Real and causal hysteresis elements.

Area of Science:

• Physics
• Materials Science
• Engineering

Background:

• Hysteresis is a common phenomenon in materials, characterized by energy loss during cyclical loading.
• Classical frequency domain models of hysteresis, while simple, lack real and causal impulse responses, limiting their predictive power in laboratory settings.
• Existing models often lead to errors and have spurred the development of more accurate approaches.

Purpose of the Study:

• To re-examine the frequency domain requirements for hysteresis.
• To develop a family of real and causal impulse response models for hysteretic systems.
• To provide analytical solutions for predicting motion and wave propagation in hysteretic materials.

Main Methods:

• Re-evaluation of frequency domain characteristics of hysteresis.
• Development of a mathematical framework for causal impulse responses.
• Derivation of closed-form analytical solutions for highpass, lowpass, and bandpass systems.

Main Results:

• A family of hysteresis models with real and causal impulse responses has been identified.
• These models satisfy the necessary frequency domain requirements for accurate physical representation.
• The derived solutions are applicable across different frequency ranges (highpass, lowpass, bandpass).

Conclusions:

• The newly developed causal hysteresis models overcome the limitations of classical approaches.
• These models offer accurate predictions for motion and wave propagation in hysteretic materials.
• The analytical solutions provide a powerful tool for researchers and engineers working with hysteretic systems.