Graduation Year


Document Type




Degree Name

MS in Materials Science and Engineering (M.S.M.S.E)

Degree Granting Department

Chemical Engineering

Major Professor

Autar Kaw, Ph.D.

Committee Member

Ali Yalcin, Ph.D.

Committee Member

Alex Volinsky, Ph.D.


void content, design of experiments, finite element modeling, elastic moduli


In composite materials, transverse shear modulus is a critical moduli parameter for designing complex composite structures. For dependable mathematical modeling of mechanical behavior of composite materials, an accurate estimate of the moduli parameters is critically important as opposed to estimates of strength parameters where underestimation may lead to a non-optimal design but still would give one a safe one.

Although there are mechanical and empirical models available to find transverse shear modulus, they are based on many assumptions. In this work, the model is based on a three-dimensional elastic finite element analysis with multiple cells. To find the shear modulus, appropriate boundary conditions are applied to a three-dimensional representative volume element (RVE). To improve the accuracy of the model, multiple cells of the RVE are used and the value of the transverse shear modulus is calculated by an extrapolation technique that represents a large number of cells.

Comparing the available analytical and empirical models to the finite element model from this work shows that for polymeric matrix composites, the estimate of the transverse shear modulus by Halpin-Tsai model had high credibility for lower fiber volume fractions; the Mori-Tanaka model was most accurate for the mid-range fiber volume fractions; and the Elasticity Approach model was most accurate for high fiber volume fractions.

Since real-life composites have voids, this study investigated the effect of void fraction on the transverse shear modulus through design of experiment (DOE) statistical analysis. Fiber volume fraction and fiber-to-matrix Young’s moduli ratio were the other influencing parameters used. The results indicate that the fiber volume fraction is the most dominating of the three variables, making up to 96% contribution to the transverse shear modulus. The void content and fiber-to-matrix Young’s moduli ratio have negligible effects.

To find how voids themselves influence the shear modulus, the transverse shear modulus was normalized with the corresponding shear modulus with a perfect composite with no voids. As expected, the void content has the largest contribution to the normalized shear modulus of 80%. The fiber volume fraction contributed 12%, and the fiber-to-matrix Young’s moduli ratio contribution was again low.

Based on the results of this work, the influences and sensitivities of void content have helped in the development of accurate models for transverse shear modulus, and let us confidently study the influence of fiber-to-matrix Young’s moduli ratio, fiber volume fraction and void content on its value.