Effective properties of a piezocomposite containing shape memory alloy and inert inclusions

Received July 2, 2001 / Published online February 4, 2002     

Nonlinear Plane Waves in Finite Deformable Infinite Mooney Elastic Materials

For infinite perfectly elastic Mooney materials, nonlinear plane waves are examined in both two and three dimensions. In two dimensions, longitudinal and shear plane waves are examined, while in three dimensions, longitudinal and torsional plane waves are considered. These exact dynamic deformations, applying to the incompressible perfectly elastic Mooney material, can be viewed as extensions of the corresponding static deformations first derived by Adkins [1] and Klingbeil and Shield [2]. Furthermore, the Mooney strain-energy function is the most general material admitting nontrivial dynamic deformations of this type. For two dimensions the determination of plane wave solutions reduces to elementary mathematical analysis, while in three dimensions an integral of the governing system of highly nonlinear ordinary differential equations is determined. In the latter case, solutions corresponding to particular parameter values are shown graphically. This revised version was published online in June 2006 with corrections to the Cover Date.     

Analysis of Wet Pressing of Paper: The Three-Phase Model. Part II: Compressible Air Case

In this study we consider a model of wet pressing of paper. We use the techniques and results from the first part of this paper, where a simplified model is studied in details. The model is, using suitable transformation, rewritten in the standard parabolic-hyperbolic form. Numerical solution for typical example is given and the effects of plastic deformations of paper are investigated. Finally, the model is employed to adres the problem of choosing an optimal pressing regime.     

Time derivative obtained by applying the Riemannian manifold of Riemannian metrics to kinematics of continuaDérivée temporelle obtenue en utilisant la variété riemannienne des métriques riemanniennes aux cinématiques des milieux continus

The infinite dimensional Riemannian geometry of Riemannian metrics is employed to propose novel objective time derivative by means of covariant derivative. To cite this article: Z. Fiala, C. R. Mecanique 332 (2004).     

Structural analysis of anisometric colloidal iron(III)-hydroxide particles and particle-aggregates incorporated in poly(vinyl-acetate) networks

Anisometrical colloidal iron(III)hydroxide particles and particle aggregates were incorporated in elastic poly(vinyl acetate) networks. A novel method has been developed to fix the colloidal structure of deformed samples. Digitalized image analysis has been applied in order to evaluate the micrographs. The rod-like particles allow for studying the local deformation and orientation due to uniaxial and triaxial deformations. The density correlation function as well as the micrographs show that the structure of aggregates is not influenced by the strain. Due to strong attractive interactions between the colloidal particles the developing strain is not enough to destroy the aggregate structure. The orientation behavior of the model filled networks can be satisfactorily described by using the affinity principle.     

Non-linearity in rheology —an essay of classification

Different non-linear phenomena (such as non-Newtonian flow, large elastic deformations, instabilities of different types and many others) are the heart of rheology. Therefore many attempts were carried out to find quantitative, or at least qualitative, models of non-linear behavior. The general or perhaps most attractive way of developing rheological constitutive equations consists in the search for the most general method to describe everything in the framework of a single approach. Naturally, this leads to very complicated and ambiguous equations. Meanwhile, it is reasonable to try another way based on separating observed phenomena into different types depending on observed phenomena into different types depending on their physical origin. An attempt to propose such their physical origin. An attempt to propose such classification of nonlinear rheological effects is made.According to the assumed scheme three levels of non-linearity are distinguished. There is a group of phenomena which originate as a consequence of finite elastic deformations. This is weak non-linearity related to equilibrium properties of a matter. The second level can be characterized as strong non-linearity. It is related to reversible structure changes, developing in time and connected with changes in relaxation properties of a matter. This group of effects can be treated as kinetic phenomena. Lastly, the third level of non-linearity is connected with breaking or phase transitions induced by deformations. This leads to the most severe consequences and can be treated as effects of thermodynamic nature. It is shown that some well known rheological effects can be explained if we consider them as a superposition of non-linearity of different types.Presented as keynote lecture at the European Rheology Meeting, September 4–9, 1994, Sevilla, Spain     

A comparative study of kinematic hardening rules at finite deformations

Kinematic hardening models describe a specific kind of plastic anisotropy which evolves with the deformation process. It is well known that the extension of constitutive relations from small to finite deformations is not unique. This applies also to well-established kinematic hardening rules like that of Armstrong-Frederick or Chaboche. However, the second law of thermodynamics offers some possibilities for generalizing constitutive equations so that this ambiguity may, in some extent, be moderated. The present paper is concerned with three possible extensions, from small to finite deformations, of the Armstrong-Frederick rule, which are derived as sufficient conditions for the validity of the second law. All three models rely upon the multiplicative decomposition of the deformation gradient tensor into elastic and plastic parts and make use of a yield function expressed in terms of the so-called Mandel stress tensor. In conformity with this approach, the back-stress tensor is defined to be of Mandel stress type as well. In order to compare the properties of the three models, predicted responses for processes with homogeneous and inhomogeneous deformations are discussed. To this end, the models are implemented in a finite element code (ABAQUS).     

Induced formal deformations and the Cohen-Macaulay property

The main result states: if is a module finite extension of excellent local normal domains which is unramified in codimension two and if represents a deformation of the completion of , then there is a corresponding -algebra deformation such that the ring homomorphism represents a deformation of . The main application is to the ascent of the arithmetic Cohen-Macaulay property for an étale map of smooth projective varieties over an algebraically closed field.     

Generalized Deformations and Hochschild Cohomology

We present a generalization of Gerstenhaber's theory of deformations. We no longer assume that the deformation parameter t acts in its usual free and symmetric way on the elements of the original algebra A, but in the following manner: t · a = (a)t and a · t = (a)t, where and are endomorphisms of A. We develop the cohomological framework adapted to these deformations.     

The Elastic Interpretation of Electrodynamics

In his famous treatise, Maxwell presumed explicitly, without developing it, an elastic interpretation of his electrodynamics; the relevant quotation is given in the introduction. It is in that spirit that we have developed the theory of the elastic interpretation here presented. We show that the Maxwell equations and the electrodynamic forces can formally be obtained from the theory of elasticity. An electromagnetic field can be considered as a deformation of a certain elastic medium . This deformation is created by volumetric densities of deforming couples and of irrotational deforming forces that act on . A distribution of electric charges is proportional to the divergence of the deforming couples. The electrodynamic forces are due to the interactions between such deformations. Even though the consistency of the elastic interpretation of electrodynamics is demonstrated by the fact that it gives back Maxwell's equations, and the electrodynamic forces, we show that the elastic interpretation is compatible with Einstein's special relativity. Then we demonstrate that an adequate density of irrotational deforming forces can produce the same effects on light propagation as those of a Schwarzschild metric background. This fact suggests a possible extension to take into account many of the effects attributed to the geometrical structure of the general relativity. Thus, we have given an elastic interpretation to the action at distance, and contributed to eliminate the inconsistency mentioned by Einstein, implying in his view, an incompleteness of the Maxwell theory. In future works, we hope to give an elastic interpretation for additional aspects of the particle waves and of general relativity and for the electroweak and strong fields.