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International Journal for Multiscale Computational Engineering
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ISSN Imprimir: 1543-1649
ISSN En Línea: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v2.i4.80
29 pages

Nonlinear viscoelastic analysis of statistically homogeneous random composites

Michal Sejnoha
Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thakurova 7,166 29 Prague 6, Czech Republic
R. Valenta
Faculty of Civil Engineering, Department of Structural Mechanics, Czech Technical University in Prague, Thakurova 7,166 29 Prague 6, Czech Republic
Jan Zeman
Department of Mechanics, Faculty of Civil Engineering, Czech Technical University in Prague, Thakurova 7,166 29 Prague 6, Czech Republic; Centre of Excellence IT4Innovations, VSB-TU Ostrava, 17 listopadu 15/2172 708 33 Ostrava-Poruba, Czech Republic

SINOPSIS

Owing to the high computational cost in the analysis of large composite structures through a multiscale or hierarchical modeling, an efficient treatment of complex material systems at individual scales is of paramount importance. Limiting the attention to the level of constituents, the present paper offers a prosperous modeling strategy for the prediction of nonlinear viscoelastic response of fibrous graphite-epoxy composite systems with possibly random distribution of fibers within a transverse plane section of the composite aggregate. If such a material can be marked as statistically homogeneous and the mechanisms driving the material response fall within a category of the first-order homogenization scheme the variational principles of Hashin and Shtrikman emerge as an appealing option in the solution of uncoupled micro-macro computational homogenization. The material statistics up to two-point probability function that are used to describe the morphology of such a microstructure can be then directly incorporated into variational formulations to provide bounds on the effective material response of the assumed composite medium. In the present formulation the Hashin-Shtrikman variational principles are further extended to account for the presence of various transformation fields defined as local eigenstrain or eigenstress distributions in the phases. The evolution of such eigen-fields is examined here within a framework of the nonlinear viscoelastic behavior of a polymeric matrix conveniently described by the Leonov model. A fully implicit integration scheme is implemented to enhance the stability and efficiency of the underlying numerical analysis. A special choice of reference medium with a deformation-dependent shear modulus is proposed in order to improve the redistribution of averaged local fields due to local stress inhomogeneities associated with nonlinear viscoelastic response of the matrix phase. The present modeling strategy is further promoted by a good agreement of the results, including estimated effective thermoelastic properties, with the predictions of a direct microstructural computation.


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