  Recent experimental advances [Liu \textit{et al., npj 2D Materials and
Applications}, 2019, \textbf{3}, 23] propose the design of graphene nanoribbon
spring (GNRS) to substantially enhance the stretchability of pristine graphene.
GNRS is a periodic undulating graphene nanoribbon, where undulations are of
sinus or half-circles or horseshoe shapes. Besides those, GNRS geometry depends
on design parameters, like pitch's length and amplitude, thickness and joining
angle. Because of the fact that parametric influence on the resulting physical
properties are expensive and complicated to be examined experimentally, we
explore the mechanical, thermal and electromechanical properties of GNRS using
molecular dynamics simulations. Our results demonstrate that horseshoe shape
design of GNRS (GNRH) can distinctly outperform the graphene kirigami design
concerning the stretchability. The thermal conductivity of GNRS were also
examined by developing a multiscale modeling, which suggests that the thermal
transport along these nanostructures can be effectively tuned. We found that
however, the tensile stretching of GNRS and GNRH does not yield any
piezoelectric polarization. The bending induced hybridization change results in
a flexoelectric polarization, where the corresponding flexoelectric coefficient
is $25\%$ higher than graphene. Our results provide a comprehensive vision to
the critical physical properties of GNRS and may help to employ the outstanding
physics of the graphene to design novel stretchable nanodevices.
