# Concrete02 with Control of the Initial Stiffness

Although they have the same compressive envelope, Concrete02 offers more features than Concrete01--tension strength, tension stiffening, and compressive unloading/reloading loops. However, one thing Concrete02 (and Concrete01) lacks is control over the initial stiffness, which is fixed at $latex E_c=2f'_c/\varepsilon_{c0}$. To overcome this limitation with Concrete02, Dr. Nasser Marafi created Concrete02IS (Concrete02 with control of the … Continue reading Concrete02 with Control of the Initial Stiffness

# Direct Moment-Curvature

That the force-based frame element and fiber sections are in an open relationship should come as no surprise. The displacement-based and mixed frame elements can use fiber sections and all three element formulations can use stress resultant sections. While this post used a coupled stress resultant plasticity model, you can also use the section aggregator … Continue reading Direct Moment-Curvature

# Making Sense Out of Concrete02

Those three extra parameters for Concrete02 are usually enough to make me stick with Concrete01. I struggle to come up with good values for the parameters $latex \lambda$, $latex f_t$, and $latex E_{ts}$ shown in the following image from the OpenSees Concrete02 wiki page. Image developed by Dr. Silvia Mazzoni The four compressive backbone parameters … Continue reading Making Sense Out of Concrete02

# You Gotta Keep ’em Aggregated

The SectionAggregator was one of my few useful OpenSees ideas. This class gives a flexible way to combine, or aggregate, modes of force-deformation in a single section model. The idea for SectionAggregator came from the Decorator software design pattern, the same pattern from which so many UniaxialMaterial wrappers were spawned (here and here). In fact, … Continue reading You Gotta Keep ’em Aggregated

# Elastoplastic Calibration

You can do a lot with UniaxialMaterials in OpenSees--springs, fibers, trusses, section aggregators, etc. Although over 130 UniaxialMaterials are available, it's likely that only about a dozen see regular use. So, with all due respect to Concrete23, my favorite regular is HardeningMaterial. It's straight out of Simo and Hughes and was the example material for … Continue reading Elastoplastic Calibration

# Stress Resultant Verification

Verifying material nonlinear frame element formulations is pretty difficult. There are only a handful of analytical solutions that do not rely on bilinear uniaxial constitutive response. You're much better off verifying geometric nonlinearity. However, an example based on a relatively straightforward biaxial stress resultant plasticity model has intrigued me over the years. The example, described … Continue reading Stress Resultant Verification

# Fiber Section Centroids

If you define a fiber-discretized cross section in OpenSees using section coordinate systems A and B shown below, will you get the same response when you apply axial load and bending moments to the sections? The answer is yes. You will get the same response from sections A and B. The fiber sections compute the … Continue reading Fiber Section Centroids

# Hysteretic Pinching Parameters

I receive a lot of questions about the pinching parameters for the HystereticMaterial in OpenSees. Despite the best of intentions, one-off responses to these queries often went unanswered. But now, with the blog, a one-off response has staying power. So, here goes. The HystereticMaterial dates back to the G3 days. Along with Steel01 and Concrete01, … Continue reading Hysteretic Pinching Parameters

# Uniaxial Multi-Tool

UniaxialMaterial models are the work horses of OpenSees. Originally developed for the truss element, these models have proliferated thanks to fiber section models. However, because they are simply scalar functions, UniaxialMaterial models can be used in several other contexts. The calling function knows the context, not the UniaxialMaterial model--it only provides an output for a … Continue reading Uniaxial Multi-Tool

# Fibers of Higher Dimensions

When we talk about fiber sections in OpenSees, we often refer to Bernoulli sections where each fiber is in a state of uniaxial stress. This approach captures axial-moment interaction, which is important for reinforced concrete columns, whose cross-sections are defined using patch and layer commands. Those same patch and layer commands can be used for … Continue reading Fibers of Higher Dimensions