Macroscopic damage in periodic composite materials

SUMMARY In this paper a simple way to describe the eects of microscopic damage on the global behaviour of periodic composite materials is shown. The microscopic damage is interpreted as a local reduction in material stiness as presented in Zohdi et al. [1]. Choosing the damage parameters in an opportune manner a great variety of dierent damage constitutive laws can be studied. The macroscopic constitutive law for damaged periodic composites is obtained with a homogenization procedure described in Pellegrino et al. [2]. A comparison between the results of homogeneous and heterogeneous constitutive models is shown. Copyright ? 2000 John Wiley & Sons, Ltd. In this paper two simple numerical techniques are combined to study the eect of microscopic damage on the global behaviour of a periodic composite material. The microscopic damage is represented, following Zohdi et al. [1], as a reduction of the eigenvalues of the material stiness tensor aecting the point where a given condition is violated. The local consequences of the damage process, such as redistribution of stresses or development of fractures, are not the main objective of this paper. On the contrary, we aim at describing the eect that the local reduction of the stiness has on the global behaviour of a macroscopic structure. Since a precise description of the ne scale material distribution would require an enormous number of nodes, in the nite element model, and therefore a large computer time to solve the problem, a homogenization approach is considered. In this manner a much simpler mesh can be adopted for the global problem to reduce the solution time. The paper is organized as follows: in Section 2 a brief description of the damage model is given followed in Section 3 by some words on the homogenization procedure. Section 4 presents some results which highlight the potentialities of the method and nally some concluding remarks close the paper.