Formulating pinched hysteresis models of wood shear walls using time integrals of restoring force and displacement

Modeling hysteresis is highly relevant for many nonlinear vibrating systems, calling for physically insightful and computational efficient solutions. In earthquake and wind engineering, wood shear walls are subjected to lateral loads rendering highly hysteretic load–displacement responses featuring pinching, force-intercept, and strength and stiffness degradation. Existing phenomenological models directly work on the evolution of the load and displacement, often leading to complicated models with a large number of empirical parameters. Facilitated with three real-world experimental datasets for wood shear walls from an existing publication, this study showcases an alternative hysteresis modeling approach. The time integrals of load and displacement are utilized instead; modeling pinching is made front and center. This is mem-modeling transferred from electrical engineering, where “mem” is for memory, i.e., hysteresis. Grounded in bond graph theory, formulated under nonlinear state-space representation, and enriched with hybrid dynamical system concepts, the mem-modeling framework is substantiated with critical details such as choices of state variables, formulation and visualization of the governing secant modulus functions, conceptually ready for identification and simulation using real-world restoring force–displacement responses.