A multiscale approach for composite materials as multifield continua Patrizia Trovalusci 1,a , Vittorio Sansalone 2,b and Fabrizio Cleri 2,c 1 Dipartimento di Ingegneria Strutturale e Geotecnica, Università "La Sapienza, via Gramsci 53, I-00197 Roma (Italy) 2 Ente Nuove Tecnologie, Energia e Ambiente, Unità Materiali e Nuove Tecnologie, Centro Ricerche Casaccia, C.P. 2400, I-00100 Roma A. D. (Italy) a patrizia.trovalusci@uniroma1.it, b vittorio.sansalone@casaccia.enea.it, c cleri@casaccia.enea.it Keywords: fibre-reinforced composites, micro-mechanical modelling, constitutive models. Abstract. A continuum model for composite materials made of short, stiff and tough fibres embedded in a more deformable matrix with distributed microflaws is proposed. Based on the kinematics of a lattice system made of fibres, perceived as rigid inclusions, and of microflaws, represented by slit microcracks, the stress-strain relations of an equivalent multifield continuum is obtained. These relations account for the shape and the orientation of the internal phases and include internal scale parameters, which allow taking into account size effects. Some numerical analyses effected on a sample fibre-reinforced composite pointed out the influence of the size and orientation of the fibres on the gross behaviour of the material. Introduction The growing demand for high-performance structural materials in several domains of engineering and technology has spurred the research in the field of complex, composite materials, such as: polyphase metallic alloy systems, polymer blends, polycrystalline, porous or textured media, fibre- matrix composites, up to masonry-like materials and biomaterials. The ability to design such materials, and to derive their macroscopic properties relies, in turn, on the ability to take into account the (possibly evolving) internal structure, size, shape, spatial distribution of the microstructural constituents by multi-scale and multi-level computational methods [1]. Various approaches have been used to describe the mechanical behaviour of complex materials, most of them based on the homogenization theory [2]. The conventional homogenized models are based on the standard Cauchy continuum and present two major disadvantages. First, they cannot predict the effect of the size and orientation of the heterogeneities, since they deal with only the volume fraction and, in some cases, the morphology of the internal phases distribution. Second, they intrinsically assume the macroscopic uniformity of the stress-strain fields in each representative volume, which is likely to be unappropriate in critical regions of high gradients, e.g. in the vicinity of a macroscopic discontinuity such as a joint or a hole, or close to the point of application of a localized load. A way to retain memory of the fine organization of a material, without renouncing to the advantages of the continuum modelling and avoiding the above mentioned drawbacks, is to resort to the multifield theory [3]. The models developed in this framework have to be understood as continua with different material levels: the macro-structural level of the matrix and one or more micro-structural levels, characterized by the presence of descriptors additional to the standard ones. Therefore, non-standard strain and stress measures can be defined in a rational way, and suitable scale parameters naturally surface, which allow distinguishing the behaviour of media with heterogeneities of different size and orientation. The applicability of such models relies on the possibility to define constitutive functions for all the stress measures introduced. In this work a multiscale approach to derive these functions is proposed starting from the description of the material at the scale of the internal phases (micro-model), the fibres and the Materials Science Forum Vols. 539-543 (2007) pp. 2551-2556 online at http://www.scientific.net © (2007) Trans Tech Publications, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net . (ID: 82.55.228.30-11/01/07,20:44:16)