Journal ArticleDOI
Gaseous diffusion in a stressed-thermoelastic solid. Part I: The thermomechanical formulation
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In this paper, a phenomenological theory for the diffusion of a dilute solution of a gas in a thermoelastic solid is proposed, where the thermomechanical behavior of the solid is assumed to be unaffected by the presence of the gas.Abstract:
A phenomenological theory is proposed for the diffusion of a dilute solution of a gas in a thermoelastic solid. It is assumed that the thermomechanical behavior of the solid is unaffected by the presence of the gas. On the other hand the presence of the solid is recognized by the gas by letting certain thermomechanical variables of the solid to enter into the constitutive equations of the gas. The constitutive functionals of the gas are restricted by the principles of continuum physics. These principles are currently referred to as equipresence, material objectivity, entropy production inequality, as well as the balance equations of mass, linear and angular momentum and internal energy. By this approach, axiomatic statements on the existence of equations of state are avoided and the classical results of linear irreversible thermodynamics are obtained by further specialization of the proposed theory.read more
Citations
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Journal ArticleDOI
On the problem of diffusion in solids
TL;DR: In this paper, the authors rationalize diffusion in solids on the basis of a differential equation of balance expressing conservation of momentum for the diffusing species, and derive the main results of classical theories in a unified manner.
Journal ArticleDOI
A new interpretation of diffusion in high-diffusivity paths—a continuum approach
TL;DR: In this article, the authors considered the problem of diffusion in regions containing a finite number of continuously distributed families of high-diffusivity paths and provided differential expressions for the partial and total concentrations.
Journal ArticleDOI
Introduction to Matrix Analysis. By Richard Bellman. 2nd Edition. Pp. xxiii, 403. £7·50. (McGraw-Hill.)
TL;DR: This book discusses Maximization, Minimization, and Motivation, which is concerned with the optimization of Symmetric Matrices, and its applications in Programming and Mathematical Economics.
Journal ArticleDOI
On the theory of stress-assisted diffusion, II
TL;DR: In this article, the authors derived similar steady-state solutions of a recently developed strees-assisted diffusion theory for certain classes of stress distributions and used them to model embrittlement and stress corrosion cracking phenomena.
Journal ArticleDOI
Precipitate-induced anisotropy in binary Al-Cu alloys
Frédéric Barlat,Jiantao Liu +1 more
TL;DR: In this paper, a model based on kinematic hardening concepts was developed to quantitatively describe the plastic behavior of materials containing hard precipitates such as θ′ in Al-Cu alloys.
References
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Book
Introduction to Matrix Analysis
TL;DR: In this article, the Second Edition Preface is presented, where Maximization, Minimization, and Motivation are discussed, as well as a method of Hermite and Quadratic Form Index.
Book ChapterDOI
The Thermodynamics of Elastic Materials with Heat Conduction and Viscosity
TL;DR: The basic physical concepts of classical continuum mechanics are body, configuration of a body, and force system acting on a body as mentioned in this paper, which can be expressed as follows: a body is regarded as a smooth manifold whose elements are the material points; a configuration is defined as a mapping of the body into a three-dimensional Euclidean space, and a force system is defined to be a vector-valued function defined for pairs of bodies.