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How to Model Concrete Reinforcement Using Finite Elements

Rebar Modeled with Spar Elements | FEA Consulting
May 1, 2015 By: Peter Barrett

Concrete structures include all types of reinforcement: rebars, wire mesh, steel/composite wraps or plates, pre-tensioned or post-tensioned cables, glass fiber reinforcement polymer (GFRP), etc. All have the purpose of carrying tensile forces while relying on the concrete to carry the compression loads. A common question in the finite element modeling of concrete reinforcement is: How do I model this reinforcement? It’s a straight forward question, but not easy to answer since it depends on the goal of the analysis.

For elastic design analyses, the reinforcement is usually neglected in the finite element modeling since the stiffness contribution of the concrete is much greater than the reinforcement. The reinforcement can safely be assumed to keep the composite structure intact, and thus act (for analysis purposes) as a homogenous elastic body. Forces and moments are then extracted from the FEA solution and used as a basis to size the reinforcement needed to carry the net tensile forces in the section while taking into account code requirements, concrete cover etc.

If a nonlinear analysis is needed, like in a situation where the ultimate capacity is to be determined, then modeling of reinforcement is needed. The two most common options include smeared reinforcement modeling to include the independent nonlinear response, but not calculate discrete rebar stresses; and discrete reinforcement modeling which can capture yield and/or slippage of individual bars.

Smeared rebar elements are added to the stiffness of the continuum elements, or added as a layer to a composite brick or shell element. The rebar element effectively sits on top of the existing concrete elements, and thus uses the same nodes as the underling concrete elements. Additional stiffness properties are typically defined by a percentage of the element area in up to three discrete directions controlled by the user input.This hybrid element behaves similarly to 2 elements on top of each other (1 concrete and 1 steel).   Be careful when you define the reinforcement ratio since it is a function of the element size! For the same rebar spacing, if you change the mesh you must also change the reinforcement ratio. Be sure to define the correct orientations of the elements since the rebar is typically based on the element coordinate system (See Figure 1).

The value of this method is that it does not require explicit modeling of the rebar, and thus a much coarser mesh can be defined. For overcoming difficult convergence issues, I find that using a very small smeared rebar reinforcement ratio, to add a small tensile stiffness after cracking, is often useful for mass concrete applications (where no rebar exists) and even when discrete rebar is also modeled. ANSYS and LS-DYNA are two finite element codes that employ these types of smeared reinforcement elements.

Figure 1: Smeared Rebar Orientation in ANSYS Solid65 Element

Alternately, reinforcement can be modeled in a discrete manner using link, spar or beam elements found in all finite element software. These reinforcing spars can either be merged to the solid concrete elements (shared nodes), or may be tied to the concrete elements using either point-to-point or surface to surface contact, with the added advantage of providing the ability to model bond slip. Figure 2 illustrates rebar modeled explicitly in an abutment retaining wall.

Rebar Modeled with Spar Elements

Sometimes a combination of methods is best. For stirrup or spiral reinforcement, it might not make sense to try and model these explicitly. When modeling post-tensioned tendons, explicit modeling is the best approach since the pre-load plays a major factor in the structural response. One can then use features such as initial strain to incorporate the pre-stress into the model.

How do you currently model concrete reinforcement? I would love to hear how others approach the successful modeling of reinforced concrete structures using finite elements.