ASPID: An asymmetric pinching damaged hysteresis model for timber structures

Abstract

This paper presents a new high-fidelity phenomenological-based hysteretic model called ASPID that includes asymmetry, pinching, and strength/stiffness degradation for timber members. To capture asymmetry, one force–displacement envelope and ten physical-based hysteretic parameters are used for each loading direction. Pinching is added with an unloading–reloading monotone smooth piecewise function composed of two quadratic Bézier polynomials and one linear segment. Strength degradation at target displacement is taken using a novel fatigue law based on the maximum displacement and hysteretic dissipated energy. Exponential stiffness degradation of pinching and reloading phases is adopted in terms of their maximum displacement, whereas irreversible damage is captured using two threshold displacements independent of each loading direction. The update force algorithm is included for their computational implementation, and a Python version can be downloaded for free. The model is validated using six experimental benchmark tests of mass and lightweight timber connections and assemblies with symmetric/asymmetric behavior, where an optimized parameter identification process is considered. Moreover, the model test responses are compared with three well-known hysteretic models: SAWS, Pinching4, and DowelType. The ASPID model’s test results show an error less than 7.6% for the capacity and 2.9% for the cumulative dissipated energy as well as fits with high precision the force and dissipated energy history, getting a Normalized Root Mean Square (NRMS) error less than 4.3% and 2.8%, a Normalized Mean Absolute (NMA) error less than 2.7% and 1.5%, and a coefficient of determination R2 over 94.88% and 99.09%, respectively. Finally, comparing the four hysteretic models, the ASPID model gives the highest R2 values in all tests and has the smallest NRMS and NMA errors regarding force history and the smallest NMA errors for the dissipated energy history.