A simple method for quantifying the size effect on fiber orientation distribution functions (ODFs) in fiber-reinforced concrete

Fiber orientations are constrained by boundary effects (e.g. size effect), which play a significant role in the macroscopic rigidity of fiber-reinforced concrete (FRC). However, how to quantify the size effect on the fiber orientation distribution functions (ODFs) remain to be open issues. In this work, a simple method to quantify the sectional-size impact on fiber ODFs is proposed. By disassembling the fiber rotatable range and fiber location on the cross-section into several small facets and points, respectively, we draw out the fiber ODFs with different sectional sizes through superposition. Then, the calculation method of the fiber orientation factor based on the ODF is proposed, and the framework of applying an ODF to calculate the stiffness matrix is given. Our results revealed the influence of the cross-section size on the elastic properties of FRC, which can provide a sound guidance for the design and optimization of fiber-based cement composites. Highlights 1. A practical method for discretizing the cross-section of fiber-reinforced concrete (FRC) into a point set is proposed. 2. A quantitative interplay between boundary constraints and size effects on fiber ODFs is developed. 3. The calculation framework of the fiber orientation factor and elastic modulus of the FRC based on the ODF is established. 4. The difference between the effective elastic modulus and Poisson’s ratio of FRCs with different boundary constraints is discussed.