A reduced-order model from high-dimensional frictional hysteresis.

Area of Science:

• Materials Science
• Mechanical Engineering
• Nonlinear Dynamics

Background:

• Component-level hysteretic behavior is often modeled empirically.
• Existing models struggle with the high dimensionality and signum nonlinearities inherent in hysteresis.
• There is a need for physics-based, reduced-order models for hysteresis.

Purpose of the Study:

• To derive a low-order, rate-independent model for hysteresis.
• To develop a model from a high-dimensional, massless frictional system.
• To provide a foundation for improved empirical hysteresis modeling.

Main Methods:

• Formulated the high-dimensional frictional system using a linear complementarity problem.
• Employed singular value decomposition to select basis vectors for model reduction.
• Approximated a dissipation-related function to identify the slip direction.
• Derived a reduced-order evolution equation for key system states.

Main Results:

• Successfully derived a low-order model for rate-independent hysteresis.
• The reduced-order model accurately matches the solutions of the full high-dimensional system.
• Identified the slip direction by minimizing an analytically approximated dissipation function.
• The model captures signum nonlinearities effectively.

Conclusions:

• The derived low-order model offers a physics-based approach to hysteresis.
• This work provides new insights into the nature of hysteresis.
• The model can potentially improve empirical modeling of hysteretic material behavior.