Inverse design of face-like 3D surfaces via bi-material 4D printing and shape morphing

Shape morphing from two-dimensional (2D) to three-dimensional (3D) structures enables novel fabrication approaches beyond conventional methods but often requires costly tools. Here, we demonstrate a low-cost, bi-material four-dimensional (4D) printing approach to fabricate human face-like 3D gridshells from 2D grids. Using fused deposition modelling, we print planar grids composed of bilayer rods made of shape memory polymer (SMP) and polylactic acid (PLA). Upon uniform heating, these grids transform into 3D shapes, guided by programmed material properties. To solve the inverse design problem, we employ a Fully Convolutional Network (FCN) trained on over 100,000 face designs simulated via nonlinear finite element analysis. The model accurately predicts 2D grid configurations from 3D depth images, achieving pixel accuracy and mean intersection-over-union exceeding 90%. Experimental validation includes the successful fabrication of face-like samples, including three Japanese ‘Noh’ masks, highlighting the robustness of our approach. This work advances 4D printing by enabling precise, data-driven inverse design for shell-like morphing structures.