Modeling of fiber orientation in viscous fluid flow with application to self-compacting concrete

• Fiber orientation during fiber-reinforced fresh concrete casting process is modeled.
• Solutions of Fokker–Planck equation and orientation tensors are compared.
• Fresh concrete is modeled as a Bingham fluid.
• Model is validated against real casting experiment.

In recent years, the application of Self Compacting Concrete (SCC) in industry is rapidly growing, which makes modeling of SCC casting an important part of the design process. The SCC is often combined with fiber reinforcement to deliver a high performance material, the properties of which depend on fiber orientation. Fiber reinforced SCC plays a fundamental role in reducing shrinkage effects in structures. The aim of this paper is to present a numerical model for the prediction of the fiber orientation state, determined on the basis of the knowledge of the velocity field. Statistical approach is employed, where orientation of a fiber is described by a probability distribution of the fiber angle, which evolves with the flow. Two ways how to solve the evolution of the probability distribution are presented. In the first way, evolution equation for the orientation distribution function (ODF) is derived and solved by FEM. In the second way, evolution equation for second-order orientation tensor, which represents the second statistical moment of ODF, is solved instead. The model is validated against experimental results.