Definition Of Free Energy Research Articles

Elasto-viscoplastic model for rayon yarns

AbstractIn this paper we develop a new model for the simulation of the mechanical behavior of rayon twisted yarns, at macroscopic level. A yarn with its continuous filaments is represented by an equivalent three-dimensional solid of cylindrical shape, discretized by finite elements, with properly defined local anisotropic material properties. The new constitutive model, inspired by experimental results on rayon untwisted yarns, is formulated in the framework of the thermodynamics of irreversible processes and includes visco-elastic and visco-plastic dissipation mechanisms. The effect of twist is taken into account by including the direction of the fibers in the free energy definition. The overall model is validated comparing numerical and experimental results on twisted rayon yarns.

CALCULATION OF THERMAL CONDUCTIVITY FOR CRYSTALLINE NANOSTRUCTURES

<p>We have introduced a theory for the calculation of thermodynamic characteristics for some characteristic nanostructures (ultrathin films and superlattices), using the adapted method of two-time temperature Green's functions. In this paper, he has determined the coefficient of thermal conductivity using the definition of free energy and then compared their temperature dependence to the thermal conductivity behavior of the bulk structures. For the observed nanostructures, the thermal conductivity coefficient values are almost equal at low temperatures, but at the same time, significantly lower than the bulk sample values. That result could be useful for the possible achievement of better superconducting conditions in the observed compound nanostructures.</p>

Information and Self-Organization

The process of “self-organization” takes place in open and complex systems that acquire spatio-temporal or functional structures without specific ordering instructions from the outside. [...]

Thermodynamic Consistent Formulations of Viscoplastic Deformations in FCC Metals

A general consistent thermodynamic framework for small strain thermoviscoplastic deformations of face-centered cubic (FCC) metals is presented in this study. An appropriate and consistent Helmholtz free energy definition is incorporated, after considering the strain rate effect imbedded through the hardening definition, in deriving the proposed three-dimensional kinematical model. Microstructural physically based thermal and athermal yield function definitions (von Mises type) are utilized in this work for dynamic and static deformations of FCC metals. A length scale parameter introduced implicitly through the viscosity parameter is related to the waiting time of dislocations at an obstacle. The role of material dependence in setting the character of the governing equations is illustrated in the context of a simple uniaxial tensile problem in order to check the effectiveness and the performance of the proposed framework and its finite-element implementation. Results obtained for OFHC copper at low and high strain rates and temperatures show, generally, good comparisons with experimental results.

A coupled temperature and strain rate dependent yield function for dynamic deformations of bcc metals

A coupled temperature and strain rate microstructure physically based yield function is proposed in this work. It is incorporated along with the Clausius–Duhem inequality and an appropriate free energy definition in a general thermodynamic framework for deriving a three-dimensional kinematical model for thermo-viscoplastic deformations of body centered cubic (bcc) metals. The evolution equations are expressed in terms of the material time derivatives of the elastic strain, accumulated plastic strain (isotropic hardening), and the back stress conjugate tensor (kinematic hardening). The viscoplastic multipliers are obtained using both the Consistency and Perzyna viscoplasticity models. The athermal yield function is employed instead of the static yield function in the case of the Perzyna viscoplasticity model. It is found that the static strain rate value, at which the material shows rate-independent behavior, varies with the material deformation temperature. Computational aspects of the proposed model are addressed through the finite element implementation with an implicit stress integration algorithm. Finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program ABAQUS/Explicit [ABAQUS, 2003. User Manual, Version 6.3. Habbitt, Karlsson and Sorensen Inc., Providence, RI] via the user material subroutine coded as VUMAT. Numerical implementation for a simple compression problem meshed with one element is used to validate the proposed model implementation with applications to tantalum, niobium, and vanadium at low and high strain rates and temperatures. The analysis of a tensile shear banding is also investigated to show the effectiveness and the performance of the proposed framework in describing the strain localizations at high velocity impact. Results show mesh independency as a result of the viscoplastic regularization used in the proposed formulation.

Ratio of entropy to enthalpy in thermal transitions in biological tissues

Thermal transitions in biological tissues that have been reported in the literature are summarized in terms of the apparent molar entropy (DeltaS) and molar enthalpy (DeltaH) involved in the transition. A plot of DeltaS versus DeltaH for all the data yields a straight line, consistent with the definition of free energy, DeltaG=DeltaH+TDeltaS. Various bonds may be involved in cooperative bond breakage during thermal transitions; however, for the sake of description, the equivalent number of cooperative hydrogen bonds can be cited. Most of the tissue data behave as if 10 to 20 hydrogen bonds are cooperatively broken during coagulation, with one transition, the expression of heat shock protein, involving 90 cooperative hydrogen bonds. The data are consistent with DeltaS=a+bDeltaH, where a=-327.5 J(mol K) and b=31.47 x 10(-4) K(-1). If each additional hydrogen bond adds 19 x 10(3) Jmol to DeltaH, then each additional bond adds 59.8 J(mol K) to DeltaS. Hence, the dynamics of irreversible thermal transitions can be described in terms of one free parameter, the apparent number of cooperative hydrogen bonds broken during the transition.

Cohesive Layer Modeling of Time-Dependent Debond Growth in Aggressive Environments

Abstract The objective of this paper is to model the synergistic bond-degradation mechanisms that may occur at the interface between a fiber-reinforced polymer (FRP) that is adhesively bonded to a substrate and subjected to elevated temperature and humidity. For this purpose, a two-dimensional cohesive-layer constitutive model with a prescribed traction-separation law is constructed from fundamental principles of continuum mechanics and thermodynamics, taking into account strain-dependent, non-Fickian hygrothermal effects as well as diffusion-induced degradation in the cohesive layer. In the interest of solution tractability, a simplified approach is employed where the rate-dependent behavior in the cohesive layer is implemented through the characterization of rate dependence of the maximum stresses and maximum strains in the cohesive layer, rather than through the use of convolution integrals in the free-energy definition. The remainder of the polymeric adhesive outside the cohesive layer is modeled as a nonlinear viscoelastic continuum with time-dependent constitutive behavior. The influence of temperature and moisture concentration on the work-of-separation and on crack growth is derived from first principles. The model is implemented in a test-bed finite element code. Results predicted by the computational model are benchmarked through comparison to experimental data from mixed-mode fracture experiments performed using a moving wedge test.

Use of quasi‐Newton methods for large strain elastic‐plastic finite element computations

AbstractIn this paper, quasi‐Newton methods are used to solve large strain elastic‐plastic problems. The governing nonlinear equations are derived from the principle of virtual work written in an updated Lagrangian manner. The constitutive equations result directly from the definition of free energy and plastic potential that involve a convex functional form. A mixed algorithm is proposed that combines the Newton‐Raphson method and modified Newton‐;Raphson method with symmetric quasi‐Newton update. The efficiency of the algorithm, measured in terms of rate of convergence and computation time is studied on numerical tests. The procedure has a very wide field of application in nonlinear elastic‐plastic analysis.

Statistical mechanics of electronic energy levels in semiconductors

It is shown, using Guggenheim's pressure ensemble that partial Gibbs free energies are the quantities determining equilibrium occupations of electronic levels and hence are the quantities that enter detailed balance relationships. It is also shown that the energy of an optical no-phonon transition between band states equals the corresponding free energy change. This is also true for transitions involving localized impurity states provided: 1. (a) the effects of electronic degeneracy are excluded from the free energy definition, and 2. (b) the localized state does not couple to a local phonon mode.

Statistical mechanics of band states and impurity states in semiconductors

Thermodynamic analogies have previously been invoked to interpret the temperature- and pressure-dependent electronic levels in a semiconductor as standard Gibbs free energies. In this paper it is shown by means of statistical mechanical arguments using the pressure ensemble that standard Gibbs free energies are the quantities determining equilibrium occupations of electronic levels and hence are the thermodynamic quantities that enter detailed balance relationships. Optical band gaps are identified with the 'nophonon line' gap for a transition in which the occupation numbers for the phonons and remaining electrons are unchanged. An exact expression for no phonon optical transition energies is given. It is shown rigorously that the optical no-phonon-line energy is identical to the corresponding free-energy change for any transition between band states and also for transitions involving localised states provided: (i) the effects of electronic degeneracy changes are excluded from the free energy definition; (ii) the localised state is not associated with a local lattice mode.