Dissipative flow model based on dissipative surface and irreversible thermodynamics

Summary A dissipative flow model is presented to describe dissipative deformation processes in a macroscopic solid continuum. Dissipative process may consist of material plasticity, material damage and other intrinsic mechanical phenomena represented by internal variables. The concept of a dissipative surface is introduced in the paper to distinguish between conservative and dissipative processes. Conventional plastic yielding and damage initiation are expressed by a unique condition which may else include other possible intrinsic mechanical dissipations. The proposed model is based on the principles of irreversible thermodynamics and the minimum free energy theorem. A modified material stability postulate, modified Drucker's postulate, in thermodynamic stress space is also used to obtain the same results. Received 1 July 1998; accepted for publication 13 January 1999     

Linear viscoelasticity and irreversible thermodynamics

The underlying thermodynamic aspects of linear viscoelasticity are discussed. In particular, from the Extended Irreversible Thermodynamics theory we systematically derive the Maxwell model exhibiting its compatibility with thermo-dynamics and assessing its conditions of validity. We also calculate the equilibrium transverse velocity auto-correlation function and the frequency dependent shear viscosity. Nonlinear generalizations of our model are suggested and the possible role of extended thermodynamics in selecting constitutive equations is also discussed.     

A damping term based on material properties for the volume-based contact dynamics model

The Gonthier et al. volume-based contact dynamics model addressed many different phenomena that influence the force of contact between two objects. This work extends Gonthier et al.'s work by proposing an alternate damping model based on material properties. The normal contact force based on volumetric interference information is derived using principles of mechanics of materials. The volume of interference and its rate of change are shown to be analogues to the material deformation and deformation rate. Simulations of the free direct central impact between two identical spheres are run using the proposed model, the Hunt–Crossley model and the Gonthier et al. model; these are compared to experimental data from the literature. This is followed by a discussion of those models.     

A forced-vibration technique for measurement of material damping

This article describes a technique for measuring material damping in specimens under forced flexural vibration. Although the method was developed for testing fiber-reinforced composite materials, it could be used for any structural material. The test specimen is a double-cantilever beam clamped at its midpoint and excited in resonant flexural vibration by an electromagnetic shaker. Under steady state conditions, material damping is defined in terms of the ratio of input energy to strain energy stored in the specimen. If external losses are negligible, the input energy must equal the energy dissipated in the specimen. Input energy and strain energy are found from measured specimen dimensions, resonant frequency, input acceleration and bending strain. Problems associated with minimization of external energy losses in the apparatus and verification of measurements are discussed in detail. Measured damping of aluminum-alloy calibration specimens shows good agreement with calculated thermoelastic damping. Examples of measured damping showing amplitude and frequency dependence in fiber-reinforced plastic materials are presented.     

Flow-induced nonequilibrium thermodynamics of lamellar semicrystalline polymers

In this work we present a first attempt to quantify the effect of flow deformation on the microstructure of semicrystalline polymers. This necessitates bridging the macroscopic flow length scale with the microscopic (segment) length scale of the semicrystalline structure. To achieve this connection we developed a hierarchical approach where a thermodynamically consistent macroscopic constitutive equation is interfaced with a microscopic lattice-based Monte Carlo (MC) simulation of the polymer chain conformation. We first illustrate this approach in a two-dimensional (2D) “toy” application where the 2D equivalent of a macroscopic constitutive equation based on reptation theory is applied to describe the chain deformation and extended free energy in the amorphous bulk phase. The values for the derivative of the free energy with respect to the mean segment orientation tensor, calculated for a planar extensional flow, are then used as an extended nonequilibrium thermodynamic forcing term. This is added in a traditional Metropolis Monte Carlo scheme, developed for a 2D lattice representation of a lamellar semicrystalline polymer, to drive the flow-induced microstructure. Significant flow-induced changes are calculated, steadily increasing as the Weissenberg number increases.We subsequently extend these ideas further in a much more realistic three-dimensional (3D) application where the information for the thermodynamics of the bulk amorphous phase under a uniaxial extensional flow is extracted from a macroscopic network model, such as that of Phan-Thien and Tanner (PTT), connecting the free energy to the second moment of the end-to-end distance of a multisegment chain. Through a series of 3D nonequilibrium Monte Carlo simulations of both the amorphous and the semicrystalline microscopic morphologies, it is shown that the interaction of the flow-induced deformation with the semicrystalline microstructure is nonlinear: the amorphous interlamellar structure changes significantly from its corresponding homogeneous bulk amorphous state, even far away from the crystalline interface. Our approach allows for a quantitative estimation of this effect on both thermodynamic quantities, like the extended microscopic free energy, as well as various statistics of the chain conformations.     

On the thermodynamics of fractional damping elements

Constitutive models of viscoelasticity in combination with fractional differential operators are successfully used by many authors to describe the mechanical properties of polymers. The topic of the present paper is the investigation of rheological models incorporating fractional damping elements from the point of view of thermodynamics. We take the Clausius Duhem inequality as admissibility criterion and investigate uniaxial and three-dimensional deformation processes at constant temperature. We specify sufficient conditions and show that rheological models, which consist of springs in combination with fractional dashpots, are compatible with the dissipation principle. As a new aspect of the subject, we present a systematic method for deriving the free energy functionals. With the help of two examples we demonstrate that the free energy of fractional systems can be derived as a generalisation of related discrete systems. To illustrate this method, we study in detail an isolated fractional dashpot (also known as a power-law model) and a fractional standard solid (Zener model). Finally, we propose a three-dimensional formulation of the fractional Zener model and specify the corresponding free energy functional. Received: July 3, 1996     

Variational irreversible thermodynamics of physical-chemical solids with finite deformation

A new thermodynamics of open thermochemical systems and a variational principle of virtual dissipation are applied to the finite deformation of a solid coupled to thermomolecular diffusion and chemical reactions. A variational derivation is obtained of the field differential equations as well as Lagrangian equations with generalized coordinates. New formulas for the affinity and a new definition of the chemical potential are presented. An outline is given of an unusually large field of applications, such as active transport in biological systems, finite element methods, plastic properties as analogous to chemical reactions, phase changes and recrystalization, porous solids, heredity and initially stressed solids. A new and unified insight is thus provided in highly diversified problems.     

Extended irreversible thermodynamics as a framework for transport phenomena in porous media

A theoretical extended thermodynamic approach to describe transport in porous media is presented. For a particular model of the porous medium, approximate time evolution equations for the fluxes in the system are derived. The use of these equations is illustrated by considering three different transport problems. A finite velocity for the propagation of thermal disturbances within the medium is predicted in the case of heat transport in a system where the effective porosity is zero. Also, a generalization of the Darcy-Brinkman law that incorporates thermal effects, independently of the presence of external forces, arises when consideration is given to the combined mass and heat transport problem. Finally, for the isothermal transport of fluid, the thermodynamic framework provides a possible interpretation of the origin and the role played by both the Brinkman and the Forchheimer corrections to Darcy's law.Work supported by PAPIID of DGAPA-UNAM under project IN-100-289.On sabbatical leave from Area de Física, Universidad Autónoma Chapingo.     

A thermodynamics based damage mechanics model for particulate composites

A micro-mechanical damage model is proposed to predict the overall viscoplastic behavior and damage evolution in a particle filled polymer matrix composite. Particulate composite consists of polymer matrix, particle fillers, and an interfacial transition interphase around the filler particles. Yet the composite is treated as a two distinct phase material, namely the matrix and the equivalent particle-interface assembly. The CTE mismatch between the matrix and the filler particles is introduced into the model. A damage evolution function based on irreversible thermodynamics is also introduced into the constitutive model to describe the degradation of the composite. The efficient general return-mapping algorithm is exploited to implement the proposed unified damage coupled viscoplastic model into finite element formulation. Furthermore, the model predictions for uniaxial loading conditions are compared with the experimental data.     

Lie groups in nonequilibrium thermodynamics: Geometric structure behind viscoplasticity

Poisson brackets provide the mathematical structure required to identify the reversible contribution to dynamic phenomena in nonequilibrium thermodynamics. This mathematical structure is deeply linked to Lie groups and their Lie algebras. From the characterization of all the Lie groups associated with a given Lie algebra as quotients of a universal covering group, we obtain a natural classification of rheological models based on the concept of discrete reference states and, in particular, we find a clear-cut and deep distinction between viscoplasticity and viscoelasticity. The abstract ideas are illustrated by a naive toy model of crystal viscoplasticity, but similar kinetic models are also used for modeling the viscoplastic behavior of glasses. We discuss some implications for coarse graining and statistical mechanics.     

Nonlocal approach to nonequilibrium thermodynamics and nonlocal heat diffusion processes

We study some aspects of nonequilibrium thermodynamics and heat diffusion processes based on Suykens’s nonlocal-in-time kinetic energy approach recently introduced in the literature. A number of properties and insights are obtained in particular the emergence of oscillating entropy and nonlocal diffusion equations which are relevant to a number of physical and engineering problems. Several features are obtained and discussed in details.     

Fundamentals of two-phase flow by the method of irreversible thermodynamics

The paper explores thermodynamic aspect of modelling two-phase systems by the methods of irreversible thermodynamics in both classical (CIT) and extended (EIT) formulation. The conservation laws for two-phase model-continuum are derived. Then, the entropy production is analysed for two-fluid and homogeneous systems. Different equations of state are taken into consideration, namely that corresponding to the accompanying equilibrium state of physical element and more complex resulting from EIT. Obtained expressions for rate of entropy production per unit volume allow to identify the dissipative mechanisms in the two-phase system and suggest the forms of phenomenological relations to be adopted in the constitutive equations.     

Extended irreversible thermodynamics and its relation with other continuum approaches

We present an introduction to extended irreversible thermodynamics (EIT) as applied to polymer solutions in the presence of shear flow and of diffusion flux. We discuss with special attention the definition of chemical potential in non-equilibrium situations and its use in the analysis of shear-induced phase transitions. In the second part, we compare EIT with other contemporary continuum approaches: theories with internal variables, the GENERIC approach, and the matrix model. All these theories share an emphasis on the relations between dynamics and thermodynamics at a deeper level than in the classical theory, but each of them has some peculiar advantage in the analysis of some specific aspects of physical problems.     

Some relations of nonequilibrium thermodynamics for a two-temperature and two-velocity gas with phase transitions

We study the nonequilibrium thermodynamics of two-phase media with nonequilibrium phase transitions. Assuming local (point) equilibrium within the limits of the phase and assuming mass additivity of the mixture entropy with respect to the phases, we obtain an expression for the mixture entropy production.We consider the motion of such media and derive formulas for the thermodynamic friction forces, heat transfer, condensation, and evaporation.In conclusion the author wishes to thank V. N. Nikolaevskii and V. V. Gogosov for helpful discussions.     

An explicit formulation of a three-dimensional material damping model with transverse isotropy

A constitutive three-dimensional (3D) damping model is derived for transversely isotropic material symmetry, using the augmented Hooke's law [Intl. J. Solids Struct. 32 (1995) 2835] as a starting point. The proposed material model is tested numerically, via finite-element techniques, on a laminate structure built from stacked aluminium and Plexiglas plates. Effective 3D transversely isotropic material properties are given in terms of homogeneous material damping functions in connection with homogenised elastic laminate properties. Comparisons made between the results from the elastic (undamped) eigenvalue problem of the detailed (layerwise) model of the laminate and the effective 3D elastic model show that the homogenised model is reasonably accurate, in terms of predicted elastic eigenfrequencies for the first 20 modes. The dynamic homogenisation process, with damping included, is evaluated in terms of forced vibration response for the laminate structure, using effective transversely isotropic frequency dependent material properties. The dynamic 3D effective homogeneous material model is found to simulate very closely the detailed model in the studied frequency interval for the numerical test case.