity are often taken as a signature of immiscibility of the two components. The aim of this thesis is to characterize the rheological behavior in shear and elongation of five series of LLDPE/LDPE blends whose parent polymers have been chosen with different viscosity and SCB content and length. Synergistic effects have been measured for both zero shear viscosity and melt strength. Both SCB length and viscosity ratio between the components have been found to be key parameters for the miscibility of the pure polymers. In particular the miscibility increases with increasing SCB length and with decreasing the LDPE molecular weight and viscosity. This rheological behavior has significant effects on the processability window of these blends when the uni or biaxial elongational flows are involved. The film blowing is one of the processes for which the synergistic effects above mentioned can be crucial. Small scale experiments of film blowing performed for one of the series of blends has demonstrated that the positive deviation of the melt strength enlarges the processability window. In particular, the bubble stability was found to improve or disappear when the melt strength of the samples increased. The blending of LDPE and LLDPE can even reduce undesired melt flow instability phenomena widening, as a consequence, the processability window in extrusion. One of the series of blends has been characterized by means of capillary rheometry in order to allow a careful morphological analysis of the surface of the extruded polymer jets by means of Scanning Electron Microscopy (SEM) with the aim to detect the very early stages of the small scale melt instabilty at low shear rates (sharksin) and to follow its subsequent evolution as long as the shear rate was increased. With this experimental procedure it was possible to evaluate the shear rate ranges corresponding to different flow regions: smooth extrudate surface (absence of instability), sharkskin (small scale instability produced at the capillary exit), stick-slip transition (instability involving the whole capillary wall) and gross melt fracture (i.e. a large scale "upstream" instability originating from the entrance region of the capillary). A quantitative map was finally worked out using which an assessment of the flow type for a given shear rate and blend composition can be predicted.

Slip complexity in dynamic models of earthquake faults.

We summarize recent evidence that models of earthquake faults with dynamically unstable friction laws but no externally imposed heterogeneities can exhibit slip complexity. Two models are described here. The first is a one-dimensional model with velocity-weakening stick-slip friction; the second is a two-dimensional elastodynamic model with slip-weakening friction. Both exhibit small-event complexity and chaotic sequences of large characteristic events. The large events in both models are composed of Heaton pulses. We argue that the key ingredients of these models are reasonably accurate representations of the properties of real faults.

Molecular dynamics simulation of mechanical behavior of osteopontin-hydroxyapatite interfaces

Bone is characterized with an optimized combination of high stiffness and toughness. The understanding of bone nanomechanics is critical to the development of new artificial biological materials with unique properties. In this work, the mechanical characteristics of the interfaces between osteopontin (OPN, a noncollagenous protein in extrafibrillar protein matrix) and hydroxyapatite (HA, a mineral nanoplatelet in mineralized collagen fibrils) were investigated using molecular dynamics method. We found that the interfacial mechanical behaviour is governed by the electrostatic attraction between acidic amino acid residues in OPN and calcium in HA. Higher energy dissipation is associated with the OPN peptides with a higher number of acidic amino acid residues. When loading in the interface direction, new bonds between some acidic residues and HA surface are formed, resulting in a stick-slip type motion of OPN peptide on the HA surface and high interfacial energy dissipation. The formation of new bonds during loading is considered to be a key mechanism responsible for high fracture resistance observed in bone and other biological materials.

Effect Of Directionality Of Grinding Marks On Friction And Formation Of Transfer Layer

Surface texture influences friction and transfer layer formation during sliding. In the present investigation, basic studies were conducted using inclined pin-on-plate sliding tester to understand the effect of directionality of surface grinding marks of hard material on friction and transfer layer formation during sliding against soft materials. 080 M40 steel plates were ground to attain different surface roughness with unidirectional grinding marks. Then pins made of soft materials such as pure Al, pure Mg and Al-Mg alloy were slid against the prepared steel plates. Grinding angle (i.e., the angle between direction of sliding and grinding marks) was varied between 0 degrees and 90 degrees in the tests. Experiments were conducted under both dry and lubricated conditions on each plate in ambient environment. It was observed that the transfer layer formation and the coefficient of friction, which has two components adhesion and plowing - depend primarily on the directionality of grinding marks of the harder mating surface, and independent of surface roughness of the harder mating surface. For the case of pure Mg, stick-slip phenomenon was observed under dry condition for all grinding angles and it was absent upto 20 degrees grinding angles under lubricated condition. However, for the case of Al, it was observed only under lubricated conditions for angles exceeding 20 degrees. As regards the alloy, namely, Al-Mg alloy, it, was absent in both conditions. For the case of pure Mg and Al, it was observed that the amplitude of stick-slip motion primarily depends on plowing component of friction. The grinding angle effect on coefficient of friction was attributed to the variation of plowing component of friction with grinding angle.

Studies On Friction And Formation Of Transfer Layer In Hcp Metals

Surface texture plays an important role in the frictional behavior and transfer layer formation of contacting surfaces. In the present investigation, basic experiments were conducted using an inclined pin-on-plate sliding apparatus to better understand the role of surface texture on the coefficient of friction and the formation of a transfer layer. In the experiments, soft HCP materials such as pure Mg and pure Zn were used for the pins and a hardened 080 M40 steel was used for the plate. Two surface parameters of the steel plates—roughness and texture—were varied in tests that were conducted at a sliding speed of 2 mm/s in ambient conditions under both dry and lubricated conditions. The morphologies of the worn surfaces of the pins and the formation of the transfer layer on the counter surfaces were observed using a scanning electron microscope. In the experiments, the occurrence of stick-slip motion, the formation of a transfer layer, and the value of friction were recorded. With respect to the friction, both adhesion and plowing components were analyzed. Based on the experimental results, the effect of surface texture on the friction was attributed to differences in the amount of plowing. Both the plowing component of friction and the amplitude of stick-slip motion were determined to increase surface textures that promote plane strain conditions and decrease the textures that favor plane stress conditions.

Preparation of cast aluminium alloy-mica particle composites

The optimum conditions for producing cast aluminium alloy-mica particle composites, by stirring mica particles (40 to 120 mgrm) in molten aluminium alloys (above their liquidus temperatures), followed by casting in permanent moulds, are described. Addition of magnesium either as pieces along with mica particles on the surface of the melts or as a previously added alloying element was found to be necessary to disperse appreciable quantities (1.5 to 2 wt.%) of mica particles in the melts and retain them as uniform dispersions in castings under the conditions of present investigation. These castings can be remelted and degassed with nitrogen at least once with the retention of about 80% mica particles in the castings. Electron probe micro-analysis of these cast composites showed that magnesium added to the surface of the melt along with mica has a tendency to segregate around the mica particles, apparently improving the dispersability for mica particles in liquid aluminium alloys. The mechanical properties of the aluminium alloy-mica particle composite decrease with an increase in mica content, however, even at 2.2% the composite has a tensile strength of 14.22 kg mm–2 with 1.1% elongation, a compression strength of 42.61 kg mm–2, and an impact strength of 0.30 kgm cm–2. The properties are adequate for certain bearing applications, and the aluminium-mica composite bearings were found to run under boundary lubrication, semi-dry and dry friction conditions whereas the matrix alloy (without mica) bearings seized or showed stick slip under the same conditions.

Hidden order in crackling noise during peeling of an adhesive tape

We address the longstanding problem of recovering dynamical information from noisy acoustic emission signals arising from peeling of an adhesive tape subject to constant traction velocity. Using the phase space reconstruction procedure we demonstrate the deterministic chaotic dynamics by establishing the existence of correlation dimension as also a positive Lyapunov exponent in a midrange of traction velocities. The results are explained on the basis of the model that also emphasizes the deterministic origin of acoustic emission by clarifying its connection to stick-slip dynamics.

Lifting the singular nature of a model for peeling of an adhesive tape

We investigate the dynamics of peeling of an adhesive tape subjected to a constant pull speed. Due to the constraint between the pull force, peel angle and the peel force, the equations of motion derived earlier fall into the category of differential-algebraic equations (DAE) requiring an appropriate algorithm for its numerical solution. By including the kinetic energy arising from the stretched part of the tape in the Lagrangian, we derive equations of motion that support stick-slip jumps as a natural consequence of the inherent dynamics itself, thus circumventing the need to use any special algorithm. In the low mass limit, these equations reproduce solutions obtained using a differential-algebraic algorithm introduced for the earlier singular equations. We find that mass has a strong influence on the dynamics of the model rendering periodic solutions to chaotic and vice versa. Apart from the rich dynamics, the model reproduces several qualitative features of the different waveforms of the peel force function as also the decreasing nature of force drop magnitudes.

Influence of surface texture and roughness parameters on friction and transfer layer formation during sliding of aluminium pin on steel plate

Surface texture of harder mating surfaces plays an important role during sliding against softer materials and hence the importance of characterizing the surfaces in terms of roughness parameters. In the present investigation, basic studies were conducted using inclined pin-on-plate sliding tester to understand the surface texture effect of hard surfaces on coefficient of friction and transfer layer formation. A tribological couple made of a super purity aluminium pin against steel plate was used in the tests. Two surface parameters of steel plates, namely roughness and texture, were varied in the tests. It was observed that the transfer layer formation and the coefficient of friction along with its two components, namely, the adhesion and plowing, are controlled by the surface texture and are independent of surface roughness (R-a). Among the various surface roughness parameters, the average or the mean slope of the profile was found to explain the variations best. Under lubricated conditions, stick-slip phenomena was observed, the amplitude of which depends on the plowing component of friction. The presence of stick-slip motion under lubricated conditions could be attributed to the molecular deformation of the lubricant component confined between asperities. (C) 2009 Elsevier B. V. All rights reserved.

Influence of tilt angle of plate on friction and transfer layer—A study of aluminium pin sliding against steel plate

In the present investigation, unidirectional grinding marks were attained on the steel plates. Then aluminium (Al) pins were slid at 0.2°, 0.6°, 1.0°, 1.4°, 1.8°, 2.2° and 2.6° tilt angles of the plate with the grinding marks perpendicular and parallel to the sliding direction under both dry and lubricated conditions using a pin-on-plate inclined sliding tester to understand the influence of tilt angle and grinding marks direction of the plate on coefficient of friction and transfer layer formation. It was observed that the transfer layer formation and the coefficient of friction depend primarily on the grinding marks direction of the harder mating surface. Stick-slip phenomenon was observed only under lubricated conditions. For the case of pins slid perpendicular to the unidirectional grinding marks stick-slip phenomenon was observed for tilt angles exceeding 0.6°, the amplitude of which increases with increasing tilt angles. However, for the case of the pins slid parallel to the unidirectional grinding marks the stick-slip phenomena was observed for angles exceeding 2.2°, the amplitude of which also increases with increasing tilt angle. The presence of stick-slip phenomena under lubricated conditions could be attributed to the molecular deformation of the lubricant component confined between asperities.

Effect of directionality of unidirectional grinding marks on friction and transfer layer formation of Mg on steel using inclined scratch test

Surface topography has been known to play an important role in the friction and transfer layer formation during sliding. In the present investigation, EN8 steel flats were ground to attain different surface roughness with unidirectional grinding marks. Pure Mg pins were scratched on these surfaces using an Inclined Scratch Tester to study the influence of directionality of surface grinding marks on coefficient of friction and transfer layer formation. Grinding angle (i.e., the angle between direction of scratch and grinding marks) was varied between 0 degrees and 90 degrees during the tests. Experiments were conducted under both dry and lubricated conditions. Scanning electron micrographs of the contact surfaces of pins and flats were used to reveal the surface features that included the morphology of the transfer layer. It was observed that the average coefficient of friction and transfer layer formation depend primarily on the directionality of the grinding marks but were independent of surface roughness on the harder mating surface. In addition, a stick-slip phenomenon was observed, the amplitude of which depended both on the directionality of grinding marks and the surface roughness of the harder mating surface. The grinding angle effect on the coefficient of friction, which consists of adhesion and plowing components, was attributed to the variation of plowing component of friction. (c) 2006 Elsevier B.V. All rights reserved.

Influence of Inclination Angle and Machining Direction on Friction and Transfer Layer Formation

In the present investigation, unidirectional grinding marks were created on a set of steel plates. Sliding experiments were then conducted with the prepared steel plates using Al-Mg alloy pins and an inclined pin-on-plate sliding tester. The goals of the experiments were to ascertain the influence of inclination angle and grinding mark direction on friction and transfer layer formation during sliding contact. The inclination angle of the plate was held at 0.2 deg, 0.6 deg, 1 deg, 1.4 deg, 1.8 deg, 2.2 deg, and 2.6 deg in the tests. The pins were slid both perpendicular and parallel to the grinding marks direction. The experiments were conducted under both dry and lubricated conditions on each plate in an ambient environment. Results showed that the coefficient of friction and the formation of transfer layer depend on the grinding marks direction and inclination angle of the hard surfaces. For a given inclination angle, under both dry and lubricated conditions, the coefficient of friction and transfer layer formation were found to be greater when the pins slid perpendicular to the unidirectional grinding marks than when the pins slid parallel to the grinding marks. In addition, a stick-slip phenomenon was observed under lubricated conditions at the highest inclination angle for sliding perpendicular to the grinding marks direction. This phenomenon could be attributed to the extent of plane strain conditions taking place at the asperity level during sliding. DOI: 10.1115/1.4002604]