Problem description

The embedded beam structural element in PLAXIS 2D provides two options to elastoplastic behaviour: “Elastoplastic” and “Elastoplastic (M-κ)”:

 

Since the release of PLAXIS 2D 2024.2, an issue occurs when embedded beam material data sets using both material type options are present within the same project, i.e., using both the Elastoplastic and the Elastoplastic (M-κ) material type options.
This issue is triggered even if one of the material sets is not assigned to any embedded beam and is merely stored in the project material database.

As a result, the behaviour of embedded beams which are set to material type to “Elastoplastic” is calculated incorrectly, causing the structural element to behave as purely elastic. This may lead to unconservative or misleading results.

Note that the behaviour of embedded beams which are set to material type to “Elastoplastic (M-κ)” is correctly calculated, and the values in the M-κ diagram are considered in the analysis.

The issue does not occur when only one embedded beam material type is used throughout the entire project, i.e., either exclusively “Elastoplastic” OR exclusively “Elastoplastic (M–κ)”.

Workaround

Currently, the only available workaround with PLAXIS 2D 2024.2 and later versions, is to only use a single material type option for all embedded beam material sets within a project.

All embedded beam material data sets in the material database must be defined using either:

• “Elastoplastic”, or
• “Elastoplastic (M–κ)”

Any combination of these two material types within the same project, regardless of whether the materials are actively assigned or used, will trigger the issue.

Alternative, you can use PLAXIS 2D 2024.1. You download any versions via the Software Downloads page.

We are working on solving this issue in our next release of PLAXIS 2D.

 

Example using “Elastoplastic (M–κ)” instead of “Elastoplastic” material type

Let’s consider that for the embedded beam in your project you want to simulate your “Elastoplastic” material type with the “Elastoplastic (M–κ)”.

Assumptions:
•    Stiffness, E = 10.000 E6 kN/m²
•    Moment of Inertia, I = 0.1917 E-3 m⁴
•    Maximum bending moment, |M_p| = 200 kN m
•    Maximum axial force, |N_p,tens| = |N_p,comp| = 800 kN

When using the “Elastoplastic (M–κ)” material type for embedded beams, the bending behaviour is controlled by a user-defined moment – curvature (M-κ) diagram. 
It is important to be aware that in this material type, the axial force (N) is treated as elastic and independent of the bending moment (M). Therefore, it is not possible to provide a value for the maximum axial force (N_p), and it cannot be integrated into the M-κ diagram, which exclusively governs the flexural (bending) response.

The user-defined moment – curvature (M-κ) diagram requires data in a form of a table. The first row is by default set to the starting point: (κ, Μ) = (0, 0)

Based on the assumed values, the first step is to compute the Elastic Bending Stiffness (EI):

• EI = (Stiffness) E * (Moment of Inertia) I  
• EI = 1917 kNm²

The second row of the M-κ diagram table is the elastic bending stiffness, which represents the linear elastic behaviour up to the plastic moment. The plastic moment value is provided as the maximum bending moment|M_p|. This should be the value at which the element fails. The Yield curvature (κ) value is computed as:

κ = M_p / EI
κ = 0.1043 1/m

Therefore, the second row of the table is: (κ, Μ) = (0.1043, 200)

To represent perfect plasticity after the yield point, you need to add at least one more point with an increased curvature but the same maximum plastic moment.

Therefore, for the third row in the M-κ diagram table, you need to choose a curvature value significantly larger than κ to clearly illustrate the plastic plateau. 
For example, the third row of the table can be: (κ, Μ) = (0.2000, 200)

An overview of the example is shown in the screenshot below:

We are working on solving this issue in our next release of PLAXIS 2D.