A Fully Coupled Theory and Variational Principle for Thermal–Electrical–Chemical–Mechanical Processes

2014 ◽  
Vol 81 (11) ◽  
Author(s):  
Pengfei Yu ◽  
Shengping Shen
Keyword(s):  
Variational Principle ◽  
Electrostatic Potential ◽  
Constitutive Relations ◽  
Irreversible Thermodynamics ◽  
Electrochemical Reactions ◽  
Mechanical Coupling ◽  
Field Diffusion ◽  
Chemical And Biological Systems ◽  
Fully Coupled ◽  
Large Research

Thermal–electrical–chemical–mechanical coupling controls the behavior of many transport and electrochemical reactions processes in physical, chemical and biological systems. Hence, advanced understanding of the coupled behavior is crucial and attracting a large research interest. However, most of the existing coupling theories are limited to the partial coupling or particular process. In this paper, on the basis of irreversible thermodynamics, a variational principle for the thermal electrical chemical mechanical fully coupling problems is proposed. The complete fully coupling governing equations, including the heat conduction, mass diffusion, electrochemical reactions and electrostatic potential, are derived from the variational principle. Here, the piezoelectricity, conductivity, and electrochemical reactions are taken into account. Both the constitutive relations and evolving equations are fully coupled. This theory can be used to deal with coupling problems in solids, including conductors, semiconductors, piezoelectric and nonpiezoelectric dielectrics. As an application of this work, a developed boundary value problem is solved numerically in a mixed ion-electronic conductor (MIEC). Numerical results show that the coupling between electric field, diffusion, and chemical reactions influence the defect distribution, electrostatic potential and mechanical stress.

Fully Integrating a Hydraulic Fracturing, Reservoir, and Wellbore Simulator into a Practical Engineering Tool

2021 ◽  
Author(s):  
Mark McClure
Keyword(s):  
User Interface ◽  
Hydraulic Fracturing ◽  
Volume Fraction ◽  
3D Visualization ◽  
Constitutive Relations ◽  
Coupled Processes ◽  
Tight Coupling ◽  
Member States ◽  
Proppant Transport ◽  
Fully Coupled

<p>In this talk, I give an overview of our software ResFrac, which fully integrates a ‘true’ hydraulic fracturing simulator and a multiphase reservoir simulator (McClure et al., 2020a). Conventionally, these processes have been described with separate codes, using separate meshes, and with different physics. Integrating these two categories of software is advantageous because it enables seamless description of the entire lifecycle of a well. It is possible to seamlessly integrate wells with complex histories such as frac hits from offset wells, refracs, and huff and puff EOR injection.</p><p>ResFrac has been applied on 25+ studies for operators optimizing development of oil and gas resources in shale and has been commercially licensed by 15+ companies (https://www.resfrac.com/case-studies; https://www.resfrac.com/publications; https://www.resfrac.com/about-us/our-team). The simulator has a modern user-interface with embedded help-documentation, wizards to help set up simulations, automated validators to identify issues with the setup prior to submitting, and plotting capabilities to preview 3D and tabular inputs. Simulations are run on the cloud and results are continuously downloaded to the user’s computer. This allows a user to easily run a large number of simultaneous simulations from their personal computer. The user-interface includes a custom-built and fully-featured visualization tool for 3D visualization and 2D plotting.</p><p>Hydraulic fracturing simulators must handle a diverse set of coupled physics: mechanics of crack propagation and stress shadowing, fluid flow in the fractures, leakoff, transport of fluid additives that impart non-Newtonian flow characteristics, and proppant transport. Proppant transport is particularly complex because proppant settles out into an immobile bed and may screen out at the tip. Many fracturing simulators approximate wellbore flow effects. However, because these effects are closely coupled to fracturing processes (especially in horizontal wells that have multiple simultaneously propagating fractures), we include a fully meshed, detailed wellbore model in the code, along with treatment of perforation pressure drop and near-wellbore tortuosity.</p><p>In the literature, separate constitutive relations are available to describe transport in open cracks, closed unpropped cracks, and closed propped cracks. However, there were not relations in the literature designed to describe transport under conditions transitional between these end-member states. A general numerical simulator must be able to describe all conditions (and avoid discontinuous changes between equations). To address this limitation, we developed a new set of constitutive equations that can smoothly transition between these end-member states – smoothly handling any general combination of aperture, effective normal stress, saturation, proppant volume fraction, and non-Newtonian fluid rheology (McClure et al., 2020).</p><p>The code solves all equations in a fully coupled way, using an adaptive implicit method. The fully coupled approach is chosen because of the tight coupling between many of the key physical processes. Iterative coupling converges very slowly and/or forces excessively small timesteps when tightly coupled processes are handled with iterative or explicit coupling.</p><p>McClure, Kang, Hewson, and Medam. 2020. ResFrac Technical Writeup (v5). arXiv.</p>

Study on Non-Local Damage Constitutive Model of Concrete under Freeze-Thaw Action

2010 ◽  
Vol 452-453 ◽  
pp. 133-136 ◽  
Author(s):  
Zong Min Liu ◽  
Ji Ze Mao ◽  
Hai Yan Song
Keyword(s):  
Constitutive Model ◽  
Internal State ◽  
Constitutive Relations ◽  
Irreversible Thermodynamics ◽  
Local Damage ◽  
Variable Theory ◽  
Freeze Thaw ◽  
Adjacent Point ◽  
Damage Constitutive Model ◽  
Non Local

Concrete is multi-phase composites. Due to the inhomogeneity of mechanical properties and complexity of physical properties, constitutive relations of concrete are more complicated. Starting from irreversible thermodynamics theory, internal state variable theory and nonlocal field theory, non-local damage constitutive model of concrete under freeze-thaw action is established in this paper. In the model, non-local influence functions are discussed which are used to describe interplay of damage between adjacent point.

scholarly journals Derivation of a numerical solution of the 3D coupled velocity field for an ice sheet – ice shelf system, incorporating both full and approximate stress solutions

2009 ◽  
Vol 2 (1) ◽  
pp. 81-158
Author(s):  
T. J. Reerink ◽  
R. S. W. van de Wal ◽  
P.-P. Borsboom
Keyword(s):  
Sparse Matrix ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Constant Density ◽  
Ice Shelf ◽  
Ice Flow ◽  
Mechanical Coupling ◽  
Hydrostatic Approximation ◽  
Fully Coupled ◽  
Single Set

Abstract. To overcome the mechanical coupling of an ice sheet with an ice shelf, one single set of velocity equations is presented covering both the sheet and the shelf. This set is obtained by applying shared sheet-shelf approximations. The hydrostatic approximation and a constant density are the only approximations that are applied to the full-Stokes momentum equations. The remaining stress terms from the momentum equations and the stress terms from the usual ice-flow law are multiplied by coefficients which can be put to zero or one, facilitating several stress approximations per domain within one model. In addition we derived a matrix format for the discretized set of the fully coupled velocity equations on a three-dimensional vertically scaled grid, in which all linear derivative terms are treated implicitly. The compact vector format of this sparse matrix equation is developed, including the boundary conditions.

A Fully Coupled Chemomechanical Formulation With Chemical Reaction Implemented by Finite Element Method

2019 ◽  
Vol 86 (4) ◽  
Author(s):  
Jianyong Chen ◽  
Hailong Wang ◽  
K. M. Liew ◽  
Shengping Shen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Chemical Reactions ◽  
Chemical Reaction ◽  
Reaction Diffusion ◽  
Irreversible Thermodynamics ◽  
Free Energy Function ◽  
Stress Dependent ◽  
Fully Coupled ◽  
Element Method

Based on the irreversible thermodynamics, a fully coupled chemomechanical model, i.e., the reaction–diffusion–stress model, is proposed and implemented numerically into the finite element method (FEM) with user-defined element (UEL) subroutines in abaqus. Compositional stress and growth stress are induced by the diffusion and chemical reactions in the solid, and in turn, both the diffusion and chemical reactions are stress-dependent. By providing specialization of the chemical reaction and free energy function, the specialized constitutive equations are introduced, which are highly coupled and nonlinear. The FE formulations are derived from the standard Galerkin approach and implemented via UEL subroutines in abaqus. Several illustrative numerical simulation examples are shown. The results demonstrate the validity and capability of the UEL subroutines, and show the interactions among mechanical deformation, diffusion, and chemical reaction.

New variational-Lagrangian thermodynamics of viscous fluid mixtures with thermomolecular diffusion

1979 ◽  
Vol 365 (1723) ◽  
pp. 467-494 ◽  
Keyword(s):  
Variational Principle ◽  
Viscous Fluid ◽  
Open Systems ◽  
Irreversible Thermodynamics ◽  
Field Equations ◽  
Fluid Mixtures ◽  
Generalized Coordinates ◽  
Partial Pressures ◽  
Simplified Analysis ◽  
Dynamical Field

A principle of virtual dissipation generalizing d’Alembert’s principle to nonlinear irreversible thermodynamics is applied to viscous fluid mixtures with coupled thermomolecular diffusion. Original dynamical field equations are obtained directly from the variational principle. The use of new fundamental concepts and methods in the thermodynamics of open systems avoids the difficulties inherent in the classical Gibbs approach.The dissipative forces incorporated explicitly in the field equations are expressed by means of a dissipation invariant evaluated in detail in terms of coupled viscous and diffusive properties. Partial pressures and dissipative stresses are given new, unambiguous thermodynamic definitions. Lagrangian type equations with generalized coordinates are also obtained directly from the variational principle. They provide a powerful tool of simplified analysis of complex open systems as well as the foundation of a variety of finite element methods.

A Finite Element Implementation of a Fully Coupled Mechanical–Chemical Theory

2017 ◽  
Vol 09 (03) ◽  
pp. 1750040 ◽  
Author(s):  
Jianyong Chen ◽  
Hailong Wang ◽  
Pengfei Yu ◽  
Shengping Shen
Keyword(s):  
Finite Element ◽  
Irreversible Thermodynamics ◽  
Mass Diffusion ◽  
Chemical Processes ◽  
Gibbs Function ◽  
Finite Element Implementation ◽  
Chemical Theory ◽  
Fully Coupled ◽  
Finite Element Formulations ◽  
Coupled Theory

A finite element implementation with UEL user-defined element (UEL) subroutines in ABAQUS for fully coupled mechanical–chemical processes, which accounts for deformation, mass diffusion, and chemical reactions based on irreversible thermodynamics, is presented. The finite element formulations are deduced from the Gibbs function variational principle. To demonstrate the robustness of the numerical implementation, one- and two-dimensional numerical simulations with different boundary conditions are conducted. The results present the validity and capability of the UEL subroutines and the coupled theory, and show the interaction among deformation, mass diffusion and chemical reaction. This work provides a valuable tool to the researchers for the study of coupled problems.

Thermodynamics of Infinitesimally Constrained Equilibrium States

2008 ◽  
Vol 76 (1) ◽  
Author(s):  
Q. Yang ◽  
L. J. Xue ◽  
Y. R. Liu
Keyword(s):  
Constitutive Relations ◽  
Hessian Matrix ◽  
Coefficient Matrix ◽  
Internal Variable ◽  
Irreversible Thermodynamics ◽  
Equilibrium States ◽  
Variable Theory ◽  
Constrained Equilibrium ◽  
Flow Potential ◽  
Nonequilibrium States

This paper is concerned with infinitesimally constrained equilibrium states, which are nonequilibrium states and infinitesimally close to equilibrium states. The corresponding thermodynamics is established in this paper within the thermodynamic framework of Rice (1971, “Inelastic Constitutive Relations for Solids: An Internal Variable Theory and Its Application to Metal Plasticity,” J. Mech. Phys. Solids, 19, pp. 433–455). It is shown that the thermodynamics of infinitesimally constrained equilibrium states belongs to linear irreversible thermodynamics. The coefficient matrix is the Hessian matrix of the flow potential function at the equilibrium state. The process of a state change induced by an infinitesimal stress increment in time-independent plasticity can be viewed as a sequence of infinitesimally constrained equilibrium states. The thermodynamic counterpart of yield functions are flow potential functions, and their convexity is required by intrinsic dissipation inequality. Drucker and Il’yushin’s inequalities are not essential thermodynamic requirements.

Thermal Stress Analysis of Water-Cooling Brake Disc Based on 3D Thermo-Mechanical Coupling Model

2011 ◽  
Vol 314-316 ◽  
pp. 1581-1586 ◽  
Author(s):  
Wen Xian Tang ◽  
Yun Di Cai ◽  
Cheng Cheng ◽  
Qiu Yun Huang
Keyword(s):  
Thermal Stress ◽  
Stress Field ◽  
Circumferential Stress ◽  
Brake Disc ◽  
Water Cooling ◽  
Mechanical Coupling ◽  
Emergency Braking ◽  
Disc Surface ◽  
Thermal Stress Field ◽  
Fully Coupled

As the key part of offshore drilling drawworks brake system, the brake disc plays a vital role in guaranteeing the working reliability and operational security of the drawworks. To obtain the distributions and variations of thermal stress field in the water-cooling bake disc in an emergency braking, the 3D thermo-mechanical coupling theoretical model and FEM were established in this paper. Meanwhile the displacement and thermal boundary conditions for solution were determined, and then fully coupled analysis of thermal stress field in the disc was carried out by using ABAQUS software. The analysis results showed that, temperature field and stress field in the process of emergency braking were fully coupled. The temperature, radial stress and circumferential stress on the disc surface were presented as a hackle. The circumferential stress was significantly greater than the radial stress. Thermal stress has a periodic effect on the brake disc during braking, so the circumferential stress is the main factor that accounts for the initiation and propagation of crack on the brake disc surface.

Continuum thermo-electro-mechanical model for electrostrictive elastomers

2012 ◽  
Vol 24 (6) ◽  
pp. 761-778 ◽  
Author(s):  
Rocco Vertechy ◽  
Giovanni Berselli ◽  
Vincenzo Parenti Castelli ◽  
Massimo Bergamasco
Keyword(s):  
Constitutive Relations ◽  
Experimental Tests ◽  
Elastic Model ◽  
Mechanical Stimuli ◽  
Elastic Continuum ◽  
Minimum Number ◽  
Analysis Design ◽  
And Control ◽  
Fully Coupled ◽  
General Balance

This article presents a finite-deformation fully-coupled thermo-electro-elastic continuum model that is suited for the analysis, design, and control of solid-state transduction devices based on electrostrictive elastomers. In the model, electrostrictive elastomers are considered as isotropic modified-entropic hyperelastic dielectrics that deform in response to a simultaneous combination of electrical, thermal, and mechanical stimuli. The model is thermodynamically consistent and comprises general balance equations, which do not require the postulation of any force or stress tensor of electrical origin, together with phenomenological invariant-based constitutive relations, which necessitate the minimum number of material parameters to be determined via experimental tests only. Comparison with existing theories and experimental results are provided that validate the proposed thermo-electro-elastic model.

Time Domain Turret Load and Motion Analyses for a FPSO

2020 ◽  
Author(s):  
Hyoungchul Kim ◽  
Bonjun Koo ◽  
Johyun Kyoung
Keyword(s):  
Time Domain ◽  
Interaction Model ◽  
Hydrodynamic Interactions ◽  
Test Results ◽  
Mechanical Coupling ◽  
Body Interaction ◽  
Nonlinear Springs ◽  
Frictional Damping ◽  
Multi Body ◽  
Fully Coupled

Abstract Fully coupled time domain turret/FPSO simulations are conducted using TechnipFMC proprietary software MLTSIM. To analyze hydrodynamic interactions and mechanical coupling effects between an FPSO and its turret, a multi-body interaction model is developed and analyzed. In the multi-body interaction model, full coupled hydrodynamic interactions are considered, and the bearing connections are modeled with nonlinear springs and frictional damping. The global performance analysis results are systematically compared with model test results (Kim et al. [1]), and hydrodynamic loads and mechanical coupling loads on the turret are presented in this paper.

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