The work by Greenwood and Williamson (GW) has initiated a simple but effective method of contact mechanics: statistical modeling based on the mechanical response of a single asperity. Two main assumptions of the original GW model are that the asperity response is purely elastic and that there is no interaction between asperities. However, as asperities lie on a continuous substrate, the deformation of one asperity will change the height of all other asperities through deformation of the substrate and will thus influence subsequent contact evolution. Moreover, a high asperity contact pressure will result in plasticity, which below tens of microns is size dependent, with smaller being harder. In this paper, the asperity interaction effect is taken into account through substrate deformation, while a size-dependent plasticity model is adopted for individual asperities. The intrinsic length in the strain gradient plasticity (SGP) theory is obtained by fitting to two-dimensional discrete dislocation plasticity simulations of the flattening of a single asperity. By utilizing the single asperity, response in three dimensions and taking asperity interaction into account, a statistical calculation of rough surface contact is performed. The effectiveness of the statistical model is addressed by comparison with full-detail finite element simulations of rough surface contact using SGP. Throughout the paper, our focus is on the difference of contact predictions based on size-dependent plasticity as compared to conventional size independent plasticity. (C) 2017 Elsevier Ltd. All rights reserved

SUMMARY Trap-jaw ants of the genus Odontomachus produce remarkably fast predatory strikes. The closing mandibles of Odontomachus bauri, for example, can reach speeds of over 60 m s^–1. They use these jaw strikes for both prey capture and locomotion – by striking hard surfaces, they can launch themselves into the air. We tested the hypothesis that morphological variation across the genus is correlated with differences in jaw speeds and accelerations. We video-recorded jaw-strikes at 70 000–100 000 frames s^–1 to measure these parameters and to model force production. Differences in mean speeds ranged from 35.9±7.7 m s^–1 for O. chelifer, to 48.8±8.9 m s^–1 for O. clarus desertorum. Differences in species9 accelerations and jaw sizes resulted in maximum strike forces in the largest ants (O. chelifer) that were four times those generated by the smallest ants (O. ruginodis). To evaluate phylogenetic effects and make statistically valid comparisons, we developed a phylogeny of all sampled Odontomachus species and seven outgroup species (19 species total) using four genetic loci. Jaw acceleration and jaw-scaling factors showed significant phylogenetic non-independence, whereas jaw speed and force did not. Independent contrast (IC) values were used to calculate scaling relationships for jaw length, jaw mass and body mass, which did not deviate significantly from isometry. IC regression of angular acceleration and body size show an inverse relationship, but combined with the isometric increase in jaw length and mass results in greater maximum strike forces for the largest Odontomachus species. Relatively small differences (3%) between IC and species-mean based models suggest that any deviation from isometry in species9 force production may be the result of recent selective evolution, rather than deep phylogenetic signal.