An empirical transcendental hysteresis model for structural systems with pinching and degradation

The authors present a novel transcendental hysteresis model based on the piecewise definition of arctangent functions. The definition of the shape parameters of the arctangent functions originates from the features of the experimental hysteresis curves directly. In the first step, the authors present this model's application to the experimental cyclic response of cross-laminated timber (CLT), light-timber frame (LTF) shear walls, and a steel angle bracket. Then, the response of a plywood-coupled laminated-veneer lumber (LVL) shear wall is used for validation purposes. The paper introduces the arctangent-based model, labeled Atan model, by illustrating some possible shortcomings of hysteresis models with pinching. The paper concludes with a simple demonstration of these issues in the case of a Bouc-Wen class hysteresis model, the extended energy-dependent generalized Bouc-Wen (eegbw) model. The numerical instabilities of the eegbw model are used to endorse the advantages of the proposed formulation in modeling complex structural arrangements, like wood joints and structural systems. The proposed model originates from the analysis of the experimental response of wood joints. However, it can be of more general application, and the particular reference to wood joints does not preclude other application fields.