Gianfranco Capriz

Symmetries and Hamiltonian Formalism for Complex Materials

Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are reported: we invoke the invariance under the action of a general Lie group of the balance of substructural interactions. Poisson brackets are also introduced in the material representation to account for general material substructures. A Hamilton-Jacobi equation suitable for multifield models is presented. Finally, a spatial version of all these topics is discussed without making use of the notion of paragon setting.

Interactions in general continua with microstructure

A satisfactory axiomatic treatment of the interaction among bodies modelled as standard continua was achieved by Noll almost thirty years ago and was presented in the seminal paper [1], variously reprinted. A full review of the matter is also available in the first chapters of the treatise [2].

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

Smectic liquid crystals as continua with latent microstructure

Smectic liquid crystals are quasi solids, which possess microstructure both of the material and local type (the nematic mictrostructure and the lamellae, respectively). They also exhibit phase transitions: from smectic B to smectic A, to nematic, to isotrtopic liquid (see [1], Ch. 7). Their study, though special, might show up general advantages and drawbacks of different types of mathematical models. Here, while intent on proving the property announced in the title, we set forth the groundwork for the continuum model (see, in a more specific and concrete mode [2]).SommarioI cristalli liquidi smettici sono quasi-solidi che possiedono una microstruttura sia di tipo materiale che locale (la microstruttura nematica e le lamelle, rispettivamente). Essi esibiscono anche transizioni di fase: smettici B a smettici A, a nematici, a liquidi isotropi. Il loro studio, sebbene speciale, potrebbe evidenziare vantaggi generali e difetti di vari tipi di modelli matematici. Qui, nel provare la proprietà annunciata nel titolo, si prepara il lavoro di base per il modello continue.

Spatial Variational Principles in Continuum Mechanics

In order to obtain balance equations for non-simple continua, particularly in cases where the suggestive power of Newtonian dynamics fails, it is customary to resort to variational techniques and principles. The list of pertinent quotations could be long, starting with the book by the brothers Cosserat (see Section 98 of [1] for a review and for an outline of the work of Toupin).

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.

Balance at a Junction among Coherent Interfaces in Materials with Substructure

The junction among coherent interfaces separating phases in continua exhibiting material substructure is modeled as a virtual bar endowed by its own measures of interaction (macro- and microstresses and self-forces); balance equations at the junction are derived within a multifield theory. To involve bodies with substructure is not an idle formal exercise; strong anchoring conditions at the boundary rarely allow the existence of smooth solutions. Thus interfaces are more frequent and junctions inevitable if overall substructural order need be preserved. Besides, our development frames together old remarks (e.g., a remark by Gibbs) and new suggestions. Also we have the chance, here, to return to some nontrivial open issues of the general theory.

On surface biaxiality

Abstract We propose the following: on the boundary of a nematic liquid crystal, the function which describes the molecular orientation is subject to a further symmetry condition, besides that reflecting apolarity. This additional symmetry delimits a class of biaxial states; within that class we study a model problem for a thin layer in which the anchoring energy prevails over the elastic energy in the presence of an electric field. We show that, when the anchoring and electric energies favour uniaxial states with optic axes at right angles, the equilibrium configuration migrates from one state to the other, traversing a whole family of biaxial states as the strength of the electric field increases.

Control of Beams and Chains Through Distributed Gyroscopes

DOI: 10.2514/1.29250 The control of deformable bodies through a large number of small gyroscopes has received attention in the past 20 years. Promising in principle for the control of spacecraft structures, the idea needs the design of fit control algorithms to be developed in practice. Aiming at this design, here we develop two special but technically important cases, which can be easily implemented and of possible use in spacecraft appendages: an elastic beam with an embeddedarrayofcoaxialrotorsdistributedalongthebeam’saxisandspinningaboutit,andachain,eachrigidlink ofwhichcontainsarotorwhoseaxisispinnedalongthelink-to-linkdirection.Weshowsomeresultsforthedynamics of such structures that are made possible by the control of the rotors and can be implemented to deal with and eventually damp small disturbances: the propagation of screw waves of small amplitude through chains or beams, and the diversion of energy from one mode to another in the linear transversal vibrations of beams.