Stanisław J. Matysiak

Micromorphic effects in a modelling of periodic multilayered elastic composites

Abstract The paper deals with the problems of modelling of multilayered periodic composites. The proposed models take into account certain micromorphic effects resulting from the periodic structure of the body. The governing equations describing motions and stresses of the nonhomogeneous elastic materials with microperiodic structure in the nonlinear as well as linear cases have been derived. As an example the time-harmonic vibrations of laminated medium consisting of alternating layers of two homogeneous, isotropic, linear-elastic materials have been discussed.

On the modelling of heat conduction problem in laminated bodies

SummaryThe paper deals with the heat conduction modelling problem for micro-periodic composites. The models proposed there take into account certain micromorphic effects resulting from the fine periodic structure of the body. The governing equations describing heatfluxes and temperature distributions in these composites in the nonlinear as well as linear cases have been derived. Two examples of the application of the presented models are detailed.

Contact temperature and wear of composite friction elements during braking

The analytical model for the determination of contact temperature and wear on a working surface of friction brakes is presented. It is assumed that one of the friction element is composed of a periodic two-layered composite and the second element is a homogeneous half-space. In the frictional process, the wear coefficient is linearly dependent on the contact temperature. The influences of composite parameters as well as a parameter characterizing the changing of loading from zero to the nominal value on the distribution of contact temperature and wear during braking is considered.

Influence of periodically layered material structure on the frictional temperature during braking

Abstract A closed form model for computation of temperature distribution in a semi-infinite periodic layered solid subjected to frictional heat flow at the surface is investigated. The transient heat conducting equations have been solved using Hankel and Laplace transforms technique. The appropriate dimensionless parameters are given and the reduced temperature as a function of these parameters are presented in the graphic farm. It is shown that the solutions obtained in this paper cover the case of frictional heat generation in the homogeneous solid as well as describing some new results.

Thermal stresses in a laminate composite with a row of interface cracks

Abstract In this paper two-dimensional stationary problems of periodic two-layered thermoelastic space weakened by a finite or infinite periodic system of interface thermally insulated cracks under a uniform heat flux are investigated. The analysis is performed on the basis of a homogenized model with microlocal parameters presented in Refs [11–14]. We have derived a complex potential representation suitable for solving the interface crack problems and exact solutions of those are obtained. The stress singularities at the crack tips are discussed.

Thermal stresses in a periodic two-layered composite weakened by an interface crack

SummaryThis paper deals with the two-dimensional thermoelastic problem of interface thermally insulated crack in a microperiodic layered space. Within the framework of the homogenized model of the linear thermoelasticity with microlocal parameters [10]–[13] the exact solution of the considered problem is obtained by using the complex potentials method [13]. The stress singularities at the crack tips are discussed.

Plane contact problems for a periodic two-layered elastic composite

SummaryThis paper deals with the two-dimensional static punch problems in the presence of friction for a periodically layered half-space. Within the framework of the homogenized model of linear elasticity with microlocal parameters [8–11] the exact solutions of the considered problems are obtained. The case of the indentation of the composite body by a rigid rectangular punch has been discussed in detail.ÜbersichtIn dieser Arbeit wird das zweidimensionale statische Stempelproblem mit Reibung für einen periodisch geschichteten Halbraum betrachtet. Im Rahmen eines Homogenisierungsmodells der linearen Elastizitätstheorie mit mikropolaren Parametern werden die exakten Lösungen der betrachteten Probleme gewonnen. Im Detail wird das Eindringen eines rechteckigen starren Stempels behandelt.

Plane contact problem for periodic laminated composite involving frictional heating

SummaryThe stationary problem of a rigid thermally insulated punch sliding over the boundary surface of a periodic two-layered thermoelastic half-space is considered. The heat generated in the contact area is assumed to be caused by frictional forces. The problem is formulated within the framework of thermoelasticity with microlocal parameters, and it is reduced to a system of two integral equations, which is solved numerically. The effects connected with the composite structure are analyzed.

On the complex potentials of the linear thermoelasticity with microlocal parameters

SummaryThe linear theory of thermoelasticity with microlocal parameters was proposed lately in [1], [2], [3] as a certain alternative approach to the modelling of microperiodic composites. In this paper we adopt the complex variable method for two-dimensional problems of the periodically layered thermoelastic composites treated within the framework of the linear thermoelasticity with microlocal parameters. The presented complex potentials reduce two-dimensional static problems of the microperiodically layered thermoelastic composites to the boundary values problems for analytical functions. As an example illustrating this method the plane-strain problem of stress and temperature distribution in the microperiodic two-layered half-space subjected to general loading and temperature on the boundary is considered.

On homogenization of diffusion processes in microperiodic stratified bodies

Abstract The aim of this contribution is to present the homogenized model of the diffusion processes in microperidic stratified bodies. The considerations are based on the linear Ficks theory of diffusion and the procedure of microlocal modelling [11]. The obtained model takes into account certain microlocal structure of the body. As the illustration of the application of presented model, a simple example is given.