Fractal Circuit Architectures for Spatially Controlled Heating and Multi-Modal Shape Programming of Electro-Active Shape Memory Polymers

Abstract

Shape memory polymers (SMPs) are commonly activated through external heating or rigid embedded heaters, which lack precise temperature control and restrict programmable shape transformations. This study demonstrates integrating thin films of hard electronic materials patterned in fractal designs into SMPs yields novel thermomechanical responses, enabling flexible implementation of stretchable electronic functionality. Space-filling Hilbert, Moore and Peano fractal curves generate distributed electronic circuitry patterns within the SMP matrices. To investigate the coupled electro-thermal-mechanical behavior, a multi-physics modeling approach is adopted. A nonlinear thermo-visco-hyperelastic constitutive model captures the SMP’s shape memory characteristics. Governing equations for the multi-physics problem are formulated. Experimental data validates the model’s predictions of the SMP’s nonlinear material response under uniaxial loading. This validated framework analyzes SMP composites with integrated fractal circuits. Findings reveal composites with higher-order fractal circuits’ exhibit faster, more uniform resistive heating and smaller electrical resistance changes during stretching, enabling consistent and predictable shape recovery under various deformations. Notably, these advantageous heating and resistance characteristics enhance the force recovery rate during the shape memory cycle. Furthermore, the composites demonstrate excellent shape recovery under bending. Remarkably, uniaxial stretching can induce controlled out-of-plane shape transformations, enabling novel actuation modalities. This work provides insights into leveraging fractal circuit integration to enhance SMP performance and expand capabilities, enabling multi-functional actuators, sensors and programmable soft grippers.