Mellon Institute of Industrial Research

About: Mellon Institute of Industrial Research is a based out in . It is known for research contribution in the topics: Infrared spectroscopy & Infrared. The organization has 667 authors who have published 751 publications receiving 28034 citations.

The Thermodynamics of Elastic Materials with Heat Conduction and Viscosity

Abstract: The basic physical concepts of classical continuum mechanics are body, configuration of a body, and force system acting on a body. In a formal rational development of the subject, one first tries to state precisely what mathematical entities represent these physical concepts: a body is regarded to be 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 bodies1. Once these concepts are made precise one can proceed to the statement of general principles, such as the principle of objectivity or the law of balance of linear momentum, and to the statement of specific constitutive assumptions, such as the assertion that a force system can be resolved into body forces with a mass density and contact forces with a surface density, or the assertion that the contact forces at a material point depend on certain local properties of the configuration at the point. While the general principles are the same for all work in classical continuum mechanics, the constitutive assumptions vary with the application in mind and serve to define the material under consideration.

Thermodynamics with Internal State Variables

Abstract: This is a study of the thermodynamics of nonlinear materials with internal state variables whose temporal evolution is governed by ordinary differential equations. After employing a method developed by Coleman and Noll to find the general restrictions which the Clausius—Duhem inequality places on response functions, we analyze various types of dynamical stability that can be exhibited by solutions of the internal evolution equations. We also discuss integral dissipation inequalities, conditions under which temperatures can be associated with internal states, and the forms taken by response functions when the material is a fluid.

An Approximation Theorem for Functionals, with Applications in Continuum Mechanics

Abstract: We start with a brief discussion of the physical motivation behind the mathematical considerations to be presented in Part I of this paper.