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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 51
2D Finite Element Model for the Analysis of Elastic-Plastic Composites Subjected to 3D Stresses A. Taliercio
Department of Structural Engineering, Politecnico di Milano, Italy Full Bibliographic Reference for this paper
A. Taliercio, "2D Finite Element Model for the Analysis of Elastic-Plastic Composites Subjected to 3D Stresses", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 51, 2004. doi:10.4203/ccp.79.51
Keywords: fiber-reinforced composites, metal-matrix composites, plasticity, finite elements, homogenization, generalized plane strain.
Summary
A numerical model is formulated to predict the macroscopic response of
ductile-matrix composites reinforced by a regular array of long, parallel fibers,
subjected to any 3D stress. A micromechanical
approach is employed, based on homogenization theory for periodic media,
which consists in submitting a Representative Volume Element (RVE)
to any prescribed increasing macroscopic strain
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Special finite elements
are formulated to analyze any cross-section of the RVE (a prism of unlimited length,
embedding a single fiber) under `generalized
plane strain conditions' (i.e., with strain fields invariant along the fiber axis
where
The six independent (infinitesimal) engineering strains associated with eq. (12) are collected into an array
where
Finite elements of this type, with 3 or 4 nodes each, are employed to discretize
any cross-section of the RVE of a metal-matrix composite. Both the fiber and the matrix
material are supposed to be perfectly plastic and to comply with
It is well known that finite element solutions dealing with incompressible materials are
prone to `locking' effects when approaching the fully plastic range. According to [1],
this problem is circumvented by introducing some `modified strains' (
where Finally, particular kinematic conditions are enforced along the boundary of the model to accommodate the periodicity of the microscopic strain field over the RVE. The effectiveness of the proposed model in predicting the macroscopic response of MMCs beyond the elasticity limit was assessed through a number of numerical applications, where the macroscopic strains were monotonically increased until a macroscopic yielding was detected. The numerical results obtained were compared both with theoretical approximations for the macroscopic strength domain of the composite, available in the literature [2,3], and with experimental results obtained by other authors [4]. All the comparisons were quite satisfactory. Such a model turns out to be definitely advantageous in terms of allocated memory and number of kinematic constraints to be enforced, in comparison with fully 3D finite element models. References
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