  Contact force--indentation depth measurements in contact experiments
involving compliant materials, such as polymers and gels, show a hysteresis
loop whose size depends on the maximum indentation depth. This depth-dependent
hysteresis (DDH) is not explained by classical contact mechanics theories and
was believed to be due to effects such as material viscoelasticity, plasticity,
surface polymer interdigitation, and moisture, etc. It has been observed that
the DDH energy loss initially increases and then decreases with roughness. A
mechanics model based on the occurrence of adhesion and roughness related
small-scale instabilities was presented by one of the authors for explaining
DDH. However, that model only applies in the regime of infinitesimally small
surface roughness, and consequently it does not capture the decrease in energy
loss with surface roughness at the large roughness regime. We present a new
mechanics model that applies in the regime of large surface roughness based on
the Maugis--Dugdale theory of adhesive elastic contacts and Nayak's theory of
rough surfaces. The model captures the trend of decreasing energy loss with
increasing roughness. It also captures the experimentally observed dependencies
of energy loss on the maximum indentation depth, and material and surface
properties.
