Mori-Tanaka Stiffness Homogenization for Short Fibers

Calculate the homogenized stiffness for an RVE of short fibers in a matrix material where the orientation state is described using Advani's orientation tensor.

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Version 1.0 - published on 01 Jun 2018

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This tool uses the Mori-Tanaka model [1,2] to predict the stiffness of a short fiber composite with an orientation state described with a second-order orientation tensor[3].

Stiffness, as a fourth-order tensor property, requires the fourth-order orientation tensor, but since this is not often used in practice, we approximate it using one of several closure approximations.

The linear closure approximation gives exact results for random orientation states, the quadratic closure approximation gives exact results from aligned orientation states, and the hybrid closure approximation provides a linear combination of the linear and quadratic methods[3].

The final closure approximation provided is a quadratic, orthotropic fitted closure approximation[4-5].


[1] T Mori, and K. Tanaka. “Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions.” Acta Metallurgica 21, no. 5 (May 1973): 571–74.

[2] Benveniste, Y. “A New Approach to the Application of Mori-Tanaka’s Theory in Composite Materials.” Mechanics of Materials 6, no. 2 (June 1987): 147–57.

[3] Advani, Suresh G., and Charles L. Tucker III. “The Use of Tensors to Describe and Predict Fiber Orientation in Short Fiber Composites.” Journal of Rheology (1978-Present) 31, no. 8 (November 1, 1987): 751–84.

[4] Cintra Jr, Joaquim S., and Charles L. Tucker III. “Orthotropic Closure Approximations for Flow‐induced Fiber Orientation.” Journal of Rheology (1978-Present) 39, no. 6 (November 1, 1995): 1095–1122.

[5] Chung, Du Hwan, and Tai Hun Kwon. “Improved Model of Orthotropic Closure Approximation for Flow Induced Fiber Orientation.” Polymer Composites 22, no. 5 (n.d.): 636–49.

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Researchers should cite this work as follows:

  • Nicholas Smith (2018), "Mori-Tanaka Stiffness Homogenization for Short Fibers,"

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