http://link.springer.com/content/pdf/10.1007/978-3-642-69569-8_2.pdf

Theory of Elastic Stability

A unified treatment of the mechanics of deformation and acoustic propagation in porous media is presented, and some new results and generalizations are derived. The writer's earlier theory of deformation of porous media derived from general principles of nonequilibrium thermodynamics is applied. The fluid‐solid medium is treated as a complex physical‐chemical system with resultant relaxation and viscoelastic properties of a very general nature. Specific relaxation models are discussed, and the general applicability of a correspondence principle is further emphasized. The theory of acoustic propagation is extended to include anisotropic media, solid dissipation, and other relaxation effects. Some typical examples of sources of dissipation other than fluid viscosity are considered.

/pdf/mechanics-of-deformation-and-acoustic-propagation-in-porous-hqnj8g3pho.pdf

Mechanics of deformation and acoustic propagation in porous media

T he macroscopic elastic moduli of two-phase composites are estimated by a method that takes account of the inhomogeneity of stress and strain in a way similar to the Hershey-Kroner theory of crystalline aggregates. The phases may be arbitrarily aeolotropic and in any concentrations, but are required to have the character of a matrix and effectively ellipsoidal inclusions. Detailed results arc given for an isotropic dispersion of spheres.

A self-consistent mechanics of composite materials

This book describes and explains the fundamental physical processes involved in bubble dynamics and the phenomenon of cavitation. It is intended as a combination of a reference book for those scientists and engineers who work with cavitation or bubble dynamics and as a monograph for advanced students interested in some of the basic problems associated with this category of multiphase flows. A basic knowledge of fluid flow and heat transfer is assumed but otherwise the analytical methods presented are developed from basic principles.

The book begins with a chapter on nucleation and describes both the theory and observations of nucleation in flowing and non-flowing systems. The following three chapters provide a systematic treatment of the dynamics of the growth, collapse or oscillation of individual bubbles in otherwise quiescent liquids. Chapter 4 summarizes the state of knowledge of the motion of bubbles in liquids. Chapter 5 describes some of the phenomena which occur in homogeneous bubbly flows with particular emphasis on cloud cavitation and this is followed by a chapter summarizing some of the experiemntal observations of cavitating flows. The last chapter provides a review of the free streamline methods used to treat separated cavity flows with large attached cavities.

/pdf/cavitation-and-bubble-dynamics-1vfop84jck.pdf

Cavitation and Bubble Dynamics

The Classical Field Theories

The settlement of soils under load is caused by a phenomenon called consolidation, whose mechanism is known to be in many cases identical with the process of squeezing water out of an elasticporous medium. The mathematical physical consequences of this viewpoint are established in the present paper. The number of physical constants necessary to determine the properties of the soil is derived along with the general equations for the prediction of settlements and stresses in three‐dimensional problems. Simple applications are treated as examples. The operational calculus is shown to be a powerful method of solution of consolidation problems.

/pdf/general-theory-of-three-dimensional-consolidation-226gv91sjq.pdf

General Theory of Three‐Dimensional Consolidation

A theory is developed for the propagation of stress waves in a porous elastic solid containing compressible viscous fluid. The emphasis of the present treatment is on materials where fluid and solid are of comparable densities as for instance in the case of water‐saturated rock. The paper denoted here as Part I is restricted to the lower frequency range where the assumption of Poiseuille flow is valid. The extension to the higher frequencies will be treated in Part II. It is found that the material may be described by four nondimensional parameters and a characteristic frequency. There are two dilatational waves and one rotational wave. The physical interpretation of the result is clarified by treating first the case where the fluid is frictionless. The case of a material containing viscous fluid is then developed and discussed numerically. Phase velocity dispersion curves and attenuation coefficients for the three types of waves are plotted as a function of the frequency for various combinations of the characteristic parameters.

/pdf/theory-of-propagation-of-elastic-waves-in-a-fluid-saturated-1mvj036y9f.pdf

Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range

The theory of propagation of stress waves in a porous elastic solid developed in Part I for the low‐frequency range is extended to higher frequencies. The breakdown of Poiseuille flow beyond the critical frequency is discussed for pores of flat and circular shapes. As in Part I the emphasis of the treatment is on cases where fluid and solids are of comparable densities. Dispersion curves for phase and group velocities along with attenuation factors are plotted versus frequency for the rotational and the two dilational waves and for six numerical combinations of the characteristic parameters of the porous systems. Asymptotic behavior at high frequency is also discussed.

/pdf/theory-of-propagation-of-elastic-waves-in-a-fluid-saturated-s8k1qncn46.pdf

Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range

A unified treatment is presented of thermoelasticity by application and further developments of the methods of irreversible thermodynamics. The concept of generalized free energy introduced in a previous publication plays the role of a ``thermoelastic potential'' and is used along with a new definition of the dissipation function in terms of the time derivative of an entropy displacement. The general laws of thermoelasticity are formulated in a variational form along with a minimum entropy production principle. This leads to equations of the Lagrangian type, and the concept of thermal force is introduced by means of a virtual work definition. Heat conduction problems can then be formulated by the methods of matrix algebra and mechanics. This also leads to the very general property that the entropy density obeys a diffusion‐type law. General solutions of the equations of thermoelasticity are also given using the Papkovitch‐Boussinesq potentials. Examples are presented and it is shown how the generalized coordinate method may be used to calculate the thermoelastic internal damping of elastic bodies.

/pdf/thermoelasticity-and-irreversible-thermodynamics-304hlf2dne.pdf

Thermoelasticity and Irreversible Thermodynamics

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