Frame indifferent elastoplasticity of frictional materials at finite strain

Karrech, Ali; Regenauer-Lieb, Klaus; Poulet, Thomas

doi:10.1016/j.ijsolstr.2010.09.026

Cited by 25 publications

(11 citation statements)

References 71 publications

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“…Although some artificial numerical diffusion is expected to emerge from the mesh interpolation, no adaptive remeshing is required for the given small numerical errors. Testing various numerical mesh sizes confirms that localization is mesh insensitive, which is in good agreement with previous studies [e.g., Karrech et al , ; Needleman , ]. As an initial condition, we assume a homogeneous field for the temperature and introduce modest thermal perturbations randomly (size: T ∗ =0.001) for the sole purpose of reducing the numerical time that is required for the appearance of instabilities, if they were to appear in the appropriate instability regime (see previous section).…”

Section: Numerical Analysis In Layered Structuressupporting

confidence: 86%

Boudinage and folding as an energy instability in ductile deformation

et al. 2016

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We present a theory for the onset of localization in layered rate‐ and temperature‐sensitive rocks, in which energy‐related mechanical bifurcations lead to localized dissipation patterns in the transient deformation regime. The implementation of the coupled thermomechanical 2‐D finite element model comprises an elastic and rate‐dependent von Mises plastic rheology. The underlying system of equations is solved in a three‐layer pure shear box, for constant velocity and isothermal boundary conditions. To examine the transition from stable to localized creep, we study how material instabilities are related to energy bifurcations, which arise independently of the sign of the stress conditions imposed on opposite boundaries, whether in compression or extension. The onset of localization is controlled by a critical amount of dissipation, termed Gruntfest number, when dissipative work by temperature‐sensitive creep translated into heat overcomes the diffusive capacity of the layer. Through an additional mathematical bifurcation analysis using constant stress boundary conditions, we verify that boudinage and folding develop at the same critical Gruntfest number. Since the critical material parameters and boundary conditions for both structures to develop are found to coincide, the initiation of localized deformation in strong layered media within a weaker matrix can be captured by a unified theory for localization in ductile materials. In this energy framework, neither intrinsic nor extrinsic material weaknesses are required, because the nucleation process of strain localization arises out of steady state conditions. This finding allows us to describe boudinage and folding structures as the same energy attractor of ductile deformation.

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Section: Numerical Analysis In Layered Structuressupporting

confidence: 86%

Boudinage and folding as an energy instability in ductile deformation

et al. 2016

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“…Knowledge on the energy dissipation of the individual deformation mechanisms is required and could be tracked down by approaches as published in Karrech et al . [, , ]. Microstructures related to the presence of diffusion creep are typically very fine grained and consist of equi‐axed grains with no or only weak crystallographic preferred orientation [ Rutter , ; Schmid and Handy , ].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…We describe in this paper only a formulation for shear strains smaller than 1. A different continuum formulation must be used for higher strains that include logarithmic elastic rotations as implemented in Karrech et al [2011c]. Therefore, the present model is not cyclic in X and Y directions.…”

Section: Implementation Of Grain Size Evolutionmentioning

confidence: 99%

From transient to steady state deformation and grain size: A thermodynamic approach using elasto-visco-plastic numerical modeling

Herwegh

Poulet

Karrech

et al. 2014

J. Geophys. Res. Solid Earth

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Numerical simulation experiments give insight into the evolving energy partitioning during high-strain torsion experiments of calcite. Our numerical experiments are designed to derive a generic macroscopic grain size sensitive flow law capable of describing the full evolution from the transient regime to steady state. The transient regime is crucial for understanding the importance of microstructural processes that may lead to strain localization phenomena in deforming materials. This is particularly important in geological and geodynamic applications where the phenomenon of strain localization happens outside the time frame that can be observed under controlled laboratory conditions. Our method is based on an extension of the paleowattmeter approach to the transient regime. We add an empirical hardening law using the Ramberg-Osgood approximation and assess the experiments by an evolution test function of stored over dissipated energy (lambda factor). Parameter studies of, strain hardening, dislocation creep parameter, strain rates, temperature, and lambda factor as well as mesh sensitivity are presented to explore the sensitivity of the newly derived transient/steady state flow law. Our analysis can be seen as one of the first steps in a hybrid computational-laboratory-field modeling workflow. The analysis could be improved through independent verifications by thermographic analysis in physical laboratory experiments to independently assess lambda factor evolution under laboratory conditions.

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“…As explained in details by Karrech et al (2011) the assumption of local equilibrium as well as the second law of thermodynamics deliver the following expression for dissipation…”

Section: Governing Equationsmentioning

confidence: 99%

Coupling of thermal-hydraulic-mechanical processes for geothermal reservoir modelling

et al. 2015

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This paper uses a fully coupled framework of thermal-hydraulic-mechanical processes to investigate how the injection and extraction of fluid within a geothermal reservoir impacts on the distributions of temperature, pore pressure, and deformation within the rock formations. Based on this formulation, a numerical model is developed in light of the thermodynamics of porous materials. The proposed procedure relies on the derivation of dissipative flow rules by postulating proper storage and dissipation functions. This approach opens new horizons for several resource engineering applications. Since it allows for full coupling, this formulation can play a key role in predicting risks when used for reservoir simulation. The results indicate that the injection-extraction process and temperature change have a definite impact on altering the in-situ properties of the reservoir. KEY WORDS: poro-mechanics, resource engineering, fluid injection and extraction, temperature change, pore pressure, stress, deformation, uplift, subsidence. INTRODUCTIONAs the population of the world is set to double by the end of this century, sustaining our current lifestyle requires the production of clean energy at affordable prices. While fossil fuels are still expected to be important energy resources for the next decades, the share of renewable energies is expected to increase significantly. The need to increase the supply of renewable energy sources has led to an increasing amount of research on harvesting geothermal energy. The geothermal energy process involves the utilisation of the Earth's natural geothermal gradient to extract heat and transform it into a directly useful energy such as electricity. To maintain recoverability and limit the footprint of geothermal energy, the process involves injecting cold fluids into an underground reservoir of hot permeable rock, allowing the fluid to flow through the rock formation and then extracting the heated fluid. The injection and extraction of fluids and subsequent temperature change throughout the reservoir impacts the physical properties of the permeable formations. The basic mechanism underlying the geo-mechanical response of a reservoir is related to the magnitude of the pore pressure and temperature variations. Deep underground reservoirs that have low values of porosity, permeability and compressibility result in greater pressure

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Frame indifferent elastoplasticity of frictional materials at finite strain

Cited by 25 publications

References 71 publications

Boudinage and folding as an energy instability in ductile deformation

Boudinage and folding as an energy instability in ductile deformation

From transient to steady state deformation and grain size: A thermodynamic approach using elasto-visco-plastic numerical modeling

Coupling of thermal-hydraulic-mechanical processes for geothermal reservoir modelling

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