A new Finite Element approach for studying the effect of surface stress on microstructures

The traditional Finite Element Method, when applied to the micro- and nanoscale, lacks of contemplating stress on surfaces. In macroscopic mechanics, stress is a prerogative of bulks as displayed by the standard form of Principle of Virtual Work (PVW). On the other hand, the progressive increase of surface/volume ratio that occurs moving from macro- to micro- and nano-structures imposes to FE method to change accordingly, thus including surface stresses too in the underlying equations.In this paper a new FE approach is proposed, based on the modification of the PVW with a term representing the work of surface deformation. The addition of such a contribution to the standard PVW allows a straightforward analysis of the effect of surface stress on microcantilevers, probably one of the most important current issues related to MEMSs (Micro-Electro-Mechanical Systems) and BioMEMSs (Biological Micro-Electro-Mechanical Systems). Both static and dynamic aspects have been worked out and the benchmarks with the theoretical and experimental results available in literature confirm the correctness of the proceeding.