Opensees – New uniaxial material – ASD SMA 3K

Try it on Opensees

ASD_SMA_3K is a new uniaxial material of opensees written by Eng. Luca Aceto (, University of Chieti-Pescara, InGeo department, in collaboration with ASDEA Software Technology: 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.

Opensees - SMA_3K

  • 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.

Opensees - SMA_3K

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.

Opensees - SMA_3K

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.

Opensees - SMA_3K

Opensees - SMA_3K

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