We provide an overview of the basic concepts of scaling and dimensional analysis, followed by a review of some of the recent work on applying these concepts to modeling instrumented indentation measurements. Specifically, we examine conical and pyramidal indentation in elastic-plastic solids with power-law workhardening, in power-law creep solids, and in linear viscoelastic materials. We show that the scaling approach to indentation modeling provides new insights into several basic questions in instrumented indentation, including, what information is contained in the indentation load-displacement curves? How does hardness depend on the mechanical properties and indenter geometry? What are the factors determining piling-up and sinking-in of surface profiles around indents? Can stress-strain relationships be obtained from indentation load-displacement curves? How to measure time dependent mechanical properties from indentation? How to detect or confirm indentation size effects? The scaling approach also helps organize knowledge and provides a framework for bridging micro-and macroscales. We hope that this review will accomplish two purposes: (1) introducing the basic concepts of scaling and dimensional analysis to materials scientists and engineers, and (2) providing a better understanding of instrumented indentation measurements. # 2004 Published by Elsevier B.V.

Superhydrophobic surfaces have important technical applications ranging from self-cleaning window glasses, paints, and fabrics to low-friction surfaces. The archetype superhydrophobic surface is that of the lotus leaf. When rain falls on lotus leaves, water beads up with a contact angle in the superhydrophobic range of about 160°. The water drops promptly roll off the leaves collecting dirt along the way. This lotus effect has, in recent years, stimulated much research effort worldwide in the fabrication of surfaces with superhydrophobicity. But, is the lotus surface truly superhydrophobic? This work shows that the lotus leaves can be either hydrophobic or hydrophilic, depending on how the water gets on to their surfaces. This finding has significant ramifications on how to make and use superhydrophobic surfaces.

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The work done during indentation is examined using dimensional analysis and finite element calculations for conical indentation in elastic-plastic solids with work hardening. An approximate relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work in indentation is found. Consequently, the ratio of hardness to elastic modulus may be obtained directly from measuring the work of indentation. Together with a well-known relationship between elastic modulus, initial unloading slope, and contact area, a new method is then suggested for estimating the hardness and modulus of solids using instrumented indentation with conical or pyramidal indenters.

When rain falls on lotus leaves water beads up with a high contact angle. The water drops promptly roll off the leaves, collecting dirt along the way. This self-cleaning ability or lotus effect has, in recent years, stimulated much research effort worldwide for a variety of applications ranging from self-cleaning window glasses, paints, and fabrics to low friction surfaces. What are the mechanisms giving rise to the lotus effect? Although chemical composition and surface structure are believed important, a systematic experimental investigation of their effects is still lacking. By altering the surface structure of the leaves while keeping their chemical composition approximately the same, we report in this study the influence of micro- and nano-scale structures on the wetting behaviour of lotus leaves. The findings of this work may help design self-cleaning surfaces and improve our understanding of wetting mechanisms.