I am looking for guidance for analyzing composite materials that are reinforced by fibers of some sort. A good mental model would be bars of steel in concrete. The concrete will have its own physics that is essentially isotropic where the steel only plays a significant role in a given direction.

My actual problem has more than one orientation but if I can at least understand how they do this in principle I may be able to take it from there.

I am not sure how to specify a "fiber" and give it a length and orientation. The papers I have been reading do not seem to explicitly model the fibers but some how capture this anisotropic behavior in the elements. I am somewhat of a novice on this space and the papers I have seen thus far assume a level of competence to fill on the gaps.

Any advice or reference to a tutorial that does something similar would be much appreciated.

  • $\begingroup$ Also consider if the fibres are fixed to the material along the complete length or they slide past each other. $\endgroup$
    – Solar Mike
    Apr 16, 2021 at 18:54
  • $\begingroup$ @Solar Mike these fibers would not allow relative motion between the fiber and the bulk material $\endgroup$ Apr 16, 2021 at 20:28
  • $\begingroup$ Are you interested in developing a solver for analysis or do you want to use an already developed material model? If that the latter have you decided on the platform you will be using? ( because as I stated in my answer its very much platform specific) $\endgroup$
    – NMech
    Apr 16, 2021 at 20:53
  • $\begingroup$ @NMech I am very much a consumer and I am just looking for guidance in setting up my problem. I am working with deal.II which is opensourced. I think what you suggested of doing something to conditionally have an addtional term in the stress would suit my needs but I am not sure at a general level how that could be done. A reference paper that I am following is doi:10.1016/S0021-9290(03)00267-7 $\endgroup$ Apr 16, 2021 at 22:06
  • $\begingroup$ I have some trouble accessing the article you are referencing (doi:10.1016/S0021-9290(03)00267-7). Is it an article in Journal of Biomechanics, 2005 by Wilson ? $\endgroup$
    – NMech
    Apr 16, 2021 at 23:34

2 Answers 2


You should first identify the purpose of using fiber reinforced concrete (FRC), what it is for, and what it is to improve, then how to achieve the goal.

In the attached article, it states:

" Fiber-reinforced concrete is used to overcome the difficulty of plain cement concrete which gives very low tensile strength, low ductility strength, and a little strength to cracking. Also in plain cement concrete is a chance of brittle fracture because of the propagation of micro-cracks present in the concrete that makes poor tensile strength."

However, it continues to state:

"By using conventional in first steel bars and by applying restraint techniques engineers and scientists want to improve the tensile property of concrete. Both of the above meters increase compressive strength to concrete members but do not increase the inherent tensile strength of concrete in their own way."

Next, you need to know the different types of fibers, their properties, and advantages and disadvantages.

Other than the type of fiber, one of the most important properties of fiber reinforced concrete is the "aspect ratio" of the fiber.

"The aspect ratio (ratio of its length to its diameter) (l/d) of the fibre is one of the important properties. Its value is in the range of 30 to 150. The properties and behavior of the fiber composite are also dependent upon the aspect ratio. According to research the relation between aspect ratio and ultimate strength of the composite is linear up to an aspect ratio of 75. But more than 75 of the aspect ratio relative strength and toughness is reduced. As shown in the table below."

enter image description here

Also, "The strength and toughness of the fiber and cement composite are depended upon the volume of the fibers used, the relation is generally linear, means a form of fibers increases the strength and toughness of the composite also increases. The drawbacks of the large value of fiber cause segregation of concrete and mortar."

enter image description here

The above are excerptions from the linked article, https://cementconcrete.org/concrete/fiber-reinforced-concrete-frc/2524/

  • $\begingroup$ Good point. I do want to play with the fiber density but I consider that step 2 from actually having them in the model. $\endgroup$ Apr 16, 2021 at 20:30
  • $\begingroup$ @TheCodeNovice See this article which discusses the evaluation of Yong's Modulus for steel fiber reinforced concrete. ceij.ut.ac.ir/… $\endgroup$
    – r13
    Apr 16, 2021 at 20:52
  • $\begingroup$ this is great info and I think most of it transfers. I am not working in concrete actually I was just using it as an example. A relevant paper is doi:10.1016/S0021-9290(03)00267-7 . I still would need to think about much of what you raise. Thank you for the great answer! $\endgroup$ Apr 16, 2021 at 22:08
  • $\begingroup$ You are welcome. Best wishes toward your research. $\endgroup$
    – r13
    Apr 16, 2021 at 22:13

This is very much platform specific. In general there are many ways of approaching this.

A common approach among solvers for unidirectional fiber composite materials (until up to a last decade, because I am a bit rusty on recent developments), is that use 2d elements (see shell elements), and through the thickness they define layers with the orientation of the composites.

Sometimes you can get away with defining only the fibre and matrix material properties and their interface and sometimes you can just define the full "stiffness" matrix of the layer with the anisotropic properties ($E_{11}, E_{22}, E_{33}, G_{12},G_{23}, G_{13}, \nu_{12},\nu_{13}, \nu_{22}$.

The main problems with this approach are mainly:

  • It is difficult to obtain the mechanical properties which are based on the interaction between the fibre and the matrix, which more often than not has an effect on the accuracy of the simulation.
  • it is difficult to follow the contour of complex 3d geometries and therefore map the properties of the material (usually there are preprocessing addons that do that job but they used to be expensive)

Additionally, another problem is the modelling of fabric, but that is another issue.

  • $\begingroup$ I like the idea of having an additional layer on top of the elements I have representing the non fiber part. Not sure how to do that though. $\endgroup$ Apr 16, 2021 at 22:06
  • $\begingroup$ I've never worked with deal.II. Have you checked whether it has a composite material model? $\endgroup$
    – NMech
    Apr 16, 2021 at 23:47

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Not the answer you're looking for? Browse other questions tagged or ask your own question.