Hysteresis is the process of energy dissipation through deformation (displacement), as opposed to viscosity which is energy dissipation through deformation rate (velocity). Hysteresis is typical of solids, whereas viscosity is typical of fluids, although this distinction is not rigid.
Hysteretic behavior may affect nonlinear static and nonlinear time-history load cases that exhibit load reversals and cyclic loading. Monotonic loading is not affected.
Several different hysteresis models are available to describe the behavior of different types of materials. For the most part, these differ in the amount of energy they dissipate in a given cycle of deformation, and how the energy dissipation behavior changes with an increasing amount of deformation.
Each hysteresis model may be used for the following purposes:
Material stress-strain behavior, affecting frame fiber hinges and layered shells that use the material
Single degree-of-freedom frame hinges, such as M3 or P hinges. Interacting hinges, such as P-M3 or P-M2-M3, currently use the isotropic model
Link/support elements of type multi-linear plasticity
For each material, hinge, or link degree of freedom, a uniaxial action vs. deformation curve defines the nonlinear behavior under monotonic loading in the positive and negative directions.
Here action and deformation are an energy conjugate pair as follows:
For materials, stress vs. strain
For hinges and multi-linear links, force vs. deformation or moment vs. rotation, depending upon the degree of freedom to which it is applied
For each model, the uniaxial action-deformation curve is given by a set of points that you define. This curve is called the backbone curve, and it can take on almost any shape, with the following restrictions:
One point must be the origin, (0,0)
At least one point with positive deformation, and one point with negative deformation, must be defined
The deformations of the specified points must increase monotonically, with no two values being equal
The action at each point must have the same sign as the deformation (they can be zero)
The slope given by the last two points specified on the positive deformation axis is extrapolated to infinite positive deformation, or until it reaches zero value. Similarly, the slope given by the last two points specified on the negative deformation axis is extrapolated to infinite negative deformation, or until it reaches zero value.
The given curve defines the action-deformation relationship under monotonic loading. The first slope on either side of the origin is elastic; the remaining segments define plastic deformation. If the deformation reverses, it typically follows the two elastic segments before beginning plastic deformation in the reverse direction, except as described below.
Several hysteresis models are available in SAP2000, ETABS, and CSiBridge. The available models may vary from product to product, and may include any or all of the models described below.
Typical for all models, cyclic loading behaves as follows:
Initial loading in the positive or negative direction follows the backbone curve
Upon reversal of deformation, unloading occurs along a different path, usually steeper than the loading path. This is often parallel or nearly parallel to the initial elastic slope.
After the load level is reduced to zero, continued reversal of deformation causes reverse loading along a path that eventually joins the backbone curve on the opposite side, usually at a deformation equal to the maximum previous deformation in that direction or the opposite direction.
In the descriptions below of cyclic deformation, "loading" refers to increasing the magnitude of deformation in a given positive or negative direction, and "unloading" refers to subsequent reduction of the deformation until the force level reaches zero. Continued reduction of the deformation is "reverse loading" until the deformation reaches zero, after which the deformation increases again with the same sign as the load and is "loading" again. Loading and unloading occur in the positive (first and third) quadrants of the action-deformation plot, and reverse loading occurs in the negative (second and fourth) quadrants.
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