Could you please drop some references elucidating such jargon? Generally speaking, I am inclined to figure out what gives rise to hysteretic loops in soil constitutive models whilst the authors did not point out anything as respects damping. In this regard, please have a butcher's at the paper below:
Constitutive model for cyclic behavior of clays. I: Theory
GW Wathugala, CS Desai - Journal of geotechnical engineering, 1993 - ascelibrary.org
To sum up, I wonder what factor leads to such closed loops in the attachment.
hysteretic behavior: describes the nonlinear stress-strain characteristics of the material
hysteretic loops: the actual representation of the response
hysteretic damping: area of the loop indicating the work done or energy dissipation
Check any structural dynamics text book. E.g., that of chopra
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