Post-Critical Analysis

Technical Article

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In the case of a post-critical failure, a substantial change in the geometry of a structure occurs. After reaching the instability of the equilibrium, a stable, strong position is reached again. The post-critical analysis requires an experimental approach. It is necessary to manually load the structure in increments step by step.


In the following, the punch-through problem is shown. The structural component can be thought of as a flat roof that is subjected to pressure from the outside. If the pressure is increased slowly, it first appears that the load is absorbed by a compressive stress and transferred to the support.

Figure 01 - Internal Forces According to Large Deformation Analysis

For a certain size of the compression load, the system becomes unstable, there is a breakdown.

Figure 02 - Unstable System: Post-Critical Failure

Figure 03 - Post-Critical Analysis

Then, the load can be increased again, which is then absorbed mainly by tension in the component.

Figure 04 - Post-Critical Analysis: Increasing Load

The second-order analysis can basically not cover the punch-through problem due to the linearization of the description of the deformation geometry.

Further information and examples can be found in [1] and [2].


[1]  Werkle, H .: Finite Elements in Structural Analysis - Structural Analysis and Dynamics of Member and Surface Structures, 3rd Edition. Berlin: Springer, 2008
[2] Lumpe, G .; Gensichen, V .: Evaluation of Linear and Nonlinear Member Structural Analysis in Theory and Software - Test Examples, Causes of Faults, Precise Theory. Berlin: Ernst & Sohn, 2014



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