Exploring the applicability of gradient elasticity to certain micro/nano reliability problems

It has long been assessed that continuum mechanics can be used successfully to address a variety of mechanical problems at both macroscopic and microscopic scales. The term “micromechanics”, in particular, has been used in considering elasticity, plasticity, damage, and fracture mechanics problems at the micron scale involving metallic, ceramic and polymeric materials, as well as their composites. Applications to automobile, aerospace, and concrete industries, as well as to chemical and microelectronic technologies have already been documented. The recent developments in the field of nanotechnology have prompted a substantial literature in nanomechanics. While this term was first introduced by the author in the early 90’s to advance a generalized continuum mechanics framework for applications at the nanoscale, it is mainly used today in considering “hybrid” ab-initio/molecular dynamics/finite element simulations, usually based on elasticity theory, to interpret the mechanical response of nano-objects (nanotubes, nanowires, nanoaggregates) and extract information on nano-configurations (dislocation cores, crack tips, interfaces). The modest goal of this article is to show that continuum elasticity can indeed be extended to describe a variety of problems at the micro/nano regime. The resultant micro/nanoelasticity theory includes long-range or nonlocal material point interactions and surface effects in the form of (phenomenological) higher-order stress/strain gradients. Coupled thermo-diffuso-chemo-mechanical processes can also be considered within such a higher-order theory. Size effects on micro/nano holes and micro/nano cracks can conveniently be modeled, and some standard strength of materials formulas routinely used for micro/nano beams can be improved, with potential applications to MEMS/NEMS devices and micro/nano reliability components.