Add FrictionSpringDamper docs

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

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