Enhanced smooth hysteretic model with degrading properties

The elastic and inelastic nonlinear behavior of structural members use constitutive relations in which restoring forces and deformations are not proportional and often follow different paths in loading and unloading using hysteretic functions. There are numerous available models that can trace the stiffness and strength changes through yielding, softening, and hardening; however, models that can address more complex behavior such as degradations, large deformation, bond slip, and joint gap, do so by complex polygonal rules or smooth continuous functions describing momentary (tangent) behavior. There is a need for a unified model on the basis of a combination of mechanical springs that can trace the instantaneous combined stiffness used in system analyses. In this study, a one-dimensional smooth hysteretic model using series and parallel springs, designed for nonlinear structural analysis, is enhanced to incorporate (1) time-independent properties, (2) nonlinear elastic and postelastic softening and hardening, (3) sudden or continuous variation of strength, (4) degradation of elastic and inelastic stiffness, (5) a modified bond-slip model, and (6) an alternative joint-gap model with a variable gap closing length. Using spring analogues or reciprocal structures, the instantaneous force-displacement incremental relations are formulated, which can be further used to determine the instantaneous tangent-stiffness matrices of the elements used in the analyses of complex structures.