Periodic necking of misfit hyperelastic filaments embedded in a soft matrix

The necking instability is a precursor to tensile failure and rupture of materials. A quasistatically loaded free-standing uniaxial specimen typically exhibits at single location, thus corresponding long wavelength bifurcation mode. If confined substrate or embedded in matrix the same filament can exhibit periodic fragmentation creating segments finite length. While such instabilities have been extensively studied ductile metal filaments thin sheets, less known about hyperelastic Nonetheless, recent years, there has renewed interest role novel materials, for advancement fabrication processes explain phenomena observed 3D printed active biological matter. In both cases materials are not well described by existing frameworks that employ J2 deformation theory plasticity, studies do account significant misfit stretches may emerge these systems through chemical, contraction. To address limitations, this paper we begin experimentally demonstrating surrounding on compliant tunable rubber matrix. Using generalized model with strain softening, our analytical analysis explains experimental observations shown agree numerical predictions. reveals three distinct modes: necking, recovering Considère criterion; experiments; short mode characterized localization along center cord independent film-to-matrix stiffness ratio. We find softening coefficient stretch significantly influence stability threshold wavelength, respectively. Our results guide design composite