Nonlinear shells may exhibit strain localization when materials or components lose strength. This phenomenon is well-described in engineering literature, readily observed in reality, and implemented within CSI Software. It may be challenging to create a model such that localization occurs as it will in a real structure, though mathematical simulation does capture the mechanical attributes, and correlate with the underlying principles.
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When the model uses nonlinear layered shells, stresses are nearly uniform until the concrete reaches its cracking strength, at which point nonuniform distributions may be observed, as shown in Figure 1:
Figure 1 - Localization of material nonlinearity
As expected, this behavior is the result of localization. In both the analytical model and the real structure, localized cracks will form in distinct locations. Reinforced concrete will not lose strength uniformly, and the entire slab will not simultaneously crumble under tension. Instead, steel will carry the entire load across crack openings, and where cracking has not occurred, concrete will share the load with steel reinforcement. The example shown in Figure 1 is consistent with this explanation. Cracking is found to occur across the upper row of elements, vertical steel is found to carry all tension, and displacement is more pronounced in the region of cracking. Once this region begins to crack, stresses are relieved within the rest of the domain, which does not crack.
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