Search results for "Thermodynamic potential"

Effects of Electron Correlation inside Disordered Crystals

2022

S.P.K. acknowledges support by the National Academy of Sciences of Ukraine (Project No.0116U002067). Calculations were performed using Latvian Super Cluster (LASC), located in the Center of Excellence at Institute of Solid State Physics, the University of Latvia, which is supported by European Union Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-Teaming. Phase two under Grant Agreement No. 739508, project CAMART2.

Thermodynamic potentials, identities and stability

2004

Elastic-Viscoplastic Solids Subjected to Thermal and Loading Cycles

1995

— A class of elastic-viscoplastic materials with dual internal variables, thermodynamic potential and temperature-dependent plastic and creep data is considered. For solids (or structures) of such materials, subjected to cyclic loads and temperature variations, the existence of a steady-state response is ascertained and its periodicity characteristics established. Particular steady-state responses, like, elastic and inelastic shakedown, are addressed. By means of a sensitivity analysis of the steady cycle with respect to the load parameter changes, a number of basic features of inelastic shakedown (the viscoplastic counterpart of plastic shakedown) are also addressed.

Internal-variable constitutive model for rate-independent plasticity with hardening saturation surface

1998

An elastic-plastic material model with internal variables and thermodynamic potential, not admitting hardening states out of a saturation surface, is presented. The existence of such a saturation surface in the internal variables space — a consequence of the boundedness of the energy that can be stored in the material's internal micro-structure — encompasses, in case of general kinematic/isotropic hardening, a one-parameter family of envelope surfaces in the stress space, which in turn is enveloped by a limit surface. In contrast to a multi-surface model, noad hoc rules are required to avoid the intersection between the yield and bounding/envelope surface. The flow laws of the proposed mode…

Double-well thermodynamic potentials and spinodal curves: how real are they?

2007

The concept of double-well thermodynamic potentials, ubiquitous since the van der Waals description of the vapour-to-liquid transition and the Landau theory of phase transitions, is critically re-examined. Particular emphasis is put on the extent to which spinodal curves (separating ‘metastable’ from ‘unstable’ states) are meaningful. It is argued that in full thermodynamic equilibrium spinodals are well-defined when one either considers finite subsystems of an infinitely large system, or systems with all linear dimensions finite. Evidence is given that in a finite (cubic) d-dimensional box the spinodals correspond (in a fluid) to the rounded ‘droplet evaporation’ or ‘bubble condensation’ t…

A Consistent Boundary/Interior Element Method for Evolutive Elastic Plastic Structural Analysis

1993

A symmetric/sign-definite formulation of the BEM to address the evolutive elastic plastic analysis of structures is presented. A wide class of material models with internal variables and thermodynamic potential is considered. Different energy methods—namely the boundary min-max principle, the Helmholtz free energy and the maximum intrinsic dissipation theorem—axe employed in order to provide the discretization operations by boundary elements and cell elements with inherent variational consistency. The resulting space-discretized equations can be solved by a step-by-step procedure and a predictor/corrector iteration scheme, with corrections operated locally cell-by-cell, just as with the FEM…

Beyond the Vegard's law: solid mixing excess volume and thermodynamic potentials prediction, from end-members

2020

Abstract A method has been developed, herein presented, to model binary solid solutions' volume, enthalpy and Gibbs energy using the energy state functions, E ( V , S ) , of the end-members only. The E ( V , S ) s are expanded around an unknown mixing volume, V Mix , and the fundamental equilibrium equation − ( ∂ E / ∂ V ) S = P is used to determine V Mix . V Mix allows us to model enthalpy, straightforwardly. The same argument holds using Helmholtz energy, F ( V , T ) , in place of E ( V , S ) , and the equilibrium equation becomes − ( ∂ F / ∂ V ) T = P . One can readily determine the Gibbs free energy, too. The method presented remarkably simplifies computing of solid mixings' thermodynam…

Thermal field theories and shifted boundary Conditions

2014

The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary conditions. The Poincare' invariance underlying a relativistic theory implies a dependence of the free-energy on the compact length L_0 and the shift xi only through the combination beta=L_0(1+xi^2)^(1/2). This in turn implies that the energy and the momentum distributions of the thermal theory are related, a fact which is encoded in a set of Ward identities among the correlators of the energy-momentum tensor. The latter have interesting applications in latti…

An alternative formulation of Classical Mechanics based on an analogy with Thermodynamics

2013

We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of transformations are considered, the new formulation is found to be completly equivalent to the usual Lagrangian formulation, recovering well established results like the conservation of the angular momentum. Furthermore, a natural generalization of the Poisson Bracket is found to be inherent to the formalism introduced. On the other hand, we find that with a convenient redefinition of the Lagrangian, $\mathcal{L}^{\prime}=-\mathcal{L}$, it is possible to establish an …

Classical Statistical Mechanics

2003

Some aspects of statistical mechanics that are particularly important for computer simulation approaches are recalled. Using Ising and classical Heisenberg models as examples, various statistical ensembles and appropriate thermodynamic potentials are introduced, and concepts such as Legendre transformations between ensembles and the thermodynamic integration method to obtain the entropy are mentioned. Probability distributions characterizing statistical fluctuations are discussed, fluctuation relations for response functions are derived, and the behavior of these quantities at first and second order phase transitions are described qualitatively. Also the general consequences of phase coexis…