Strain localization regularization and patterns formation in rate-dependent plastic materials with multiphysics coupling

Strain localization is an instability phenomenon occurring in deformable solid materials which undergo dissipative deformation mechanisms. Such instability is characterized by the localization of the displacement or velocity fields in a zone of finite thickness and is generally associated with the failure of materials. In several fields of material engineering and natural sciences, estimating the thickness of localized deformation is required to make accurate predictions of the evolution of the physical properties within localized strain regions and of the material strength. In this context, scientists and engineers often rely on numerical modeling techniques to study strain localization in solid materials. However, classical continuum theory for elasto-plastic materials fails at estimating strain localization thicknesses due to the lack of an internal length in the model constitutive laws. In this study, we investigate at which conditions multiphysics coupling enables to regularize the problem of strain localization using rate-dependent plasticity. We show that coupling the constitutive laws for deformation to a single generic diffusion-reaction equation representing a dissipative state variable can be sufficient to regularize the ill-posed problem under some conditions on the softening parameters in the plastic potential. We demonstrate in these cases how rate-dependent plasticity and multiphysics coupling can lead to material instabilities depicting one or several internal length scales controlled by the physical parameters resulting in the formation of regular or erratic patterns. As we consider a general form of the equations, the results presented in this study can be applied to a large panel of examples in the material engineering and geosciences communities

Permeability of matrix-fracture systems under mechanical loading – constraints from laboratory experiments and 3-D numerical modelling

The permeability of single fractures is commonly approximated by the cubic law assumption, which is however only valid under the condition of a single phase laminar flow between parallel plates. Departure from cubic law are related to many features like aperture fluctuations due to fracture surface roughness, relative shear displacement, the amount of flow exchange between the matrix and the fracture itself, etc. In order to quantify constitutive relationships among the aforementioned aspects, we have conducted a flow-through experiment with a porous rock sample (Flechtinger sandstone) containing a single macroscopic fracture. Based on this experiment, we obtained range of variations of intrinsic rock parameters, permeability and stress-strain relationships of the combined matrix-fracture system under hydrostatic loading. From the measured deformation of the matrixfracture system, we derived the evolution in the mechanical aperture of the fracture. In order to quantify the processes behind the laboratory observations, we carried out coupled hydro-mechanical simulations of the matrix-fracture system. Navier–Stokes flow was solved in the 3-dimensional open rough fracture domain, and back-coupled to the Darcy flow and the poroelastic behaviour of the rock matrix. The results demonstrate that the elastic behaviour and the related permeability alteration of the fracture domain could be captured by the numerical simulation. Furthermore, the stress-strain values obtained in the vicinity of the fracture asperities suggest that inelastic deformation develops at low mechanical load. An attempt was made to quantify the inelastic deformation by using the failure envelope obtained by laboratory experiments (whether tensile, shear, compaction, or a combination of those). However, change in permeability observed in the experiments are significantly larger than that in the simulation showing the importance of plastic deformation during opening and closure of the fracture and its impact on the cubic law approximation

Flexible parallel implicit modelling of coupled thermal-hydraulic-mechanical processes in fractured rocks

Abstract. Theory and numerical implementation describing groundwater flow and the transport of heat and solute mass in fully saturated fractured rocks with elasto-plastic mechanical feedbacks are developed. In our formulation, fractures are considered as being of lower dimension than the hosting deformable porous rock and we consider their hydraulic and mechanical apertures as scaling parameters to ensure continuous exchange of fluid mass and energy within the fracture–solid matrix system. The coupled system of equations is implemented in a new simulator code that makes use of a Galerkin finite-element technique. The code builds on a flexible, object-oriented numerical framework (MOOSE, Multiphysics Object Oriented Simulation Environment) which provides an extensive scalable parallel and implicit coupling to solve for the multiphysics problem. The governing equations of groundwater flow, heat and mass transport, and rock deformation are solved in a weak sense (either by classical Newton–Raphson or by free Jacobian inexact Newton–Krylow schemes) on an underlying unstructured mesh. Nonlinear feedbacks among the active processes are enforced by considering evolving fluid and rock properties depending on the thermo-hydro-mechanical state of the system and the local structure, i.e. degree of connectivity, of the fracture system. A suite of applications is presented to illustrate the flexibility and capability of the new simulator to address problems of increasing complexity and occurring at different spatial (from centimetres to tens of kilometres) and temporal scales (from minutes to hundreds of years).</jats:p

Multiphysics Modeling of a Brittle-Ductile Lithosphere: 2. Semi-brittle, Semi-ductile Deformation and Damage Rheology

The brittle-ductile transition is a domain of finite extent characterized by high differential stress where both brittle and ductile deformation are likely to occur. Understanding its depth location, extent, and stability through time is of relevance for diverse applications including subduction dynamics, mantle-surface interactions, and, more recently, proper targeting of high-enthalpy unconventional geothermal resources, where local thermal conditions may activate ductile creep at shallower depths than expected. In this contribution, we describe a thermodynamically consistent physical framework and its numerical implementation, therefore extending the formulation of the companion paper Jacquey and Cacace (2020, https://doi.org/10.1029/2019JB018474) to model thermo-hydro-mechanical coupled processes responsible for the occurrence of transitional semi-brittle, semi-ductile behavior in porous rocks. We make use of a damage rheology to account for the macroscopic effects of microstructural processes leading to brittle-like material weakening and of a rate-dependent plastic model to account for ductile material behavior. Our formulation additionally considers the role of porosity and its evolution during loading in controlling the volumetric mechanical response of a stressed rock. By means of dedicated applications, we discuss how our damage poro-visco-elasto-viscoplastic rheology can effectively reconcile the style of localized deformation under different confining pressure conditions as well as the bulk macroscopic material response as recorded by laboratory experiments under full triaxial conditions

GOLEM, a MOOSE-based application

GOLEM is a numerical simulator for modelling coupled Thermo-Hydro-Mechanical processes in faulted geothermal reservoirs. The simulator is developed by Antoine B. Jacquey and Mauro Cacace at the GFZ German Research Centre for Geosciences from the section Basin Modelling. GOLEM is a MOOSE-based application. Visit the MOOSE framework page for more information. GOLEM is distributed under the GNU GENERAL PUBLIC LICENSE v3. If you use GOLEM for your work please cite: This data publication: Antoine B. Jacquey, & Mauro Cacace. (2017, September 29). GOLEM, a MOOSE-based application. Zenodo. http://doi.org/10.5281/zenodo.999400 The publication presenting GOLEM: Cacace, M. and Jacquey, A. B.: Flexible parallel implicit modelling of coupled thermal–hydraulic–mechanical processes in fractured rocks, Solid Earth, 8, 921-941, https://doi.org/10.5194/se-8-921-2017, 2017

Strain localization regularization and patterns formation in rate-dependent plastic materials with multiphysics coupling

Strain localization is an instability phenomenon occurring in deformable solid materials which undergo dissipative deformation mechanisms. Such instability is characterized by the localization of the displacement or velocity fields in a zone of finite thickness and is generally associated with the failure of materials. In several fields of material engineering and natural sciences, estimating the thickness of localized deformation is required to make accurate predictions of the evolution of the physical properties within localized strain regions and of the material strength. In this context, scientists and engineers often rely on numerical modeling techniques to study strain localization in solid materials. However, classical continuum theory for elasto-plastic materials fails at estimating strain localization thicknesses due to the lack of an internal length in the model constitutive laws. In this study, we investigate at which conditions multiphysics coupling enables to regularize the problem of strain localization using rate-dependent plasticity. We show that coupling the constitutive laws for deformation to a single generic diffusion–reaction equation representing a dissipative state variable can be sufficient to regularize the ill-posed problem under some conditions on the softening parameters in the plastic potential. We demonstrate in these cases how rate-dependent plasticity and multiphysics coupling can lead to material instabilities depicting one or several internal length scales controlled by the physical parameters resulting in the formation of regular or erratic patterns. As we consider a general form of the equations, the results presented in this study can be applied to a large panel of examples in the material engineering and geosciences communities

Thermomechanics for Geological, Civil Engineering and Geodynamic Applications: Numerical Implementation and Application to the Bentheim Sandstone

Abstract Observations of the mechanical behavior of porous rocks subject to external loading indicate the existence of complex dependencies on the level of confining pressure, fluid pressure and rate of deformation. Due to the heterogeneous nature of porous rocks, their macroscopic response is the result of underlying microscopic processes which can alter the microstructural organization of the grain–pore network. The impacts of the multiscale and poromechanical behavior of geomaterials are relevant for a number of applications ranging from civil engineering, reservoir engineering, geological and geodynamic. The use of thermodynamic-consistent approaches to construct constitutive laws which span a large range of time scales is particularly relevant in this context. In this two-part contribution, we present extensions of the thermomechanics theory to account for the poromechanics of path- and rate-dependent critical state line models and we cover the relevance of this thermodynamic-consistent model for civil engineering, geological and geodynamic applications. In this second paper, we extend the thermomechanics theory to account for the poromechanics of geomaterials in agreement with the theory of poroelasticity and considering in addition dissipative inelastic processes. We illustrate using experimental data how the thermodynamic-consistent model derived can account for the macroscopic mechanical and porous responses in triaxial loading experiments. We particularly focus on the transition from dilation to compression regime with confining pressure and the resulting localization styles ranging from shear dilation to compaction bands

Numerical Investigation of Thermoelastic Effects on Fault Slip Tendency during Injection and Production of Geothermal Fluids

AbstractThis study deals with numerical analysis of fault slip behaviour within deep faulted geothermal reservoirs during injection and pro- duction of fluid. A coupled approach for thermo-hydro-mechanical process modelling is used to describe and quantify the effects of thermoelastic stress on the slip tendency. The results show that the slip tendency of a fault can increase when the cold fluid front reaches the fault due to thermal stress enhancement. Magnitudes of increase in slip tendency depend on the injection temperature and the dip angle of the fault, and under specific configurations, may lead to a reactivation of the fault