Hysteretic damping in an elastic body with frictional microcracks

• ABAQUS study of a cyclically loaded plate with frictional cracks.
• Narrow hysteresis loops, pinched at the origin, are found.
• Results give theoretical justification for such pinched loops, seen elsewhere.
• New scalar evolution equation matches these hysteresis loops well.
• Useful for low-dimensional simulations of similar frictionally damped objects.

Material stress strain curves often show dissipation via rate-independent hysteresis. Here we study an elastic plate with several randomly distributed and oriented frictional microcracks, loaded cyclically in plane stress. Computational solutions in ABAQUS show narrow hysteresis loops. Unlike the loops from Rowett׳s classic experiment (1914), or from simple hysteresis models such as the Bouc–Wen model (1967 and 1976), the present loops are pinched at the origin and partially resemble an ad hoc model proposed by Reid (1956). Such pinched loops have been revisited lately by others, but our results provide new justification for the same. We also propose a new simple scalar model that gives a better qualitative match with the numerically obtained hysteresis loops than any other model presently available. Our scalar hysteresis model may lead to better interpretations and modeling in, e.g., vibration response of structures with such internal frictional damping. Thus the contribution of this paper lies in adopting a dissipation model from micromechanics, idealizing the resulting dissipation loops, and presenting a new simple scalar equation that models such loops and can be easily incorporated into structural vibration damping models.