Quantum mechanics

Mathematics education

Shape-memory alloy

Engineering

Curvature

Materials science

Inkwell

Electric field

3D printing

Electronic circuit

Electric heating

Polymer

Mechanical engineering

Fractal

Physics

Nanotechnology

Mathematics

Mathematical analysis

Geometry

Composite material

Microscale chemistry

Printed electronics

Shape-memory polymer

Heating element

Electrical engineering

Electrical conductor

ACS Applied Materials & Interfaces

Thermally responsive shape memory polymers (SMPs) used in 4D printing are often reported to be activated by external heat sources or embedded stiff heaters. However, such heating strategies impede the practical application of 4D printing due to the lack of precise control over heating or the limited ability to accommodate the stretching during shape programming. Herein, we propose a novel 4D printing paradigm by fabricating stretchable heating circuits with fractal motifs via electric-field-driven microscale 3D printing of conductive paste for seamless integration into 3D printed structures with SMP components. By regulating the fractal order and printing/processing parameters, the overall electrical resistance and areal coverage of the circuits can be tuned to produce an efficient and uniform heating performance. Compared with serpentine structures, the resistance of fractal-based circuits remains relatively stable under both uniaxial and biaxial stretching. In practice, steady-state and transient heating modes can be respectively used during the shape programming and actuation phases. We demonstrate that this approach is suitable for 4D printed structures with shape programming by either uniaxial or biaxial stretching. Notably, the biaxial stretchability of fractal-based heating circuits enables the shape change between a planar structure and a 3D one with double curvature. The proposed strategy would offer more freedom in designing 4D printed structures and enable the manipulation of the latter in a controlled and selective manner.

Fractal-Based Stretchable Circuits via Electric-Field-Driven Microscale 3D Printing for Localized Heating of Shape Memory Polymers in 4D Printing