Nonlinear Material Behavior | Isotropic | Nonlinear Elastic (Members, Surfaces/Solids)

This article describes and explains the influence of bending stiffness of cables on their internal forces. Furthermore, the text provides information on how this influence can be reduced.

The ASCE 7-22 Standard [1], Sect. 12.9.1.6 specifies when P-delta effects should be considered when running a modal response spectrum analysis for seismic design. In the NBC 2020 [2], Sent. 4.1.8.3.8.c gives only a short requirement that sway effects due to the interaction of gravity loads with the deformed structure should be considered. Therefore, there may be situations where second-order effects, also known as P-delta, must be considered when carrying out a seismic analysis.

This article presents the basic concepts in structural dynamics and their role in the seismic design of structures. Great emphasis is given to explaining the technical aspects in an understandable way, so that readers without deep technical knowledge can gain an insight into the subject.

Did you know? In contrast to other material models, the stress-strain diagram for this material model is not antimetric to the origin. You can use this material model to simulate the behavior of steel fiber-reinforced concrete, for example. Find detailed information about modeling steel fiber-reinforced concrete in the technical article about Determining the material properties of steel-fiber-reinforced concrete.

In this material model, the isotropic stiffness is reduced with a scalar damage parameter. This damage parameter is determined from the stress curve defined in the Diagram. The direction of the principal stresses is not taken into account. Rather, the damage occurs in the direction of the equivalent strain, which also covers the third direction perpendicular to the plane. The tension and compression area of the stress tensor is treated separately. In this case, different damage parameters apply.

The "Reference element size" controls how the strain in the crack area is scaled to the length of the element. With the default value zero, no scaling is performed. Thus, the material behavior of the steel fiber concrete is modeled realistically.

Find more information about the theoretical background of the "Isotropic Damage" material model in the technical article describing the Nonlinear Material Model Damage.

Did you know? When unloading the structural component with a plastic material model, in contrast to the Isotropic | Nonlinear Elastic material model, the strain remains after it has been completely unloaded.

You can select three different definition types:

• Standard (definition of the equivalent stress under which the material plastifies)
• Bilinear (definition of the equivalent stress and strain hardening modulus)
• Stress-strain diagram: definition of polygonal stress-strain diagram
• Option to save / import the diagram
• Interface with MS Excel

If you release a structural component with a nonlinear elastic material again, the strain goes back on the same path. In contrast to the Isotropic|Plastic material model, there is no strain left when completely unloaded.

You can select three different definition types:

• Standard (definition of the equivalent stress under which the material plastifies)
• Bilinear (definition of the equivalent stress and strain hardening modulus)
• Stress-Strain Diagram:
• Definition of polygonal stress-strain diagram
• Option to save / import the diagram
• Interface with MS Excel

Background information about nonlinear material models can be found in the technical article describing the yield laws in isotropic nonlinear elastic material model.