Rank-one convexity and polyconvexity of Hencky-type energies

We investigate a family of isotropic volumetric-isochorically decoupled strain energies based on the Hencky-logarithmic (true, natural) strain tensor log U. The main result of this note is that for n = 2 the considered energies are rank-one convex for suitable values of two material parameters. We also conjecture that there are values of the material parameters such that the corresponding energies are polyconvex. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Null-Lagrangians and the indeterminate couple stress model

The aims of this note is to present a new model based on a new representation of the curvature energy in the indeterminate couple stress model and to discuss some related choices from the literature. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymptotic partition of energy in micropolar mixture theory of porous media

The aim of this paper is to study the asymptotic partition of the energy associated with the solution of the initial-boundary value problem who describes the behavior of binary homogeneous micropolar mixtures of an isotropic micropolar elastic solid with an incompressible micropolar viscous fluid. Some Lagrange-Brun identities are established. Using the Cesáro means of various parts of total energy, the relations that describe the asymptotic behavior of mean energies are established. The author acknowledges support from the Romanian Ministry of Education and Research through CEEX program, contract CERES-2-CEx06-11-12/25.07.2006.     

Loss of ellipticity in additive logarithmic finite strain plasticity and related results on Hencky-type energies

The aim of this paper is to present some results regarding the Legendre-Hadamard ellipticity and loss of ellipticity of some energies depending on the logarithmic strain tensor. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On uniqueness and continuous dependence of solutions in viscoelastic mixtures

This note deals with the isothermal linear theory of porous viscoelastic mixtures. Questions of uniqueness and continuous dependence for solutions of various classes of initial boundary value problems in mixtures consisting of two constituents: a porous elastic solid and a porous Kelvin–Voigt material are studied. The Lagrange identity and Logarithmic convexity methods are used to establish uniqueness and continuous dependence results, with no definiteness assumptions upon the internal energy.     

Representation theorems and fundamental solutions for micropolar solid–fluid mixtures under steady state vibrations

The isothermal theory of binary micropolar solid–fluid mixture is considered in this paper. For the dynamical problem, a Galerkin type representation of the solution is established. Then, a fundamental solution is given for the three-dimensional partial differential system which describes the steady vibrations. Also, some basic properties of the fundamental solution and a direct application to the point load problem are presented.     

On Spatial Behavior of the Harmonic Vibrations in Kelvin-Voigt Materials

The present paper deals with the study of the amplitude of the steady-state vibrations in a right finite cylinder made of an isotropic Kelvin-Voigt material. Some exponential decay estimates, similar to those of Saint-Venant type, are obtained for appropriate cross-sectional area measures associated with the amplitude of the steady-state vibrations. It is proved that due to dissipative effects, the estimates in question hold for every value of the frequency of vibrations and for arbitrary values of the elastic coefficients. The results are extended to a semi-infinite cylinder and some alternatives of Phragmèn-Lindelöf type are established.