Józef Joachim Telega

Flows in random porous media: effective models

Abstract The aim of this paper is to provide a synthesis of results related to modeling transport in random media. Both single and two-phase flows have been considered. Special emphasis has been put on methods of stochastic homogenization.

Asymptotic method of homogenization of fissured elastic plates

This paper deals with the homogenization of thin elastic plates weakened by periodically distributed fissures. The classical Kirchhoff theory of bending plates admits five different types of unilateral fissures. To derive effective properties of fissured plates we employ the asymptotic method. As a result we obtain five effective hyperelastic plates. An illustrative example concerns the homogenization of the plate with unidirectional fissures parallel to a straight line. The constitutive equation describing the effective plate is found provided that fissures are of the flexural type resembling that observed in reinforced concrete plates in bending.

Flow of electrolyte through porous piezoelectric medium: macroscopic equations

Abstract The aim of this contribution is to elaborate a general framework for modelling flows of two-ionic species electrolytes through porous piezoelectric media. By using the method of two-scale asymptotic expansions, the macroscopic phenomenological equations describing electrokinetics of such a structure are derived and the formulae for the effective mechanical and nonmechanical coefficients are given. Natural jump conditions are assumed on the interfaces between the piezoelectric skeleton and conductive fluid.

Dual extremum principles in rate boundary value problems of non-associated plasticity

Abstract Dual extremum principles have been derived for a class of non-standard elastic-plastic solids. These principles characterize velocities of both the original and adjoint solids. The questions of existence and uniqueness have also been discussed.

Continued fractions, two-point Padé approximants and errors in the Stieltjes case

A Stieltjes function is expanded in mixed T- and S-continued fraction. The relations between approximants of this continued fraction and two-point Pade approximants are established. The method used by Gilewicz and Magnus (J. Comput. Appl. Math. 49 (1993) 79; Integral Transforms Special Functions 1 (1993) 9) has been adapted to obtain the exact relations between the errors of the contiguous two-point Pade approximants in the whole cut complex plane.

Exact controllability of anisotropic elastic bodies

The aim of this contribution is to study the exact controllability of linear, anisotropic elastic bodies by applying Lions’ Hilbert Uniqueness Method.

Homogenization and effective properties of plates weakened by partially penetrating fissures: Asymptotic analysis

Abstract A method of finding effective properties of elastic plates weakened by periodically distributed part-through-the thickness fissures is presented. The plate behaviour is described by the two-dimensional two-layer plate model. The model involves four kinematical fields standing for: the in-plane displacements of the interface plane, the independent rotations of the cross-sections of the lower and upper layers of the plate and for the common deflection of both layers. Within the framework of this model the bending mode of fissuring is considered. In contrast to the approaches of our previous papers, which were based on the Kirchhoff [ J. Elasticity 19 (1988)] and the Reissner-like [ Arch. Mech. 40 (1988)] plate models, the present approach enables one to describe the opening and closure of the fissures without the undesired effect of possible interpenetration of the adherent faces of the fissures. The homogenized formulae are derived by applying the two-scale asymptotic method. The effective plate is described by the two-layer plate model that turns out to be non-linear and hyperelastic. The hyperelastic potential involves the solution of the basic cell problem. This problem assumes here the form of a variational inequality posed on a rescaled cell of periodicity. Having found the effective two-layer plate model one can construct the effective model of Kirchhoff type. Also this model turns out to be non-linear and hyperelastic.

Derivation of variational principles for rigid-plastic solids obeying non-associated flow laws—I: Further development of the nonlinear method of adding the adjoint operator, prescribed jumps

Abstract In this paper several variational functionals have been derived for a perfectly plastic solid obeying non-associated flow rule. The nonlinear method of adding the adjoint operator has been applied. Making use of the method a basic variational functional is obtained, from which others, with a reduced number of independent fields, are derived. In the first part of the paper discontinuities of stress and velocity fields are prescribed. Also further results concerning the method of adding the adjoint operator are presented.

Controllability and Stabilization in Elasticity, Heat Conduction and Thermoelasticity: Review of Recent Developments

The aim of this paper is to review developments in exact and approximate controllability as well as stabilization of elastic, thermoelastic, and thermo-viscoelastic bodies. Heat equations are also discussed.

A non-linear elastic plate model of moderate thickness: Existence, uniquenness and duality

Three problems are solved for a nonlinear model of elastic plates with transverse shear deformations. The material of the plate may be anisotropic. An existence theorem is formulated and proved for a class of boundary conditions. A uniqueness theorem is given for small loadings. The dual problem is derived and the minimax or Lagrangian approach is discussed.