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Within layered shell objects, straight normals remain straight, which enforces full composite behavior between layers. Straight normals do not necessarily remain normal to the mid-surface, which allows transverse shear deformation. For membrane and bending behavior, quadratic displacement fields are assumed, with appropriate handling to prevent shear locking. Plane-stress behavior is assumed within each layer.
Formulation
Details on the formulation of layered shells are available in the CSI Analysis Reference Manual (The Shell Element > Layered, page 159).
Layered Shell FAQ
- Frequently Asked Questions which concern layered shells are as follows:
Are nonlinear shell objects available?
Answer: Yes, material nonlinearity may be applied to layered shell objects.
What is the multi-axial failure criteria available to nonlinear layered shells?
Extended Question: My understanding is that a failure criteria is necessary to define a yield surface for the multi-axial stress state of brittle and ductile materials. Is the failure criteria Von Mises, Rankine, Tresca, maximum principle stresses, or maximum principle strains?
Answer: Multi-axial failure criteria is not incorporated into the formulation of the nonlinear layered shell objects currently available to SAP2000.
Von Mises stresses, however, are calculated and reported when using the SVM stress-component label. Additional stresses may be calculated by post-processing reported results.
For each direction, redistribution of forces may be modeled according to the nonlinear response of the material stress-strain curve, rather than the multi-axial stress state.
What is the difference between Direction and Coupled material component behavior?
In a layered shell section, there are two types of layers: Directional and Coupled. The Directional type of layered shell will apply the uniaxial stress-strain curve defined in the material property in the S11, S22, and/or S12 directions but each direction will be independent of each other. For example, yielding in the S11 direction will not affect the S22 direction and Poisson's ratio will be 0. The Coupled type of layered shell will use the coupled nonlinear data in the material property and the S11, S22, and S12 directions of the layer are nonlinear and are dependent on each other, hence "coupled". The behavior is dependent on the material type: if concrete, the coupled material is a biaxial concrete material, and if steel, the coupled material is a Von Mises plasticity material.
More information on this can be found at:
- Analysis Reference Manual Chapter "The Shell Element", Section "Layered Section Property > (8) Layer Material Behavior"
- "Modified Darwin-Pecknold 2-D Reinforced Concrete Material Model" technical note for the coupled concrete material
- "Coupled Nonlinear Material Data Form" and "Von Mises Plasticity Model" Help topics