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Continuum mechanics
About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.
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TL;DR: In this paper, a mathematical model is presented to predict the evolution of freezing of water-saturated soil, based on the theory mixtures and the principles of continuum mechanics and macroscopic thermodynamics.
Abstract: A mathematical model is presented to predict the evolution of freezing of water-saturated soil. It is based on the theory mixtures and the principles of continuum mechanics and macroscopic thermodynamics. The numerical solution of the problem is accomplished using an enriched family of interpolation functions. Copyright © 2001 John Wiley & Sons, Ltd.
47 citations
TL;DR: In this paper, the authors considered the thermostatics of bodies whose equilibrium stress and free energy depend on the higher gradients of deformation and the bodies considered are fully compatible with continuum thermodynamics based on the Clausius-Duhem inequality and on the balance equations in their conventional forms.
Abstract: This paper deals with the thermostatics of bodies whose equilibrium stress and free energy depend on the higher gradients of deformation. The bodies considered are fully compatible with continuum thermodynamics based on the Clausius-Duhem inequality and on the balance equations in their conventional forms. Stable equilibrium states are studied that model phase transitions as smooth solutions to the equations of mechanical equilibrium with zero body forces. The following results are obtained for them:
47 citations
Journal Article•
TL;DR: In this article, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua, and the internal energy is assumed to be a function of densities, entropies and successive spatial gradients of each constituent.
Abstract: In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of densities, entropies and successive spatial gradients of each constituent. We first write the equations of motion for each constituent of an inviscid miscible mixture of fluids without chemical reactions or diffusion. Our work leads to the equations of motion in an universal thermodynamic form in which interaction terms subject to constitutive laws, difficult to interpret physically, do not occur. For an internal energy function of densities, entropies and spatial gradients, an equation describing the barycentric motion of the constituents is obtained. The result is extended for dissipative mixtures and an equation of energy is obtained. A form of Clausius-Duhem's inequality which represents the second law of thermodynamics is deduced. In the particular case of compressible mixtures, the equations reproduce the classical results. Far from critical conditions, the interfaces between different phases in a mixture of fluids are layers with strong gradients of density and entropy. The surface tension of such interfaces is interpreted.
47 citations
TL;DR: In this paper, the general formulation in Part I was extended to include the electromagnetic interactions with materials and constitutive equations for electromagnetic solids and fluids were developed for electromagnetic systems and fluids.
47 citations
TL;DR: Several types of simple flows, such as shearing flows and extensional flows, which are of greatest importance in industrial operations are restricted to, if these simple flows cannot be well described by continuum or molecular models, then it is not necessary to lavish time and energy to apply them to more complex flow problems.
Abstract: To solve problems in polymer fluid dynamics, one needs the equations of continuity, motion, and energy. The last two equations contain the stress tensor and the heat-flux vector for the material. There are two ways to formulate the stress tensor: (a) One can write a continuum expression for the stress tensor in terms of kinematic tensors, or (b) one can select a molecular model that represents the polymer molecule and then develop an expression for the stress tensor from kinetic theory. The advantage of the kinetic theory approach is that one gets information about the relation between the molecular structure of the polymers and the rheological properties. We restrict the discussion primarily to the simplest stress tensor expressions or constitutive equations containing from two to four adjustable parameters, although we do indicate how these formulations may be extended to give more complicated expressions. We also explore how these simplest expressions are recovered as special cases of a more general framework, the Oldroyd 8-constant model. Studying the simplest models allows us to discover which types of empiricisms or molecular models seem to be worth investigating further. We also explore equivalences between continuum and molecular approaches. We restrict the discussion to several types of simple flows, such as shearing flows and extensional flows, which are of greatest importance in industrial operations. Furthermore, if these simple flows cannot be well described by continuum or molecular models, then it is not necessary to lavish time and energy to apply them to more complex flow problems.
47 citations