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Research Papers

Spectral Stiffness Microplane Model for Quasibrittle Composite Laminates—Part I: Theory

[+] Author and Article Information
Gianluca Cusatis1

CEE Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180cusatg@rpi.edu

Alessandro Beghini

 Owings and Merrill LLP, 224 South Michigan Avenue, Chicago, IL 60604alessandro.beghini@som.com

Zdeněk P. Bažant2

Walter P. Murphy Professor and McCormick School Professor of Civil Engineering and Materials Science, CEE Department, Northwestern University, 2145 Sheridan Road, Evanston, IL, 60208z-bazant@northwestern.edu

1

Formerly, Research Associate at the CEE Department, Northwestern University.

2

Corresponding author.

J. Appl. Mech 75(2), 021009 (Feb 25, 2008) (9 pages) doi:10.1115/1.2744036 History: Received November 15, 2005; Revised February 07, 2007; Published February 25, 2008

The paper presents the spectral stiffness microplane model, which is a general constitutive model for unidirectional composite laminates, able to simulate the orthotropic stiffness, prepeak nonlinearity, failure envelopes, and, in tandem with the material characteristic length, also the post-peak softening and fracture. The framework of the microplane model is adopted. The model exploits the spectral decomposition of the transversely isotropic stiffness matrix of the material to define orthogonal strain modes at the microplane level. This decomposition is a generalization of the volumetric-deviatoric split already used by Bažant and co-workers in microplane models for concrete, steel, rocks, soils, and stiff foams. Linear strain-dependent yield limits (boundaries) are used to provide bounds for the normal and tangential microplane stresses, separately for each mode. A simple version, with an independent boundary for each mode, can capture the salient aspects of the response of a unidirectional laminate, although a version with limited mode coupling can fit the test data slightly better. The calibration of model parameters, verification by test data, and analysis of multidirectional laminates are postponed for the subsequent companion paper.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) Microplane orientations (normals defined by radial lines through circled points); (b) spherical coordinate system; and (c) coordinate system for laminates

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Figure 2

Effect of a macroscopic strain applied in fiber direction on (a) mode II, and (b) mode III

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Figure 3

Effect of a macroscopic strain applied in transverse direction on (a) mode II, (b) mode III, and (c) mode I

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Figure 4

Mean slope Et of the post-peak softening curve

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