Consistent Thermodynamic Framework Research Articles

Thermodynamically-consistent constitutive modeling of moisture- and thermo-responsive shape memory polymers

Abstract Taking into account that shape memory polymer (SMP)-based devices are often subject to multiple environmental conditions during application, it is difficult to accurately predict their shape memory effect (SME). Thus, constitutive modeling for SMPs in multi-field environments is of great importance. However, most of the models available are limited to describing the temperature-driven SME and do not refer to multi-field conditions. In this paper, a constitutive model for SMPs in hygrothermal environments is developed under a consistent thermodynamic framework. The derivation is based on an additive decomposition of the Helmholtz free energy density and satisfying the first law and second law of thermodynamics. In this paper, the absorbed moisture is categorized into free and bound phases and it is considered that they have different effects on the material properties. Accordingly, it is the first time to study the variation of configurational entropy with different phases in the polymer–moisture system during the moisture diffusion process. For the first time, the validity of the constitutive model proposed in this paper can be confirmed by systematically comparing the modeling results and experimental data of various types of hygrothermal-induced shape memory cycles.

Tsallis Distribution as a Λ-Deformation of the Maxwell-Jüttner Distribution.

Currently, there is no widely accepted consensus regarding a consistent thermodynamic framework within the special relativity paradigm. However, by postulating that the inverse temperature 4-vector, denoted as β, is future-directed and time-like, intriguing insights emerge. Specifically, it is demonstrated that the q-dependent Tsallis distribution can be conceptualized as a de Sitterian deformation of the relativistic Maxwell-Jüttner distribution. In this context, the curvature of the de Sitter space-time is characterized by Λ/3, where Λ represents the cosmological constant within the ΛCDM standard model for cosmology. For a simple gas composed of particles with proper mass m, and within the framework of quantum statistical de Sitterian considerations, the Tsallis parameter q exhibits a dependence on the cosmological constant given by q=1+ℓcΛ/n, where ℓc=ℏ/mc is the Compton length of the particle and n is a positive numerical factor, the determination of which awaits observational confirmation. This formulation establishes a novel connection between the Tsallis distribution, quantum statistics, and the cosmological constant, shedding light on the intricate interplay between relativistic thermodynamics and fundamental cosmological parameters.

Equation of state for confined fluids.

Fluids confined in small volumes behave differently than fluids in bulk systems. For bulk systems, a compact summary of the system's thermodynamic properties is provided by equations of state. However, there is currently a lack of successful methods to predict the thermodynamic properties of confined fluids by use of equations of state, since their thermodynamic state depends on additional parameters introduced by the enclosing surface. In this work, we present a consistent thermodynamic framework that represents an equation of state for pure, confined fluids. The total system is decomposed into a bulk phase in equilibrium with a surface phase. The equation of state is based on an existing, accurate description of the bulk fluid and uses Gibbs' framework for surface excess properties to consistently incorporate contributions from the surface. We apply the equation of state to a Lennard-Jones spline fluid confined by a spherical surface with a Weeks-Chandler-Andersen wall-potential. The pressure and internal energy predicted from the equation of state are in good agreement with the properties obtained directly from molecular dynamics simulations. We find that when the location of the dividing surface is chosen appropriately, the properties of highly curved surfaces can be predicted from those of a planar surface. The choice of the dividing surface affects the magnitude of the surface excess properties and its curvature dependence, but the properties of the total system remain unchanged. The framework can predict the properties of confined systems with a wide range of geometries, sizes, interparticle interactions, and wall-particle interactions, and it is independent of ensemble. A targeted area of use is the prediction of thermodynamic properties in porous media, for which a possible application of the framework is elaborated.

Active engines: Thermodynamics moves forward

The study of thermal heat engines was pivotal to establishing the principles of equilibrium thermodynamics, with implications far wider than only engine optimization. For nonequilibrium systems, which by definition dissipate energy even at rest, how to best convert such dissipation into useful work is still largely an outstanding question, with similar potential to illuminate general physical principles. We review recent theoretical progress in studying the performances of engines operating with active matter, where particles are driven by individual self-propulsion. We distinguish two main classes, either autonomous engines exploiting a particle current, or cyclic engines applying periodic transformation to the system, and present the strategies put forward so far for optimization. We delineate the limitations of previous studies, and propose some future perspectives, with a view to building a consistent thermodynamic framework far from equilibrium.

A Dynamic Finite-Deformation Constitutive Model for Steels Undergoing Slip, Twinning, and Phase Changes

Depending on composition, processing, microstructure, and loading mode, steels may demonstrate various inelastic deformation mechanisms, notably dislocation glide, deformation twinning, and solid-solid phase changes. Damage in the form of voids, often leading to failure by macro-cracking, is also of current interest. A finite-deformation constitutive model is constructed in order to address such mechanisms in isotropic polycrystals under static and dynamic loading, where the latter encompasses high pressures and extreme strain rates pertinent to ballistic penetration. Slip and twinning are isochoric, and their relative contributions to kinematics are not explicitly distinguished in the present application. Phase changes among, e.g., face-centered-cubic (FCC), body-centered-cubic (BCC), body-centered-tetragonal (BCT), and hexagonal (HCP) structures are admitted, with corresponding deviatoric and volumetric strains. Porosity from voids contributes to volumetric strain. A new consistent thermodynamic framework incorporating an Eulerian strain tensor and internal state variables is developed, whereby kinetic equations for slip–twinning, phase changes, and damage evolution result in contributions to dissipation. An objective rate form of the model, derived assuming small deviatoric elastic strain, is implemented numerically. The model is applied to three different primarily austenitic, medium-high Mn steels. Specifically, representations of a slip-dominated (SLIP), a TRIP (transformation-induced plasticity) and a TWIP (twinning-induced plasticity) steel are calibrated to quasi-static tension, quasi-static compression, and dynamic compression data, at both room and high temperatures. A novel functional form of material strength distinguishes hardening profiles of the different alloys. Experimental data are reasonably well represented. Model extrapolations for dynamic strength and pressure in regimes pertinent to shock compression are analyzed. Predictions for multi-axial loading of shear with simultaneous expansion or contraction demonstrate competing physical mechanisms among the alloys that could be leveraged for optimal ballistic performance.

Thermodynamic Discrimination between Energy Sources for Chemical Reactions

Summary Chemical transformations traverse large energy differences, yet the comparison of energy sources to drive a reaction is often done on a case-by-case basis; there is no fundamentally driven, universal framework with which to analyze and compare driving forces for chemical reactions. In this work, we present a reaction-independent expression for the equilibrium constant as a function of temperature, pressure, and voltage. With a specific set of axes, all reactions are represented by a single ( x , y ) point, and a quantitative divide between electrochemically and thermochemically driven reactions is visually evident. Additionally, we show that our expression has a strong physical basis in work and energy fluxes to the system, although specific data about operating conditions are necessary to provide a quantitative energy analysis. Overall, this universal equation and facile visualization of chemical reactions provides a consistent thermodynamic framework for comparing electrochemical versus thermochemical energy sources without knowledge of detailed process parameters.

High Temperature Oxidation Modeling

One of the most demanding properties for reliable high temperature structural materials is oxidation resistance. The transition from internal to external oxidation is often a basis for alloy design to slow down the oxidation process. While lots of experimental efforts have been devoted to investigating the transition, there is still a significant gap in understanding the relevant mechanisms. This can be partly attributed to a lack of physics-based modeling capabilities due to the difficulty in constructing a coherent and consistent thermodynamic framework for oxidation modeling in multi-component alloy systems and the complexity of the interplay among the various governing factors for oxidation – a rich topic for Integrated Computational Materials Engineering. To bridge this gap, one of the tasks in the on-going XMAT project sponsored by US-DOE that involves 7 National Laboratories is to develop a phase-field modeling capability for an alloy system where the oxidation transition can be simulated. In this presentation, we will describe a phase-field model for a ternary prototype system where competition of a faster-growing oxide and a thermodynamically-more-stable oxide can be considered. The model captures the oxidation reactions at the surface and in the bulk, as well as the interdiffusion of oxygen and other elements. The application of this model to investigate internal to external oxidation transition will be discussed.

A multi-field model for charging and discharging of lithium-ion battery electrodes

An electrochemical–thermomechanical model for the description of charging and discharging processes in lithium electrodes is presented. Multi-physics coupling is achieved through the constitutive relations, obtained within a consistent thermodynamic framework based on the definition of the free energy density, sum of distinct contributions from different physics. The system is characterized by finite kinematics, under the assumption of locality of deformation, and the deformation gradient is decomposed into the product of elastic and inelastic parts. Specifically, a Taylor series expansion is used to approximate the inelastic deformation due to ion intercalation. The elastic part can be described alternatively by two finite kinematics models of neo-Hookean elasticity, and a Maxwell-type viscoelastic model accounts for time-dependent mechanical aspects. The model is implemented into a finite element code that uses B-spline basis functions. We illustrate the features of the model by means of selects examples, showing that chemo-mechanical interaction affects the equilibrium concentrations of the phases. The model captures the fundamental aspects of the anode charging and discharging processes.

A thermodynamics-based damage model for the non-linear mechanical behavior of SiC/SiC ceramic matrix composites in irradiation and thermal environments

A damage model is developed and validated with experimental data for the non-linear mechanical behavior of SiC/SiC composite materials in nuclear applications. Cyclic thermal and mechanical loading associated with neutron irradiation effects of these composites leads to wide-spread and progressive micro-cracking that leads to loss of thermal conductivity and further enhancement of thermo-mechanical damage. A physics-based model of wide-spread micro-cracking is developed within the thermodynamic framework of continuum damage mechanics. Evolution equations for damage parameters that describe the growth of continuum damage are developed, where the material variables are obtained from experiments. The model novelty is in coupling mechanical, thermal, and irradiation damage through a consistent thermodynamic framework, including loss of thermal conductivity due to the evolution of mechanically induced micro-cracks. A number of thermo-mechanical experiments were conducted to confirm model assumptions. The model is shown to be validated with out-of-pile experiments, and then implemented using commercial finite element code COMSOL to the fuel cladding problem with normal and high radiation dose cases.

Thermodynamic cycles with active matter.

Active matter constantly dissipates energy to power the self-propulsion of its microscopic constituents. This opens the door to designing innovative cyclic engines without any equilibrium equivalent. We offer a consistent thermodynamic framework to characterize and optimize the performances of such cycles. Based on a minimal model, we put forward a protocol which extracts work by controlling only the properties of the confining walls at boundaries, and we rationalize the transitions between optimal cycles. We show that the corresponding power and efficiency are generally proportional, so that they reach their maximum values at the same cycle time in contrast with thermal cycles, and we provide a generic relation constraining the fluctuations of the power.

Thermodynamics of the Coarse-Graining Master Equation.

We study the coarse-graining approach to derive a generator for the evolution of an open quantum system over a finite time interval. The approach does not require a secular approximation but nevertheless generally leads to a Lindblad–Gorini–Kossakowski–Sudarshan generator. By combining the formalism with full counting statistics, we can demonstrate a consistent thermodynamic framework, once the switching work required for the coupling and decoupling with the reservoir is included. Particularly, we can write the second law in standard form, with the only difference that heat currents must be defined with respect to the reservoir. We exemplify our findings with simple but pedagogical examples.

Oxidized Derivatives of 5-Methylcytosine Alter the Stability and Dehybridization Dynamics of Duplex DNA.

The naturally occurring nucleobase 5-methylcytosine (mC) and its oxidized derivatives 5-hydroxymethylcytosine (hmC), 5-formylcytosine (fC), and 5-carboxylcytosine (caC) play important roles in epigenetic regulation and, along with cytosine (C), represent nucleobases currently implicated in the active cytosine demethylation pathway. Despite considerable interest in these modified bases, their impact on the thermodynamic stability of double-stranded DNA (dsDNA) remains ambiguous and their influence on hybridization kinetics and dynamics is even less well-understood. To address these unknowns, we employ steady-state and time-resolved infrared spectroscopy to measure the influence of cytosine modification on the thermodynamics and kinetics of hybridization by assessing the impact on local base pairing dynamics, shifts in the stability of the duplex state, and changes to the hybridization transition state. Modification with mC leads to more tightly bound base pairing below the melting transition and stabilizes the duplex relative to canonical DNA, but the free energy barrier to dehybridization at physiological temperature is nevertheless reduced slightly. Both hmC and fC lead to an increase in local base pair fluctuations, a reduction in the cooperativity of duplex melting, and a lowering of the dissociation barrier, but these effects are most pronounced when the 5-position is formylated. The caC nucleobase demonstrates little impact on dsDNA under neutral conditions, but we find that this modification can dynamically switch between C-like and fC-like behavior depending on the protonation state of the 5-position carboxyl group. Our results provide a consistent thermodynamic and kinetic framework with which to describe the modulation of the physical properties of double-stranded DNA containing these modified nucleobases.

A non-local damage model for the fatigue behaviour of metallic polycrystals

ABSTRACT The development of fatigue damage in metallic materials is a complex process influenced by both intrinsic (e.g. texture, defects) and extrinsic (e.g. loading mode, frequency) factors. To better understand this process, some efforts have been made to develop microstructure-sensitive models that consider the impact of microstructural heterogeneities on the formation of fatigue cracks. An important limitation of such models is their inability to describe the transition between the nucleation and growth stages in a consistent thermodynamic framework. To circumvent this limitation, a constitutive model, which is appropriate for the description of both nucleation and early growth, is proposed. For this purpose, non-local damage mechanics is used to construct a set of constitutive relations that explicitly considers the progressive stiffness reduction due to the formation of fatigue cracks. Specifically, a damage variable is attached to each slip system, which allows considering both the anisotropic aspect of fatigue damage and closure effects. The spatial gradients of the damage variables are treated as additional state variables to account for the increase of surface energy associated with the formation of fatigue cracks. For the evolution equations to be compatible with the second law of thermodynamics, a modified form of the entropy production inequality is adopted. For illustration purposes, the non-local damage model is implemented in a spectral solver. Some numerical examples are then presented. These examples allow discussing the ability of the proposed model to describe the impact of loading conditions and pre-existing defects on the fatigue behaviour of metallic polycrystals.

Hybrid Equilibrium Finite Element Formulation for Cohesive Crack Propagation

Equilibrium elements have been developed in hybrid formulation with independent equilibrated stress fields on each element. Traction equilibrium condition, at sides between adjacent elements and at sides of free boundary, is enforced by use of independent displacement laws at each side, assumed as Lagrangian parameters. The displacement degrees of freedom belongs to the element side, where an extrinsic interface can be embedded. The embedded interface is defined by the same stress fields of the hybrid equilibrium element and it does not require any additional degrees of freedom. The extrinsic interface is developed in the consistent thermodynamic framework of damage mechanics with internal variable and produces a bilinear response in a traction separation diagram. The proposed extrinsic interface can be modelled on every single element side or can be modelled only on a set of predefined element sides.

A Model for Low-Cycle Fatigue in Micro-Structured Materials

A microscale formulation for low-cycle fatigue degradation in heterogeneous materials is presented. The interface traction-separation law is modelled by a cohesive zone model for low-cycle fatigue analysis, which is developed in a consistent thermodynamic framework of elastic-plastic-damage mechanics with internal variables. A specific fatigue activation condition allows to model the material degradation related to the elastic-plastic cyclic loading conditions, with tractions levels lower than the static failure condition. A moving endurance surface, in the classic framework of kinematic hardening, enables a pure elastic behaviour without any fatigue degradation for low levels of cyclic traction. The developed model is then applied to micro-structured materials whose micro-mechanics is analysed using a boundary integral formulation. Preliminary results demonstrate the potential of the developed cohesive model. The future application of the proposed technique is discussed in the framework of multiscale modelling of engineering components and design of micro-electro-mechanical devices (MEMS).

On the formulation of the kinematics and thermodynamics for polycrystalline materials undergoing phase transformation

Commonly implemented material processing routines not limited to quenching, welding or heat treatment requires exposure of a part to complex thermal and mechanical loading histories that manifest as residual stress and distortion. Of interest to material designers and fabricators is modeling and simulating the evolutionary process a part undergoes for the sake of capturing this observable residual stress states and geometric distortion accumulated after processing. To move toward an overall consistent modeling approach, we premise this investigation with a consistent thermodynamic framework for a generalized multiphase material. Following this, we extend the single phase Evolving Microstructural Model of Inelasticity (EMMI) internal state variable model to multiphase affirming that the interaction between phases is through an interfacial stress. We then use a self-consistent polycrystalline model to partition each individual phase's strain field ensuring a hybrid between compatibility and equilibrium. With a synthesis of the aforementioned ideas, the additional transformation plasticity (TRIP) is accounted for by changing each phase's flow rule to accommodate an interfacial stress. Following this, we couple the mechanical multiphase model equations with a previously developed non-diffusional phase transformation kinetics model. Contrary to the classical modeling approach, our material model is based on mixture theory wherein we track the behavior of each individual phase. A numerical evaluation of the coupled model is performed and applied to a simplified quenching boundary value problem.

Predictions of Stepped Isotherms in Breathing Adsorbents by the Rigid Adsorbent Lattice Fluid

Adsorbents that undergo structural changes in the presence of adsorbate molecules are an interesting new class of materials, which could offer enhanced selectivity, purity, and recovery in separation technology. To date, however, their application in such technology is hampered by the lack of a simple, consistent thermodynamic framework, which can effectively describe and predict their adsorption behavior under a range of conditions. This becomes especially true for their behavior in multicomponent adsorbate mixtures, for which experimental data are limited and cumbersome to obtain. Here, we present how the relatively simple rigid adsorbent lattice fluid model successfully and accurately predicts stepped isotherms in the breathing metal–organic framework, MIL-53 (Al), in the presence of CO2 and CH4. Breathing transitions are predicted solely on the basis of the different densities of the material’s two structural configurations and their associated Gibbs energies. Hysteresis effects can easily be included...

A viscoelastic model for hydrothermally activated malleable covalent network polymer and its application in shape memory analysis

Covalently cross-linked network polymers are widely used in engineering applications due to the robust and irreversible nature of the covalent bonds. Recently proposed polyimine-based malleable covalent network polymers (MCNPs) show water or temperature induced shape reforming under low temperatures, which enables the green and energy neutral reprocessing and reshaping of the thermoset. The fundamental mechanisms for water/temperature triggered reforming are the water and temperature initiated bond exchange reaction (BER), which releases the stress in the macromolecular chains. In addition, the water-induced BER process is assisted by the configuration entropy change under a water diffusion-induced shift in the glass transition temperature. To set a theoretical foundation for the MCNPs-based structure design and engineering applications, a chemo-thermo-mechanically coupled 3D viscoelastic model is developed under a consistent thermodynamic framework. A field model of mass transportation is developed to couple the chemical potential, temperature, stress, and relaxation time in a polymer system. The material malleability is attributed to two main factors, i.e., water/temperature triggered BERs and the water diffusion induced “plasticization effects”, where BERs-caused stress release is characterized by a phase evolution model, while "plasticization effects" induced material relaxation is captured by the depression of relaxation time which depends on the inverse of the entropy increment. After calibration by a series of experiments, the model is applied to stress relaxation and isothermal uniaxial stretch analysis of MCNPs under humidity condition. Good agreement between experiment and simulation demonstrates the ability of the proposed model in capturing the coupled thermo-chemo-mechanical behaviors of the water/temperature malleable polymer. Moreover, experiments and simulations show the solvent-driven softening mechanism provides an alternative way to recover the fixed temporary configuration. However, for the current BERs featured MCNPs, the water triggered constantly network topology exchange release the stress, not allowing the sample to return to its original shape. This work provides understandings and design guidelines for the hydrothermal-activated malleable covalent network polymer.

Thermodynamic characterization of ionic liquids

A novel simple method is presented for the characterization of ionic liquids as regards their thermodynamic behavior in bulk phases and interfaces. For this purpose, a simple consistent thermodynamic framework has been developed which may exploit a variety of experimental information, such as activity coefficients at infinite dilution, volumetric data over a temperature/pressure range, or wetting/contact angle data over a variety of solid surfaces. This experimental information is used in order to determine LSER (Linear Solvation Energy Relationships) type molecular descriptors and surface energies that uniquely characterize each ionic liquid. The interconnection of these descriptors with the more familiar equation-of-state scaling constants is established and explored. The emerging trends in the determined molecular descriptors and the consequences and perspectives are critically discussed. As shown by a variety of examples, the efficiency and versatility of the proposed characterization method are rather promising.

A Thermodynamically Consistent CZM for Low-Cycle Fatigue Analysis

A cohesive zone model for low-cycle fatigue analysis is developed in a consistent thermodynamic framework of elastic-plastic-damage mechanics with internal variable. A specific fatigue activation condition allows to model the material degradation related to the elastic-plastic cyclic loading conditions, with tractions levels lower than the damage activation condition. A moving endurance surface, in the classic framework of kinematic hardening, enables a pure elastic behavior without any fatigue degradation for low levels loading conditions.