Mechanics, or solid mechanics in particular, is the study of deformation or motion of solid materials under the influence of forces. If you're a Civil Engineering undergrad like me, you'll probably remember the classic stress vs. strain curve of steel. The slope of the linear region (i.e., within the elastic limit) of this curve gives us the Young's modulus, a fundamental material property.  
"Nano"-mechanics is a similar concept, except the forces here are in the pico- to micro Newton range and pertains to soft matter. 
To accurately measure the mechanical properties of soft matter it is imperative that the range (of load or indentation) within which stress and strain are proportional (elastic limit) is determined. This can be called as the check for linearity. As can be seen in the graph below, the data deviate from linearity beyond a force of 4 nN. Hence to calculate the Young's modulus or for other measurements that require staying within the elastic limit, the load must be restricted to 2-3 nN (to be on the safe side) or the indentation depth must be kept within 3-20 nm. 
Here I have used the Hertzian contacts mechanics model to analyze my data. 

Different material have different stress-strain relationship. For e.g., a Hooke's spring would have stress proportional to strain but a Newton's dashpot would have stress proportional to strain rate. In real world, most material - or at least soft matter, is a combination of both and their response to load can be modelled by a  spring unit and  dash-pot unit in various combinations.