diff --git a/source/user/manual/material/uniaxialMaterial.rst b/source/user/manual/material/uniaxialMaterial.rst index 6e3e8645..d1332db6 100644 --- a/source/user/manual/material/uniaxialMaterial.rst +++ b/source/user/manual/material/uniaxialMaterial.rst @@ -121,6 +121,7 @@ The following subsections contain information about **$matType** uniaxialMaterials/JankowskiImpact uniaxialMaterials/ViscoelasticGap uniaxialMaterials/Ratchet + uniaxialMaterials/FrictionSpringDamper .. uniaxialMaterials/CastFuse .. uniaxialMaterials/ViscousDamper diff --git a/source/user/manual/material/uniaxialMaterials/FrictionSpringDamper.rst b/source/user/manual/material/uniaxialMaterials/FrictionSpringDamper.rst new file mode 100644 index 00000000..762384ce --- /dev/null +++ b/source/user/manual/material/uniaxialMaterials/FrictionSpringDamper.rst @@ -0,0 +1,106 @@ +FrictionSpringDamper Material +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +This command is used to construct a FrictionSpringDamper uniaxial material object. The material models the force-deformation response of a self-centering friction spring damper. The model is based on the behavior described by Wang et al. (2019) in series with an elastic stiffness. + +.. function:: uniaxialMaterial FrictionSpringDamper $matTag $Ke $K $Kp $preload <-initialStrain $initStrain> + +.. list-table:: + :header-rows: 1 + :widths: 15 15 70 + + * * Parameter + * Type + * Description + * * `$matTag` + * integer + * Integer tag identifying the material. + * * `$Ke` + * float + * Elastic stiffness, as shown in the figure above. + * * `$K` + * float + * Loading stiffness, as shown in the figure above. + * * `$Kp` + * float + * Unloading stiffness, as shown in the figure above. + * * `$preload` + * float + * Preload, as shown in the figure above. + * * `$initStrain` + * float + * Optional initial strain. The default value is 0.0. + +.. figure:: figures/FrictionSpringDamper.png + :align: center + :figclass: align-center + :width: 70% + + Force-deformation response of the FrictionSpringDamper material. + +The effective secondary tangent stiffness during loading is + +.. math:: + + K_{eq1} = \left(\frac{1}{K_e}+\frac{1}{K}\right)^{-1} + +and the effective tangent stiffness during unloading is + +.. math:: + + K_{eq2} = \left(\frac{1}{K_e}+\frac{1}{K_p}\right)^{-1} + +The force associated with the transition during unloading and reloading is + +.. math:: + + F_2 = F_{preload}\frac{K_p}{K} + +where :math:`F_{preload}` is the specified `$preload`. + +The optional `-initialStrain` argument shifts the strain supplied to the constitutive model such that + +.. math:: + + \epsilon = \epsilon_{applied} + \epsilon_{initial} + +Thus, a nonzero initial strain can result in a nonzero initial force. + +.. admonition:: Example + + The following example creates a FrictionSpringDamper material with a tag of 1, elastic stiffness of 1000, loading stiffness of 200, unloading stiffness of 100, and preload of 50. + + **Tcl Code** + + .. code-block:: tcl + + uniaxialMaterial FrictionSpringDamper 1 1000.0 200.0 100.0 50.0 + + **Python Code** + + .. code-block:: python + + ops.uniaxialMaterial('FrictionSpringDamper', 1, 1000.0, 200.0, 100.0, 50.0) + + An initial strain can optionally be specified. + + **Tcl Code** + + .. code-block:: tcl + + uniaxialMaterial FrictionSpringDamper 1 1000.0 200.0 100.0 50.0 -initialStrain 0.01 + + **Python Code** + + .. code-block:: python + + ops.uniaxialMaterial('FrictionSpringDamper', 1, 1000.0, 200.0, 100.0, 50.0, '-initialStrain', 0.01) + +References: + +Wang, W., Fang, C., Zhao, Y., Sause, R., Hu, S., and Ricles, J. (2019). +"Self-centering friction spring dampers for seismic resilience." +*Earthquake Engineering & Structural Dynamics*, 48(9), 1045-1065. +https://doi.org/10.1002/eqe.3174 + +Code Developed by: Mark D. Denavit, University of Tennessee, Knoxville diff --git a/source/user/manual/material/uniaxialMaterials/figures/FrictionSpringDamper.png b/source/user/manual/material/uniaxialMaterials/figures/FrictionSpringDamper.png new file mode 100644 index 00000000..a60c5209 Binary files /dev/null and b/source/user/manual/material/uniaxialMaterials/figures/FrictionSpringDamper.png differ