Conjugate Forces Research Articles

Study on migration behavior and mechanism of strong carcinogenic PAHs in oil to fume during frying using stable isotope method

The migration and distribution of four strong carcinogenic polycyclic aromatic hydrocarbons (PAH4) in oil to fume during frying were characterized by the stable isotope-labeled PAH4-d12. The results indicated that PAH4-d12 mainly migrated to heterogeneous oil fume, and their mobilities increased significantly with the increase in heating time and frying temperature, which were 0.48−1.08%, 0.96−1.21%, and 2.98−3.60% at 160, 180, and 200 °C, respectively. The established linear models proved that PAH4-d12 migrated through the carrying of heterogeneous fume, and the carrying ability of fume produced at 200 °C was significantly stronger than at 160 and 180 °C. For morphology, ultrafine fume (<1 μm) at 200 °C had the most emission and the strongest carrying ability for PAH4-d12. For components, the heterogeneous fume produced at 200 °C contained more unsaturated fatty acids and conjugated heterocyclic compounds, which could bind with PAH4-d12 in electrostatic force and π-π conjugate force for migration. This study explained the potential mechanism of oil fume components binding to PAH4 from molecular interaction.

On the development of a constitutive model for steel subjected to fire and explosion

The behavior of steel under thermal and mechanical loading including high transient temperatures and strain rates (e.g., fire, creep or explosion) is extremely complex. To study this behavior, we propose a constitutive model accordance with the laws of thermodynamic, the principle of virtual power and experimental results. The thermodynamic framework considers the Clausius-Duhem inequality and maximum dissipation rate principle, as well as the theory of finite deformations, linear isotropic viscoelasticity, nonlinear isotropic and kinematic hardening, local and non-local viscoplasticity, local and non-local anisotropic viscodamage and parameters associated to material behavior dependent on loadings. The components of the thermodynamic conjugate forces are defined from the Helmholtz free energy function and the rate of energy dissipation, which are postulated considering the creep phenomenon, thermal-mechanical transient phenomenon, cyclic phenomenon and plastic wave propagation phenomenon. The balance of microforces is defined based on the principle of virtual power. A novel rule of non-associated thermo-viscoplastic flow of the Perzyna type and a novel rate dependent local and non-local damage evolution law are introduced from constitutive model. The verification of the model was carried out in two benchmark studies composed of fire tests. The predictions of the model have shown in according with the results of the experiments. A sensitivity study was also performed with a view to analysis the influence of the parameters in achieved results. From this study a simplified constitutive model is presented. Benchmark studies composed of explosion tests are part of future work.

Multi-stress damage and healing mechanics in quasi-brittle materials: Theoretical overview

This work introduces a theoretical framework for continuum damage and healing mechanics by extending stress decomposition to account for tensile, compressive, and shear stresses. In addition to the spectral stress decomposition into tensile and compressive components, we extend the existing stress decomposition method to address shear stresses. The extraction of shear stresses employs two hypotheses, considering both same-signed and opposite-signed principal stresses. This stress decomposition approach yields three damage variables [Formula: see text] and three healing variables [Formula: see text]. The damage formulation is discussed in terms of equivalent strain and conjugate force, while the healing formulation is based on the initial damage state and healing time. We explore the influence of material parameters and healing time on damage and healing evolution. Furthermore, we analyze the relationship between nominal stress-to-effective stress ratio, damage variables, and healing time. Lastly, we present a thermodynamically consistent formulation for damage-healing processes, acknowledging that this work establishes a theoretical formulation. The proposed method is validated by analyzing the performance of an L-shaped concrete specimen using three damage variables and one healing variable. These results illustrate the model's ability to effectively capture the damage and healing phenomena. The practical implementation of the proposed formulation will be pursued numerically using innovative healing techniques and a pseudo-damage healing approach, which will be detailed in future work.

A Pre-peak Elastoplastic Damage Model of Gosford Sandstone Based on Acoustic Emission and Ultrasonic Wave Measurement

The determination of internal material damage is always an arduous challenge. Non-destructive monitoring methods show great potential in quantitatively determining the internal material properties, whereas most of the studies relying on external observations remain in a qualitative stage. They either violate the basic thermodynamic assumptions or are difficult to guide engineering practice. In this paper, following the theory of continuum mechanics, an elastoplastic damage model based on non-destructive monitoring methods (i.e., acoustic emission and ultrasonic wave velocity measurement) has been developed. To capture the continuous and precise damage evolution inside rock mass, P wave velocity obtained by ultrasonic wave measurement was utilised and then considered as an input for the proposed elastoplastic damage model. Triaxial loading test results on six Gosford sandstone samples were analysed first to characterise critical stresses along the stress–strain loading curves, such as crack closure stress, stable crack propagation stress and unstable crack propagation stress. The drop of ultrasonic wave velocity can be seen as an indicator to represent the damage evolution inside rock material. Damage initiation is also closely related to the confining stress and dilation induced volumetric expansion. The test results also suggested that the Drucker–Prager criterion is sufficient to describe the plastic yielding surface and the following material hardening. A non-associated plastic flow assumption was adopted, considering the essence of microcrack shearing in rock failure and the effect of hydrostatic pressure on plastic deformation. A modified Drucker–Prager plastic potential was also introduced to track the orientation of plastic increment with material hardening. A scalar damage variable was derived from ultrasonic wave measurement results to indirectly represent the deterioration of rock properties (modulus). The proposed model was used to match lab test results with high consistency, and the main features of rock behaviour in triaxial loading tests were successfully captured by the model. Finally, the damage evolution of rock samples was analysed, which indicates that damage is dependent on its conjugate force, namely damage energy release rate Y. This study proves that P wave velocity can be an effective approach to measure and forecast the internal damage evolution inside rock mass, which has broad prospects for engineering applications.

Non-equilibrium process of transfer of momentum in medium with relaxation microstructure

The non-equilibrium process of transfer of the momentum of polymer media with an evolving nonequilibrium relaxation microstructure is considered. For the basic conditions of deformation, the regularities for the structural and dynamic components of the stress tensor with conjugate forces are obtained and analyzed, which are consistent with experiment.

Time-Independent Plasticity Formulated by Inelastic Differential of Free Energy Function

Abstract The authors presented a time-independent plasticity approach, where a typical plastic-loading process is viewed as an infinitesimal state change of two neighboring equilibrium states, and the yield and consistency conditions are formulated based on the conjugate forces of the internal variables. In this paper, a stability condition is proposed, and the yield, consistency, and stability conditions are reformatted by the inelastic differential form of the Gibbs free energy. The Gibbs equation in thermodynamics with internal variables is a representation to the differential form of the Gibbs free energy by a single Gibbs free energy function. In this paper, we propose the so-called extended Gibbs equation, where the differential form may be represented by multiple potential functions. Various associated and nonassociated plasticity with a single or multiple yield functions can be derived from various representations based on the reformulated approach, where yield and plastic potential functions are in the form of inelastic differentials of the potential functions. The generalized Drucker inequality can only be derived from the one-potential representation as a stability condition. For a multiple-potential representation, the stability condition can be ensured if the multiple potentials are concave functions and possess the same stationary point.

Nonlocal phase field approach for modeling damage in brittle materials

In this work, we present a nonlocal phase field model for damage in brittle materials. We define a non-conservative order parameter for representing the damage. The Helmholtz free energy functional of the Ginzburg-Landau type that incorporates a new degradation function for the elastic strain energy is considered. The hypothesis of strain equivalence and strain energy equivalence from continuum damage mechanics are adopted to predict the evolution of damage. A conjugate force to damage is derived for both these hypothesis to arrive at a damage criterion. The strong interrelation between phase field models and gradient damage models has been brought out. The solution of the nonlinear system of coupled equation is achieved by a change in the modified Arc-length method and considering a staggered approach. In this approach a linearization of the Crisfield Arc-length quadratic equation for calculation of load increment factor results in an unique root. Numerical examples are presented to demonstrate the usefulness of the proposed damage model.

Internal Variable Theory Formulated by One Extended Potential Function

Abstract In the kinetic rate laws of internal variables, it is usually assumed that the rates of internal variables depend on the conjugate forces of the internal variables and the state variables. The dependence on the conjugate force has been fully addressed around flow potential functions. The kinetic rate laws can be formulated with two potential functions, the free energy function and the flow potential function. The dependence on the state variables has not been well addressed. Motivated by the previous study on the asymptotic stability of the internal variable theory by J. R. Rice, the thermodynamic significance of the dependence on the state variables is addressed in this paper. It is shown in this paper that the kinetic rate laws can be formulated by one extended potential function defined in an extended state space if the rates of internal variables do not depend explicitly on the internal variables. The extended state space is spanned by the state variables and the rate of internal variables. Furthermore, if the rates of internal variables do not depend explicitly on state variables, an extended Gibbs equation can be established based on the extended potential function, from which all constitutive equations can be recovered. This work may be considered as a certain Lagrangian formulation of the internal variable theory.

Removal of the environmental pollutant carbamazepine using molecular imprinted adsorbents: Molecular simulation, adsorption properties, and mechanisms

Carbamazepine (CBZ) is a typical pharmaceutical residue commonly found in aqueous environments, but its removal through activated carbon or advanced oxidation processes is often disrupted by co-existing organic matter. An imprinting system which consisted of the target pollutant CBZ (template molecule) and 10 different kinds of functional monomers was constructed via molecular simulation to screen for appropriate monomers, thereby addressing CBZ removal disruptions. An annealing method simulation was used to search for stable, low-energy conformations of the template-monomer interaction system to calculate the binding energy of these different monomers with CBZ. The order of binding affinity calculated was: 4-vinylbenzoic acid > itaconic acid > methacrylic acid, which was consistent with the experimental observations. The adsorption capacity of the molecular imprinted polymer (MIP) prepared using 4-vinylbenzoic acid reached 28.40 mg/g, and the imprinting factor reached 2.72. The simulation and measurement of the ultraviolet spectrum of the imprinting system showed that a new interaction system was formed between the template and monomers, and that multiple binding conformations between them took place when specific recognition occurred. Energy calculation and hydrogen bond analysis revealed that the van der Waals force, including the π-π conjugate and electrostatic forces including hydrogen bonding, played an important role during selective adsorption, which was confirmed by infrared spectroscopy analysis.

Non-isothermal Transport of Multi-phase Fluids in Porous Media. The Entropy Production

We derive the entropy production for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in pressure, temperature, and chemical potentials. Thermodynamic extensive variables on the macro-scale are obtained by integrating over a representative elementary volume (REV). Using Euler homogeneity of the first order, we obtain the Gibbs equation for the REV. From this we define the intensive variables, the temperature, pressure and chemical potentials and, using the balance equations, derive the entropy production for the REV. The entropy production defines sets of independent conjugate thermodynamic fluxes and forces in the standard way. The transport of two-phase flow of immiscible components is used to illustrate the equations.

Steepest-entropy-ascent model of mesoscopic quantum systems far from equilibrium along with generalized thermodynamic definitions of measurement and reservoir

This paper presents a nonequilibrium, first-principles, thermodynamic-ensemble based model for the relaxation process of interacting non-equilibrium systems. This model is formulated using steepest-entropy-ascent quantum thermodynamics (SEAQT) and its equation of motion for a grand canonical ensemble and is applied to a many particle system of classical or indistinguishable particles. Two kinds of interactions are discussed, including pure heat diffusion and heat and mass diffusion together. Since no local equilibrium assumption is made, the conjugate fluxes and forces are intrinsic to the subspaces of the state space of one system and/or of the state space of the two interacting systems. They are derived via the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the nonmutual equilibrium status between subspaces of the thermodynamic state space of a single system and/or of the state space of the two interacting systems. The Onsager relations are shown to be thermodynamic kinematic features of the system and are found without knowledge of the detailed mechanics of the dynamic process. A fundamental thermodynamic explanation for the measurement of each intensive property of a system in a nonequilibrium state is given. The fundamental thermodynamic definition of reservoir is also discussed. Finally, the equation of motion for a system undergoing multiple interactions is provided, which permits the modeling of a network of local systems in nonequilibrium at any spatial and temporal scale.

A thermodynamically consistent framework to derive local/nonlocal generalized nonassociative plasticity/viscoplasticity theories

We present a rigorous and consistent thermodynamic-based approach to derive generalized nonassociative rate-independent and rate-dependent plasticity theories. It is demonstrated that the nonassociative plasticity theories are a straightforward consequence of the principle of virtual power. Besides, the relationship between the plastic potential function and yield function is established on the basis of the principle of virtual power. All thermodynamic conjugate forces are decomposed into two parts referred to as the energetic and dissipative components. The energetic part is derived from the Helmholtz free energy while the dissipative component is derived from the rate of the dissipated energy by postulating the principle of maximum dissipation. It is also shown that the nonlocality energy residual, arising from plastic strain gradients, has two components: namely, the energetic nonlocality energy residual, which is stored at the interfaces; and the dissipative nonlocality energy residual, which is dissipated through the interfaces. Finally, several examples are provided focusing on the derivation of associative/nonassociative local/nonlocal plasticity and viscoplasticity models based on the presented thermodynamic framework.

Canonical Structure and Orthogonality of Forces and Currents in Irreversible Markov Chains

We discuss a canonical structure that provides a unifying description of dynamical large deviations for irreversible finite state Markov chains (continuous time), Onsager theory, and Macroscopic Fluctuation Theory (MFT). For Markov chains, this theory involves a non-linear relation between probability currents and their conjugate forces. Within this framework, we show how the forces can be split into two components, which are orthogonal to each other, in a generalised sense. This splitting allows a decomposition of the pathwise rate function into three terms, which have physical interpretations in terms of dissipation and convergence to equilibrium. Similar decompositions hold for rate functions at level 2 and level 2.5. These results clarify how bounds on entropy production and fluctuation theorems emerge from the underlying dynamical rules. We discuss how these results for Markov chains are related to similar structures within MFT, which describes hydrodynamic limits of such microscopic models.

A consistent UVLWT formulation for laminated plane frame analysis considering semi-rigid connections

In this work we present a generalization of a finite element formulation, based on the new Unconstrained Vector Layerwise Theory (UVLWT), that allows a geometrically exact description of 2D laminated plane frames with accurate stress distribution. The formulation presents a natural and easy extension for 3D applications. The proposed generalization is based on a penalty strategy to couple frames at corners in a very accurate and elegant way. It consists on the introduction of rigid, semi-rigid and hinged connections among elements, for which all degrees of freedom of each lamina are considered and their energetically conjugate forces calculated. Flexible supports of the structure regarding the static reference have also been successfully developed and implemented.Although two-dimensional frames are the main object of this study, three-dimensional connection expressions are developed in order to promote future developments and insights. In order to have complete solutions, even when a snap-back or snap-trough occur, we present the arc-length approach adapted to the complete analysis of 2D frames by the UVLWT.From the analyzed examples, we can state that the UVLWT formulation and the developed connections presents the following capabilities:(i) geometric nonlinear modeling of laminated 2D frames assembled by slender or thick bars, without presenting problems of locking and system of equations bad conditioning; (ii) geometrically exact modeling of curved bars; (iii) consistent modeling of general flexible or rigid internal corner connections; (iv) consistent modeling of elastic external supports; (v) Zig-Zag effect consideration with accurate transverse stress distribution and (vi) straightforward extension for 3D applications as the finite rotation concept is not used.

A nonlocal continuum damage model for brittle fracture

The objective of this paper is to develop a nonlocal continuum damage model for brittle fracture. A nonlocal damage conjugate force tensor is obtained from the “local” one, using an integral-type regularization technique, and the thermodynamic equations are formulated in a nonlocally generalized standard manner. A nonlocal damage model is developed based on a recently developed “local” model, which can rigorously handle damage anisotropy, distinct tensile and compressive damage behavior, and damage deactivation, so that the nonlocal model not only handles brittle fracture well but also possesses the advantageous features of the “local” model. A fully explicit integration scheme for the present model is developed and then implemented in Abaqus/Explicit via VUMAT. The present model is validated through: 1. simulating cyclic uniaxial tests on a SiC–SiC woven composite; 2. calibrating its associated material parameters via single edge notched bend (SENB) tests on concrete beams. Its versatility is demonstrated through simulating a mixed-mode fracture test on a double edge notched (DEN) specimen. It is found to be capable of producing realistic fracture paths and capturing size effects in real materials. A wide variety of mechanical behavior can be incorporated into the present model in the future.

Fluctuation-Dissipation Relations Far from Equilibrium.

Near equilibrium, where all currents of a system vanish on average, the fluctuation-dissipation relation (FDR) connects a current's spontaneous fluctuations with its response to perturbations of the conjugate thermodynamic force. Out of equilibrium, fluctuation-response relations generally involve additional nondissipative contributions. Here, in the framework of stochastic thermodynamics, we show that an equilibriumlike FDR holds for internally equilibrated currents, if the perturbing conjugate force only affects the microscopic transitions that contribute to the current. We discuss the physical requirements for the validity of our result and apply it to nanosized electronic devices.

Generalized thermodynamic relations for a system experiencing heat and mass diffusion in the far-from-equilibrium realm based on steepest entropy ascent.

This paper presents a nonequilibrium thermodynamic model for the relaxation of a local, isolated system in nonequilibrium using the principle of steepest entropy ascent (SEA), which can be expressed as a variational principle in thermodynamic state space. The model is able to arrive at the Onsager relations for such a system. Since no assumption of local equilibrium is made, the conjugate fluxes and forces are intrinsic to the subspaces of the system's state space and are defined using the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the nonmutual equilibrium status between subspaces of the thermodynamic state space. The Onsager relations are shown to be a thermodynamic kinematic feature of the system independent of the specific details of the micromechanical dynamics. Two kinds of relaxation processes are studied with different constraints (i.e., conservation laws) corresponding to heat and mass diffusion. Linear behavior in the near-equilibrium region as well as nonlinear behavior in the far-from-equilibrium region are discussed. Thermodynamic relations in the equilibrium and near-equilibrium realm, including the Gibbs relation, the Clausius inequality, and the Onsager relations, are generalized to the far-from-equilibrium realm. The variational principle in the space spanned by the intrinsic conjugate fluxes and forces is expressed via the quadratic dissipation potential. As an application, the model is applied to the heat and mass diffusion of a system represented by a single-particle ensemble, which can also be applied to a simple system of many particles. Phenomenological transport coefficients are also derived in the near-equilibrium realm.

A thermodynamic framework for constitutive modeling of coupled moisture-mechanical induced damage in partially saturated viscous porous media

A general thermodynamic-based framework is proposed to derive coupled moisture-mechanical induced damage constitutive relationships for multi-phase viscoelastic porous media. The well-known (Kachanov, 1958) effective (undamaged) configuration and the concept of effective stress space are extended to moisture-susceptible materials to couple the detrimental effects of moisture to the mechanical response of materials. A physically-based moisture-induced damage internal state variable is introduced within the proposed framework to account for the moisture aggravation effect, and to couple moisture-induced damage with mechanical responses. The principle of virtual power, Clausius–Duhem inequality and maximum rate of energy dissipation are constructed for multi-phase porous media. These principles are used to obtain the main macroscopic and microscopic balance laws, the general framework, and the constitutive relationships. The thermodynamic conjugate forces are decomposed into energetic and dissipative components, obtained from Helmholtz free energy and the rate of energy dissipation, to accurately estimate the rate of energy dissipation. The proposed thermodynamic framework is used to develop a comprehensive viscoelastic model, which takes into account the effect of pore water pressure, a constitutive relationship to model the detrimental effect of moisture diffusion inside the solid phase, Darcy’s law, Fick’s second law and, the Fourier heat conduction equation. The resulting constitutive relationships describe the coupled effects of mechanical loading and moisture-induced damage and accurately predict the response of partially saturated viscous porous media under various mechanical loading and environmental conditions.

Parameter estimation of an anisotropic damage model for concrete using genetic algorithms

This article presents an anisotropic damage model for concrete that couples between elasticity and continuum damage mechanics. The formulation of constitutive model is based on the elastic strain energy in the framework of irreversible thermodynamics. The thermodynamic free energy is represented as a scalar function of elastic strain and damage tensors and used to derive the constitutive law and thermodynamic conjugate force of damage that is used to derive the dissipation potential. The damage evolution law is governed by the normality rule. The formulation of elastic strain energy of damaged material is capable of modeling the concrete anisotropic behavior under different loadings without decoupling the stress or damage release rate. A series of unknown parameters in the model formulation was used to control the constitutive behavior and damage surface. A Genetic algorithm FORTRAN subroutine is used to estimate these parameters based on the coupling between the constitutive and damage evolution equations. The performance of the damage model is verified with the experimental data from the literature. The model has shown a good agreement with the experimental results. It describes the anisotropy induced by the crack development within the concrete.

Continuum damage-healing constitutive modeling for concrete materials through stress spectral decomposition

Self-healing concrete materials have the capability to recover a part of the weakened mechanical properties induced by damage. In this paper, a constitutive model is proposed to investigate damage and healing phenomena in concrete materials. In order to consider the different behavior of concretes in tension and compression, a spectral decomposition of the stress is utilized. In addition, employing the Clausius–Duhem inequality and considering the irreversible thermodynamics, conjugate forces of the damage and healing are expressed. The Gibbs potential energy is decomposed into three parts: elastic, damage and healing. In this regard, damage and healing behavior are distinguished from the elastic behavior via the damage and healing surfaces [Formula: see text]. Evolution equations of damage and healing variables are proposed based on these surfaces. Validity of the proposed model is shown in uniaxial tension and compression loading conditions compared to the experimental data available in the literature. Finally, parametric studies are applied on the healing parameters to show the response of the self-healing concrete materials in tension and compression.