Irreversible Thermodynamics Research Articles

Estimation of the activation energy in the Ag/SnSe/Ge2Se3/W self-directed channel memristor

In this study, we conducted an investigation into the Ag/SnSe/Ge2Se3/W ionic memristor, focusing on the determination of activation energies associated with its two primary operational processes: the formation of conductive filaments and memristor degradation. To ascertain the electrical conductivity of the memristor in both its basic electronic states, a low resistance state and a high resistance state, we constructed current-voltage characteristics. The estimation of activation energy values was carried out employing the Arrhenius law and the provisions of irreversible thermodynamics, with specific reference to Onsager's second postulate. This fundamental concept posits that the growth rate of irreversible component of entropy can be expressed as the summation of products involving fluxes and thermodynamic forces when a system tends towards its equilibrium state. In the context of this study, the equilibrium state of the memristor is defined as the condition at which the memristor can no longer function as a resistive memory cell. Our experimentation involved the application of a flux of Ag+ ions (electromigration). The calculated activation energy values were found to be 0.24 eV for the initial process and 1.16 eV for the latter. These divergent activation energy values indicate the differentiation between the agglomerative mechanism that governs the formation of conductive channels, prevalent in the Ag/SnSe/Ge2Se3/W memristor, and the "conventional" substance transfer mechanism based on a group of point defects that manifests itself during the memristor's degradation.

Observational constraints and cosmological implications of scalar–tensor f(R, T) gravity

ABSTRACT Recently, the scalar–tensor representation of f(R, T) gravity was used to explore gravitationally induced particle production/annihilation. Using the framework of irreversible thermodynamics of open systems in the presence of matter creation/annihilation, the physical and cosmological consequences of this setup were investigated in detail. In this paper, we test observationally the scalar–tensor representation of f(R, T) gravity in the context of the aforementioned framework, using the Hubble and Pantheon + measurements. The best fit parameters are obtained by solving numerically the modified Friedmann equations of two distinct cosmological models in scalar–tensor f(R, T) gravity, corresponding to two different choices of the potential, and by performing a Markov Chain Monte Carlo analysis. The best parameters are used to compute the cosmographic parameters, that is, the deceleration, the jerk, and the snap parameters. Using the output resulting from the Markov Chain Monte Carlo analysis, the cosmological evolution of the creation pressure and of the matter creation rates are presented for both models. To figure out the statistical significance of the studied scalar–tensor f(R, T) gravity, the Bayesian and the corrected Akaike information criteria are used. The latter indicates that the first considered model in scalar–tensor f(R, T) gravity is statistically better than ΛCDM, that is, it is more favoured by observations. Besides, a continuous particle creation process is present in Model 1. Alternatively, for large redshifts, in Model 2 the particle creation rate may become negative, thus indicating the presence of particle annihilation processes. However, both models lead to an accelerating expansion of the universe at late times, with a deceleration parameter equivalent to that of the ΛCDM model.

Performance analysis and design for an asymmetric membrane of a hollow fiber hemodiafilter with a two-layer membrane model

A hemodiafilter model including the two-layer membrane model based on the irreversible thermodynamics was first introduced, which considers the convective solute flux besides the diffusive solute one. This model makes it possible to analyze the solute transfer of an asymmetric membrane which is assumed to be equivalent to the two-layer membrane consisting of a skin layer and a porous support layer. Verification was performed with in-vitro data on commercial hemodiafilters for solutes of middle molecular weight, and the results were good in solute clearances. In order to increase the clearance of middle molecular weight solutes in high-performance membranes, it is necessary to increase the solute diffusive permeability in the support layer. Through the model simulation, the author was able to quantitatively grasp the relationship between myoglobin clearance versus membrane microstructure parameters and membrane thickness and to clarify the direction of increase in solute transfer amount. In addition, it made clear that the convective solute transfer is more predominant than the diffusive solute one in ultrafiltration effect of the hemodiafilter with the asymmetric membrane.

Effect of Stress on the Electrochemical Response of Amorphous Silicon Electrodes

Silicon electrodes for lithium-ion batteries exhibit a theoretical capacity ten times higher than that of the graphite electrodes currently used in commercial systems. When lithiated/delithiated, silicon experiences stresses on the order of one GPa, inducing the damage of the material, which results in poor cyclability. Concurrently, irreversible continuum thermodynamics predicts that these stresses affect the lithiation itself in different ways for monophasic and biphasic lithiation (progressive invasion of the electrode by a lithiated phase of given composition) [1,2]. When lithiation takes place homogeneously (without phase transformation), mechanical stresses affect lithiation through their effect on the chemical potential of diffusing lithium (Larché-Cahn theory). On the other hand, when lithiation is biphasic, mechanical stresses affect lithiation through an effect on both chemical potential of lithium and thermodynamic driving force acting on the phase boundary. This coupling has first been probed experimentally in homogeneous lithiation using a method where the stress state of silicon is modified indirectly through incremental delithiation [3].In this work, we investigate the interplay between the electrochemical state (electrode potential and current density) of an amorphous silicon electrode and its stress state. The electrochemical response of the amorphous silicon thin film deposited on a stainless steel substrate has been recorded under varying mechanical loading during lithiation and delithiation cycles. The mechanical loading is applied by deforming elastically the steel substrate of the amorphous silicon thin film, which allows us to directly probe the contribution of mechanics to the lithiation/delithiation processes. When carried out under galvanostatic conditions, incremental changes in stress lead to instantaneous change in the electrode potential. Experimental results from uniaxial tensile tests show that an applied strain of 0.3%, resulting in changes in stress in silicon of ~ 200-300 MPa, induces a potential variation on the order of 2.5 mV. Stress-induced changes in the potential are measured for the biphasic first lithiation, as well as subsequent monophasic lithiation and delithiation sequences at different states of charge. These results are discussed within the context of continuum thermodynamic theories of the coupling between transport of chemical species and mechanical stress.[1] A. F. Bower, E. Chason, P. R. Guduru, B. W. Sheldon, Acta Mater. 98 (2015) 229-241.[2] A. F. Bower, P. R. Guduru, E. Chason, Int. J. Solids Struct. 69 (2015) 328-342.[3] V. A. Sethuraman, V. Srinivasan, A. F. Bower, P. R. Guduru, J. Electrochem. Soc. 157 (2010) A1253.

A micromechanical fatigue damage model for quasi-brittle rocks subjected to triaxial compressive cyclic loads

This paper is devoted to a novel micromechanics-based damage constitutive model for describing the mechanical behavior of quasi-brittle rocks under cyclic loading considering the effects of confining pressure. The proposed model is successfully employed to simulate cyclic loading tests under various confining pressures and upper limit stresses. Inspired by previous studies that focus on time-dependent creep deformation of quasi-brittle materials, the number of cyclic loading is regarded as equivalent to time scale. In the same spirit, the scalar-valued internal damage variable used to describe the degradation of rock materials is decomposed into two parts, namely an instantaneous component due to monotonic loading, and a fatigue-related component attributed to cyclic loading. Within the framework of irreversible thermodynamics, we present a Coulomb-type friction criterion and a strain energy release rate-based damage criterion. To describe the evolution of fatigue damage, we also propose a damage criterion based on the microstructure evolution. By the use of returning mapping procedure, the constructed model is applied to simulate two representative quasi-brittle rocks, namely sandstone and argillaceous quartz siltstone, and successfully captures all significant behavior features.

Axial compression testing and constitutive model of a novel BF-reinforced ambient-cured LEGC

Ambient-cured lightweight expanded polystyrene geopolymer concrete (LEGC) currently undergoes early shrinkage cracking, and the low density of EPS causes segregation during the mixing process, resulting in a significant decrease in the strength of LEGC. To solve the above problems to obtain higher strength LEGC and promote its wide application, uniaxial compression tests and constitutive modeling studies of LEGC with different basalt fiber (BF) lengths (3 mm, 6 mm, 9 mm, 12 mm and 15 mm) reinforced with different expanded polystyrene (EPS) volume contents (10%, 20%, 30% and 40%) were conducted in this study. First, the damage pattern of the specimen was analyzed, and the crack development morphology was analyzed based on the Digital Image Correlation-3D (DIC-3D) technique. Additionally, the mechanism of BF-reinforced of LEGC was analyzed comprehensively at three levels: micromechanical theory, microscopic (scanning electron microscopy, SEM) and mesoscale (computerized tomography, CT). Empirical formulas for peak stress, peak strain, threshold stress, threshold strain and elastic modulus were established based on the stress‒strain curves of the specimens. In addition, the specific form of the damage evolution equation considering the energy dissipation of the specimen was derived from the energy balance principle and basic laws of irreversible thermodynamics based on composite damage theory. Finally, elastic‒plastic damage constitutive models established previously and in this study were compared, and the results showed that the method proposed in this study can better reflect the damage evolution of BF- reinforced LEGC.

First-order thermodynamics of scalar-tensor gravity

AbstractThe first-order thermodynamics of scalar-tensor theory is a novel approach that exploits the intriguing relationship between gravity and thermodynamics to better understand the space of gravity theories. It is based on using Eckart’s first-order irreversible thermodynamics on the effective imperfect fluid describing scalar-tensor gravity and characterises General Relativity as an equilibrium state, and scalar-tensor theories as non-equilibrium states, naturally describing the approach to equilibrium. Applications of this framework to cosmology, extensions to different classes of modified theories, and the formulation of two complementary descriptions based on the notions of temperature and chemical potential all contribute to a new and unifying picture of the landscape of gravity theories.

Thermodynamically consistent strain hardening variable/driving force, inelastic stored energy and self-heating in dynamic plasticity

Accounting for self-heating and subsequent thermal softening in dynamic plasticity requires an accurate estimation of the mechanical dissipation rate which is by definition the difference between the plastic work rate and the inelastic stored energy rate. Yet, in constitutive modeling, the evaluation of the inelastic stored energy strongly depends on the adopted approach, viz. irreversible thermodynamics vs microstructure-motivated approach, and, whatever the approach, does not yet lead to realistic results in terms of self-heating. The aim of the present study is to attempt to conciliate both above mentioned approaches by building constitutive models that relate strain hardening, inelastic stored energy and self-heating in a consistent way. The models in question are developed in agreement with experimental results obtained on five high-strength steels.

Thermodynamics, Infodynamics and Emergence

Emergence of novel processes, properties, structures, and systems is a poorly understood phenomenon. Emergence, information and energy are interrelated properties of nature: it takes free energy (energy that produces work, designed as F) to acquire information, and it takes information to increment free energy. Useful information (Φ), is the one that increases free energy, and differs from information not producing free energy or producing entropy. Energy obeys all laws of thermodynamics, while information may not. When energy and information of systems interact, novel properties or levels of energy and information may emerge. Information can reveal itself in different forms (as entropy, order, complexity, physically encoded, mechanical, biological, structural, in neural or social networks, etc.). Information may increase free energy by reducing entropy in an open system, or by capturing free energy from the surroundings. The dynamics of information and energy has been studied mostly in physical-chemistry and engineering. Now we find it everywhere, including in computer sciences, genetics, biotechnology, experimental social sciences, and experimental law. In emergent systems new possibilities of increasing free energy and useful information appear. Emergent complexity is visible in the transitions from subatomic particles to atoms, from atoms to molecules, to cells, to organisms, to societies and ecosystems. A law for irreversible thermodynamics stating that ΔF ~ ΔΦ, is evidenced empirically in all these levels of complexity, confirming that INCREASES IN USEFUL INFORMATION AND INCREMENTS IN FREE ENERGY ARE COUPLED. As free energy helps access more information, and more information produces more free energy, evolution by natural selection accumulates ever more useful information, giving birth to life. In contrast, increases in entropy decreases free energy and might affect the amount of useful information available in the system. More noise or misleading information decreases useful information which decreases free energy. These relationships help us understand the evolution of life, societies, ecosystems, and autonomous artificial life. Quantifying concomitant changes in energy and information is needed to understand the relationship between them. The endeavor to achieve this has begun (Jaffe 2023 [https://www.qeios.com/read/2VWCJG.5]).

A peridynamic model based on generalized thermoelastic theory in a plate with oblique cracks

In this paper, a peridynamic model based on generalized thermoelastic theory is derived by irreversible thermodynamics. This model avoids the spatial derivative and can be easily applied to generalized thermoelastic problems with discontinuities. The transient temperature response is captured using the non-Fourier CattaneoVernotte (C-V) model. The interaction integral is employed to calculate the transient thermal stress intensity factors (TSIFs). Numerical examples are presented for analyzing the effects of crack orientation angle and multi-crack distribution on transient thermoelastic response. And the crack propagation behavior under non-Fourier thermal shock is further discussed in detail. It is found that with the increase of the angle between inner crack and heating boundary, the sensitivity of mode-I TSIFs to the non-Fourier effect increases, while the sensitivity of mode-II TSIFs to the non-Fourier effect decreases. This peridynamic model may be useful for understanding the crack behaviors of thermal protection materials under thermal shock.

Onsager’s reciprocal relationship applied to multiphysics poromechanics

Onsager’s theory of linear irreversible thermodynamics has been successfully applied to explain findings from experiments. However, its application to multiphysics processes in deformable porous media is a non-trivial undertaking. This contribution presents an extension of Onsager’s theorem to include the flux of the matter of weakly coupled two-phase porous systems. It also relates Onsager to Ziegler’s nonlinear approach including the classical acoustic tensor criterion for localisation phenomena in such nonlinear media. The results are illustrated by Terzaghi consolidation problem using the well established modified Cam-Clay plasticity model. We show that a generalised dissipative stress can act as an appropriate thermodynamic force quantity rendering the non-associated yield envelope into Onsager’s associated form ensuring the thermodynamic condition of no-work free plastic deformation. We present in this contribution an attempt of using the theory of thermodynamics of internal state variables to develop a generic poromechanics approach that relaxes isothermal constraints for weakly coupled problems. This approach lends itself to a promising future extension of a dynamic Onsager diffusional operator for conditions where the multiphysics processes are strongly coupled in the porous system and emergent phenomena may occur.

Tension-compression asymmetric functional degeneration of super-elastic NiTi shape memory alloy: Experimental observation and multiscale constitutive model

The functional degeneration of super-elastic NiTi shape memory alloy (SMA) rods is investigated in the cyclic tension-unloading and compression-unloading experiments. The results show that the functional degeneration exhibits a strong tension–compression asymmetry, which originates from the initial 〈111〉 and 〈110〉 mixed textures along the axial direction of the rods, the polarity of martensite transformation, and the complex interaction between martensite transformation and dislocation slipping. Moreover, the dependence of functional degeneration on the applied stress level is discussed. To understand and predict the effect of initial texture on the cyclic deformation of polycrystalline NiTi SMA, a multiscale constitutive model is constructed at finite deformation. At the mesoscopic scale, two major inelastic deformation mechanisms, i.e., the transformation between austenite and martensite phases and the transformation-induced plasticity caused by the strain mismatch at the austenite–martensite interface, are considered. The total deformation gradient is multiplicatively decomposed into the martensite transformation, transformation-induced plasticity and elastic parts. The deformation gradient parts at the mesoscopic scale are obtained by upscaling these physical quantities at a smaller spatial scale (i.e., the microscopic scale). The proposed model is formulated within the framework of irreversible thermodynamics. The driving forces for martensite transformation and transformation-induced plasticity are derived according to the established Helmholtz free energy and Clausius-Duhem inequality. The complex interaction between martensite transformation and dislocation slipping, and the forward/reverse inheritance of dislocations caused by the moving austenite–martensite interfaces are considered. To calculate the overall cyclic responses of polycrystalline NiTi SMA at the macroscopic scale, the developed constitutive model is implemented into the finite element software ABAQUS/Explicit using a user-defined material subroutine. A polycrystalline representative volume element is constructed by introducing the initial 〈111〉 and 〈110〉 mixed textures observed in the experiment. By comparing the simulated results with the experimental data, the capability of the proposed model to predict the texture-induced tension–compression asymmetric functional degeneration is verified, and the influence of texture type on the cyclic deformation is discussed.

Irreversible Geometrothermodynamics of Open Systems in Modified Gravity.

In this work, we explore the formalism of the irreversible thermodynamics of open systems and the possibility of gravitationally generated particle production in modified gravity. More specifically, we consider the scalar-tensor representation of f(R,T) gravity, in which the matter energy-momentum tensor is not conserved due to a nonminimal curvature-matter coupling. In the context of the irreversible thermodynamics of open systems, this non-conservation of the energy-momentum tensor can be interpreted as an irreversible flow of energy from the gravitational sector to the matter sector, which, in general, could result in particle creation. We obtain and discuss the expressions for the particle creation rate, the creation pressure, and the entropy and temperature evolutions. Applied together with the modified field equations of scalar-tensor f(R,T) gravity, the thermodynamics of open systems lead to a generalization of the ΛCDM cosmological paradigm, in which the particle creation rate and pressure are considered effectively as components of the cosmological fluid energy-momentum tensor. Thus, generally, modified theories of gravity in which these two quantities do not vanish provide a macroscopic phenomenological description of particle production in the cosmological fluid filling the Universe and also lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy.

Thermodynamic stability analysis of non‐Fourier model‐based bio‐heat transfer in laser‐irradiated cylindrical‐shaped multilayered biological tissue

AbstractThe present research focuses on examining the thermic response of living tissue in the form of a triple‐layered cylindrical structure when subjected to laser light and the compatibility analysis of non‐Fourier heat transfer with thermodynamics second law. The temperature field in the triple‐layered cylindrical living tissue subjected to laser light is determined by numerically solving the transient radiative transfer equation in conjunction with the dual phase lag (DPL) based bioheat equation. Once the temperature field is known, the equilibrium and nonequilibrium entropy production rate (EPR) is calculated based on the hypothesis of classical irreversible thermodynamics and extended irreversible thermodynamics, respectively. The present results are verified against the data from the literature and found a good match between them. A comparative analysis of the Fourier and non‐Fourier models is accomplished. The equilibrium and nonequilibrium EPR values for the Fourier model are found to be positive. While the equilibrium EPR is negative for non‐Fourier heat conduction and does not satisfy the thermodynamics second law, nonequilibrium EPR is always a positive value for Fourier, DPL, and hyperbolic models and satisfies thermodynamics second law. It has been investigated how thermal relaxation times affect the temperature field and EPRs in tissue are subjected to laser light.

Relating the artificial chemotaxis of catalysts to a gradient descent of the free energy.

Recent experiments suggest that mesoscale catalysts are active materials that power their motion with chemical free energy from their environment and also "chemotax" with respect to substrate gradients. In the present work, we explore a thermodynamic framework for relating this chemotaxis to the evolution of a system down the gradient of its free energy. This framework builds upon recent studies that have employed the Wasserstein metric to describe diffusive processes within the Onsager formalism for irreversible thermodynamics. In this work, we modify the Onsager dissipation potential to explicitly couple the reactive flux to the diffusive flux of catalysts. The corresponding gradient flow is a modified reaction-diffusion equation with an advective term that propels the chemotaxis of catalysts with the free energy released by chemical reactions. In order to gain first insights into this framework, we numerically simulate a simplified model for spherical catalysts undergoing artificial chemotaxis in one dimension. These simulations investigate the thermodynamic forces and fluxes that drive this chemotaxis, as well as the resulting dissipation of free energy. Additionally, they demonstrate that chemotaxis can delay the relaxation to equilibrium and, equivalently, prolong the duration of nonequilibrium conditions. Although future simulations should consider a more realistic coupling between reactive and diffusive fluxes, this work may provide insight into the thermodynamics of artificial chemotaxis. More generally, we hope that this work may bring attention to the importance of the Wasserstein metric for relating nonequilibrium relaxation to the thermodynamic free energy and to large deviation principles.

Overpotential from Cosolvent Imbalance in Battery Electrolytes: LiPF6 in EMC:EC.

Most liquid lithium-ion-battery electrolytes incorporate cosolvent blends, but the dominant electrochemical transport models adopt a single-solvent approximation, which assumes in part that nonuniform cosolvent ratios do not affect cell voltage. For the popular electrolyte formulation based on ethyl-methyl carbonate (EMC), ethylene carbonate (EC), and LiPF6, we perform measurements with fixed-reference concentration cells, finding appreciable liquid-junction potentials when only the cosolvent ratio is polarized. A previously reported junction-potential correlation for EMC:LiPF6 is extended to cover much of the ternary composition space. We propose a transport model for EMC:EC:LiPF6 solutions grounded in irreversible thermodynamics. Thermodynamic factors and transference numbers are entwined in liquid-junction potentials, but concentration-cell measurements determine observable material properties we call junction coefficients, which appear in the extended form of Ohm's law that accounts for how composition changes induce voltage drops. Junction coefficients of EC and LiPF6 are reported and illustrate the extent to which ionic current induces solvent migration.

A new hydro-mechanical coupling constitutive model for brittle rocks considering initial compaction, hardening and softening behaviors under complex stress states

After the excavation of underground engineering, the failure and instability of surrounding rock under hydro-mechanical coupling conditions is a common type of engineering disaster. However, the hydro-mechanical coupling mechanical characteristics of rock have not been fully revealed, and suitable models for the stability analysis of surrounding rock under hydro-mechanical coupling conditions are very scarce. Therefore, a series of triaxial compression and cyclic loading and unloading hydro-mechanical coupling tests were carried out to study the mechanical characteristics, deformation and mechanical parameters of rock under different confining pressures and pore pressures. Then, based on Biot’s effective stress principle, a hydro-mechanical coupling damage constitutive model within the framework of irreversible thermodynamics was proposed to describe the initial compaction effect, pre-peak hardening and post-peak softening behaviors. The functional relationships between the proposed model key parameters (η and ζ) and the effective stress were established to characterize the pre- and post-peak nonlinear behaviors of rock. A compaction function Ck for the evolution of the undamaged Young’s modulus in initial compaction stage was introduced to characterize the pre-peak compaction effect. A user-defined material subroutine (UMAT) was compiled in ABAQUS to numerically implemented the proposed model. The numerical simulation results are highly consistent with the test results, the proposed model can also predict the hydro-mechanical coupling characteristics of rock under untested stress levels. In addition, the yield function of the proposed model considers the influence of intermediate principal stress, which is also suitable for the simulation of hydro-mechanical coupling characteristics under true triaxial stress states.Graphical abstract

Modeling energy consumption inside cutting deformation zone to predict the stress distributions, temperature and microstructure by micro irreversible entropic thermodynamics

It is important to analyze the process of chip formation by means of the energy consumption during metal cutting, which is related to the cutting power (or cutting force), the cutting temperature and the machined surface integrity. In this study, the consumed energy field inside the cutting deformation zone is established by considering four micro irreversible processes including the dislocation generation, annihilation, movement, and continuous dynamic recrystallization. A new shear-angle solution is proposed on the basis of the steady conditions of irreversible processes (i.e., the entropy production rate reaches the minimum), whose adequacy is verified by the experimental results of the shear angle and friction coefficient along the tool-chip interface. Based on the predicted consumed energy field inside the cutting deformation zone, the deformation mechanism, microstructure, stress and temperature are predicted and analyzed. The results show that three stages including the loading stage, unloading stage and steady stage are divided during chip formation according to the consumed energy field. The consumed energy and statistically stored dislocation density are both of gradient distribution in the primary shear zone, and continuous dynamic recrystallization is the main mechanism of grain refinement during chip formation, which is dominated in the secondary deformation zone. The stress and temperature inside the cutting deformation zone as well as the hardness of the machined surface are predicted according to the energy balance relationship and consumed energy field, indicating the feasibility of using energy consumption to comprehensively describe the internal changes of workpiece material inside the cutting deformation zone.

Concepts of phenomenological irreversible quantum thermodynamics II: time dependent statistical ensembles of bipartite systems

Abstract The wide-spread opinion is that original quantum mechanics is a reversible theory, but this statement is only true for undecomposed systems that are those systems for which sub-systems are out of consideration. Taking sub-systems into account, as it is by definition necessary for decomposed systems, the interaction Hamiltonians –which are absent in undecomposed systems– can be a source of irreversibility in decomposed systems. Thus, the following two-stage task arises: How to modify von Neumann’s equation of undecomposed systems so that irreversibility appears, and how this modification affects decomposed systems? The first step was already done in Muschik (“Concepts of phenomenological irreversible quantum thermodynamics: closed undecomposed Schottky systems in semi-classical description,” J. Non-Equilibrium Thermodyn., vol. 44, pp. 1–13, 2019) and is repeated below, whereas the second step to formulate a quantum thermodynamics of decomposed systems is performed here by modifying the von Neumann equations of the sub-systems by a procedure wich is similar to that of Lindblad’s equation (G. Lindblad, “On the generators of quantum dynamical semigroups,” Commun. Math. Phys., vol. 48, p. 119130, 1976), but different because the sub-systems interact with one another through partitions.

A nonlinear constitutive model for whole stress–strain behaviors of compressed rocks incorporating crack closure effect

AbstractThis paper is devoted to establishing a nonlinear constitutive model incorporating crack closure effect for capturing the whole process of rock deformation and failure behavior under compression. The model formulated in the framework of irreversible thermodynamics is based on the additive decomposition of the total strain into crack closure strain, elastic, and plastic parts. New specific criteria are proposed for the description of crack closure strain and plastic strain evolution. Notably, analytical solutions of the model under conventional triaxial compression loading conditions are derived. For application, a robust semi‐implicit return mapping (SRM) algorithm with a crack closure strain correction and a plastic strain correction is developed. The analytical solutions, herein, are subtly used to calibrate model parameters and as reference results for assessing the accuracy and robustness of the SRM algorithm. Validation of the model conducted by comparing with experimental data from the literature shows that the model can properly describe the nonlinear mechanical behaviors of rocks, including crack closure effect, strain hardening/softening, peak and residual strength, as well as volumetric compaction/dilation transition. In addition, a nonlocal formulation is introduced as an extension of the model to remedy the mesh dependency problem.