On nonlinear mechanics of nonlocal elastic trusses

A geometrically consistent framework is proposed for the nonlinear mechanics of nonlocal elastic trusses. Notably, according to the described paradigm, the elements of Nonlinear Continuum Mechanics are redefined through a geometric approach formulated in the spacetime framework. Building upon the Rate Virtual Power Principle, a stress-driven nonlocal rate elasticity theory is introduced to analyze nanotruss structures undergoing large configuration changes. The developed methodology is applied to perform large displacement analyses and to simulate snap-through instability in small-scale trusses by an incremental procedure, revealing a stiffening response with increasing nonlocal length-scale parameter, in agreement with the smaller-is-stiffer phenomenon. The main findings suggest the relevance of the presented methods in accurately capturing geometrically nonlinearities and nonlocal effects in nanoscale structural problems.