Pasquale Giovine

Dynamics and wave propagation in dilatant granular materials

The equations of motion for dilatant granular material are obtained from a Hamiltonian variational principle of local type in the conservative case. The propagation of nonlinear waves in a region with uniform state is studied by means of an asymptotic approach that has already appeared useful in an investigation on wave propagation in bubbly liquids and in fluid mixtures. When the grains are assumed to be incompressible, it is shown that the material behaves as a continuum with latent microstructure.SommarioSi ricavano le equazioni di moto per i materiali granulari dilatanti da un principio variazionale Hamiltoniano di tipo locale nel caso conservativo. Si studia la propagazione delle onde non lineari in una regione di stato costante per mezzo di un approccio asintotico già rivelatosi utile nello studio della propagazione di onde nei liquidi con bolle e nelle miscele di fluidi. Quando si supponga che i granuli siano incomprimibili, si dimostra che il materiale si comporta come un continuo con microstruttura latente.

On Microstructural Inertia

Microstructural inertia may be modified by the presence of a powerless term which derives from the partial indetermination of the kinetic coenergy of the microstructure.

Modeling and mechanics of granular and porous materials

Preface Part I. Mechanics of Porous Media Constitutive Equations and Instabilities of Granular Materials /F. Darve and F. Laouafa Micromechanical Modeling of Granular Materials /J.T. Jenkins and L. La Ragione Thermodynamic Modeling of Granular Continua Exhibiting Quasi-Static Frictional Behaviour with Abrasion /N.P. Kirchner and K. Hutter Modeling of Soil Behaviour: from Micro-Mechanical Analysis to Macroscopic Description /R. Nova Dynamic Thermo-Poro-Mechanical Stability Analysis of Simple Shear on Frictional Materials /I. Vardoulakis Part II. Flow and Transport Phenomena in Particulate Materials Mathematical Models for Soil Consolidation Problems: A State of the Art Report /D. Ambrosi, R. Lancellotta, and L. Preziosi Flow of Water in Rigid and Non-Rigid, Saturated and Unsaturated Soils /P.A.C. Raats Mass Exchange, Diffusion and Large Deformations of Poroelastic Materials /K. Wilmanski Part III. Numerical Simulations Continuum and Numerical Simulation of Porous Materials in Science and Technology /W. Ehlers A Mathematical and Numerical Model for Finite Elastoplastic Deformations in Fluid Saturated Porous Media /L. Sanavia, B.A. Schrefler, and P. Steinmann Numerical Modeling of Initiation and Propagation Phases of Landslides /M. Pastor, M. Quecedo, P. Mira, J.A. Fernandez-Merodo, L. Tongchun, and L. Xiaoqing

Mathematical Models of Granular Matter

From Granular Matter to Generalized Continuum.- Generalized Kinetic Maxwell Type Models of Granular Gases.- Hydrodynamics from the Dissipative Boltzmann Equation.- Bodies with Kinetic Substructure.- From Extended Thermodynamics to Granular Materials.- Influence of Contact Modelling on the Macroscopic Plastic Response of Granular Soils Under Cyclic Loading.- Fluctuations in Granular Gases.- An Extended Continuum Theory for Granular Media.- Slow Motion in Granular Matter.

A Linear Theory of Porous Elastic Solids

The theory of porous elastic solids with large vacuous interstices, considered by Giovine like materials with ellipsoidal structure, includes, as a particular case, the nonlinear theory of Nunziato and Cowin of elastic materials with small spherical voids finely dispersed in the matrix.In this paper we propose appropriate constitutive relations and then specialize the basic balance equations of Giovine to the linear theory. Also, generalizing the developments of Cowin and Nunziato, we formulate boundary-initial-value problems and examine classical applications as responses to homogeneous deformations and small-amplitude acoustic waves.

Nonclassical Thermomechanics of Granular Materials

The description of the flow of a granular material with rigid grains requires a combination of suggestions from both fluid and solid mechanics owing to the fact that the material has an essentially fluid-like behavior, but it can also be heaped and, moreover, its bulk compressibility depends on the initial voids distribution. Hence, for the study of this medium, a continuum theory is proposed here that follows mainly from the thermomechanical approach of Dunn and Serrin, but also takes into account characteristic postulates about flows of granular materials with inelastic granules; in particular we obtain the following result: the stress tensor, the kinetic energy and the heat flux must be additively decomposed. Moreover, the balance of angular momentum is given here in a more general form suggested by the mechanical nature of the ‘interstitial working’ of Dunn and Serrin.

Stability of liquid flow down an inclined tube

A linear stability analysis has been performed to investigate the stability of liquid flow down an inclined circular tube. To this purpose, approximate solutions which describe laminar and turbulent steady flow down an inclined tube have been developed first. The stability analysis has then been performed by an integral method. The results of the present investigation indicate that, in general, flow in a tube is more stable than in a channel and, in particular, there is a value of the liquid height at which the flow is always stable.

On wave propagation in porous media with strain gradient effects

A porous material with large irregular holes is here studied as a hyperelastic continuum with latent microstructure, and the mechanical balance equations are derived from the general ones for a medium with ellipsoidal microstructure. This is done by imposing the kinematical constraint of microstretch bounded to the macrodeformation: in this case, the microstructure disappears, apparently, and the response of the material involves higher gradients of the displacement without incurring known constitutive inconsistencies. An application to the propagation of asymptotic waves compatible with such a model is also considered. Physical situations corresponding to an axisymmetric motion either in spherical or cylindrical symmetry are considered, and it is shown that the time evolution of the wave amplitude factor is governed by the spherical and cylindrical Korteweg-deVries equations, respectively.

Wave features related to a model of compressible immiscible mixtures of two perfect fluids

SummaryThe balance equations of a compressible immiscible mixture of two perfect fluids are derived by using a variational principle. It is shown that the equations of such a mixture obey Truesdells third metaphysical principle. Then the governing equations, specialized by assuming that both phases have the same motion, are studied by means of a suitable asymptotic approach. It is derived an evolution equation representing a generalized Korteweg-de Vries equation containing also nonlinear terms in the higher order derivatives. Finally, the travelling wave solutions of this evolution equation are discussed.

On Effects of Virtual Inertia during Diffusion of a Dispersed Medium in a Suspension

Equations of motion of a binary mixture (where virtual inertia effects due to diffusion have relevance) are derived from an Eulerian variational principle. The results are consistent with general axioms of the theory of mixtures.