Cz. Woźniak

On the dynamic behavior of honeycomb based composite solids

SummaryThe aim of this contribution is twofold. First, a dispersive model of periodic composite solids made of an isotropic matrix reinforced by a hexagonal system of slender fibres or by a honeycomb-like slender skeleton is formulated. Second, this model is applied to the analysis of vibration and wave propagation problems in the above honeycomb based composites. Contrary to the known homogenized models the main feature of the proposed model is that it describes the effect of cell size on the overall dynamic behavior of a composite solid. It is shown that on the macro-level the response of honeycomb based composites is isotropic. It is also proved that there exist dispersive dilatational-type and shear-type waves, which can propagate in these composites. Simple formulae for lower and higher free vibration frequencies are derived, and the existence of certain restrictons imposed on the physically allowable wave propagation speeds is shown.

On phase transition layers in certain micro-damaged two-phase solids

A continuum model of a moving transition layer separating two different solid phases of a certain micro-damaged material is proposed. An application of this model to the analysis of the propagation of this layer in a micro-cracked solid is shown.

The dynamic modelling of elastic wavy plates

SummaryThe aim of the contribution is to formulate an engineering theory describing the dynamic behaviour of periodically waved shell-like elements, called wavy plates. On the basis of the proposed theory, the effect of coupling between free macro- and micro-vibrations of a wavy plate is investigated. It is also shown that the homogenized model of wavy plates (obtained by scaling down the wavelength parameters) cannot be applied in the analysis of dynamic problems.

A macroscopic model of the diffusion and heat transfer processes in a periodically micro-stratified solid layer

SummaryA macroscopic mathematical model for the analysis of the diffusion and heat transfer processes in a bounded periodically micro-stratified thick solid layer will be derived. Contrary to the known asymptotic homogenization approach the proposed modelling method retains the microstructure length in a macroscopic description of the process. It will be shown that this effect makes it possible to formulate correctly boundary conditions on the boundaries which intersect the stratification and is responsible for certain transient and boundary layer phenomena.

A MACROSCOPIC MODEL FOR THE HEAT PROPAGATION IN THE MICROPERIODIC COMPOSITE SOLIDS

This article deals with the problem of heat propagation in periodic composites described by the Cattaneo-type constitutive law. The simplest model for the macroscopic behavior of these composites can be obtained using results of the well-known asymptotic homogenization theory. However, this model is not able to describe the phenomena related to higher order motions and higher propagation speeds that play an important role in wave propagation analysis. The aim of this contribution is to propose a more general macroscopic model for the heat propagation in periodic composites that can be used for the analysis of the aforementioned phenomena and is based on the tolerance averaging of equations with functional coefficients.

On the microdynamics of composite plates

SummaryThe subject of the contribution is an investigation of elastic composite plates with a microperiodic structure along the plates midsurface. The computational models of the plates are largely based on the homogenization procedures leading to equations with constant coefficients. However, the homogenization theories neglect the microstructure length-scale effect on the plates dynamic behaviour. The objective of this research is to formulate and investigate a refined theory of the composite plates under consideration, which would describe the microdynamic plate behaviour caused by the microstructure. The possible applications of the proposed theory are shown by an example.

Corrected 2D-theories for composite plates

SummaryThe objective of the paper is to propose a simple method of formulation of 2D-theories for composite thin plates made of an arbitrary inhomogeneous linear-elastic material. The effect of inhomogeneity on the plate stiffness will be described by means of extra unknowns, called correctors, which have to satisfy a system of linear algebraic equations. The elimination of correctors can be performed in explicit form and leads to the formulas for effective stiffnesses of the plates under consideration.

Discrete and continuum modelling of delamination processes

SummaryThe chaotic distributions of delaminated surface elements in laminates are described by a macrodelamination density function. Using this concept a phenomenological discrete mathematical model of the interlaminar debonding processes is proposed. For multilayered periodic composites the discrete model is approximated by a certain continuum model of delamination processes.ÜbersichtEine chaotische Verteilung von gelockerten Bereichen von den Trennflächen von Schichtwerkstoffen wird durch eine Dichtefunktion der Schichtentrennung modelliert. Diese Darstellung ermöglicht die Formulierung eines phänomenologischen diskreten Modells von Schichtentrennungsvorgängen. Für vielschichtige, periodische Verbundwerkstoffe wird das diskrete Modell durch ein kontinuierliches Modell approximiert.

On the modelling of thermo-unelastic periodic composites: microlocal parameter theory

SummaryIn the paper it is shown how to formulate certain homogenized models of thermoelastic-unelastic periodic composites under large strains and large temperature gradients. The models obtained describe local stresses and heat fluxes in every material component in term of averaged displacement and temperature fields and certain extra unknowns called microlocal parameters.

Composite shells with interlaminar imperfections

SummaryIn this contribution the effect of interlaminar initial imperfections on a composite shell behavior is investigated. The constitutive equations for shells with initial interlaminar bonding imperfections are obtained.ÜbersichtIn diesem Beitrag wird der Einfluß von anfänglichen Zwischenschichtdefekten auf das Verhalten einer Verbundstoffschale untersucht und die Materialgesetze für solche Schalen werden aufgestellt.