Opensees – New uniaxial material – ASD SMA 3K

ASD_SMA_3K is a new uniaxial material of opensees written by Eng. Luca Aceto (luca.aceto@unich.it), University of Chieti-Pescara, InGeo department, in collaboration with ASDEA Software Technology: https://asdeasoft.net. Accepted on 14 November 2020.

ASD_SMA_3K It is a modified version of the Self Centering Material, already available in opensees and written by JAE (2007). With ASD_SMA_3K it is possible to replicate SMA material’s behavior with a different unloading stiffness (k3) while only 2 values of stiffness characterize self Centering Material. In this last material, the first value of stiffness (K1) governs the loading branches, and another one (k2) influences the post-activation branches.

In some cases, SMA materials exhibit the different stiffness of unloading sections of the constitutive bond. In this context, ASD_SMA_3K has become necessary to describe this behavior.

• k1 = Loading stiffness
• k2 = Post-Activation Stiffness (0<$k2<$k1)
• k3 = Unloading stiffness
• sigAct = Forward Activation Stress/Force
• beta= Ratio of forward to Reverse Activation Stress/Force

Opensees command:
uniaxialMaterial ASD_SMA_3K $matTag $k1 $k2 $k3 $sigF $beta

In the following instance, the material is tested with a simple cyclic time history as the subsequent images:

The response of the material is reported following graph.

To test the material under various load conditions, we tried some time histories like the next one.

In this first, we wanted to test the response under reloading without full unloading both if the last branch of unloading is touched and if it is untouched.

The results highlight that all the unloading branch are governate of K3 value, while the reloading is ruled by K1 stiffness. The post-peak branch is tilted as a function of K2 stiffness.

In the last instance, the material is tested with a real earthquake time history. In this case, it is manifest that the material does not have any numerical issues in quasi-random time history.