Engineering Transactions, 53, 4, pp. 363–374, 2005

Influence of Anisotropy Induced by Microcracks on Effectiye Elastic Properties

B. Gambin
Institute of Fundamental Technological Research

A. Gałka
Institute of Fundamental Technological Research

J. J. Telega
Institute of Fundamental Technological Research

S. Tokarzewski
Institute of Fundamental Technological Research

The influence of microcracks distribution on macroscopic elastic properties of composites with a specific structure is studied. The model predicts the properties of laminates made of materials in which fracture process leads to appearance of many microcracks distributed practically uniformly. The method of solution is based on the so-called reiterated homogenization with two different scales of inhomogeneities. The smaller scale is connected with microcracks size. After homogenization performed with the help of FEM an anisotropic homogeneous elastic material is obtained. The anisotropy is implied by directional distribution of microcracks. On the second larger scale, random mixture of two or more different anisotropic elastic materials is considered.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


G. ALLAIRE, Shape optimization by the homogenization method, Springer, New York 2002.

T. LEWIŃSKI, J.J. TELEGA, Plates, laminates and shells: asymptotic analysis and homogenization, World Scientific, Singapore 2000.

A. GAŁKA, B. GAMBIN, J.J. TELEGA, Multi-layered piezocomposites: homogenization and optimization, Theoretical Foundations of Civil Engineering, Polish-Ukrainian Transactions; W. Szczesniak; Oficyna Wydawnicza Politechniki Warszawskiej; 299–308; 2003; Dniepropietrowsk 2003.

G. MILTON, The theory of composites, Cambridge University Press, 2002

J.J. TELEGA, Homogenization of fissured elastic solids in the presence of unilateral conditions and friction, Computational Mech., 6, 109–127, 1990.

J.J. TELEGA, B. GAMBIN, Effective properties of an elastic body damaged by random distribution of microcracks, [in:] Continuum Models and Discrete Systems, K.Z. MARKOY [Ed.], World Scientific, Singapure 1996, 300–307.

S.A. BERGGREN, D. LUKKASSEN, A. MEIDELL, L. SIMULA, On stiffness properties of square honeycombs and other unidirectional composites, Composites: Part B, 32, 503–511, 2001

S.A. BERGGREN, D. LUKKASSEN, A. MEIDELL, L. SIMULA, Some methods for calculating stiffness properties of periodic structures, Applications of Mathematics, 48, 2, 97–110, 2003.

D. LUKKASSEN, A. MEIDELL, S. YIGDERGAUZ, On the elastic deformation of symmetric periodic structures, Q. Jl. Appl. Math., 56, 3, 441–454, 2003.

G.Z. YOYIADJIS, P.I. KATTAN, On the symmetrization of the effective stress tensor in continuum damage mechanics, Journal of the Mechanical Behavior of Materials, 7, 2, 139–165, 1996.

G.Z. YOYIADJIS, P.I. KATTAN, Advances in damage mechanics: metals and metal matrix composites, Elsevier Science, The Netherlands 1999.

DOI: 10.24423/engtrans.448.2005