Mechanics-guided 4D printing of single-material thermoplastic grids via deposition-temperature-programmed shrinkage

4D printing provides a material-efficient route for forming three-dimensional structures from flat printed precursors, reducing the need for sacrificial supports, moulds, and post-assembly operations. However, most existing strategies rely on soft active materials, multi-material systems, or deliberately anisotropic toolpaths, which limits their direct extension to conventional engineering thermoplastics. This work presents a single-material 4D-printing concept in which layerwise deposition temperature control in fused deposition modelling is used to programme differential shrinkage in thermoplastic strips. The temperature-dependent shrinkage is treated phenomenologically as a calibrated process-induced eigenstrain, without modelling its microscopic material origin. The concept is first quantified through experiments on uniform-temperature specimens, which establish the free shrinkage associated with different deposition temperatures, and multilayer specimens, which determine the axial contraction and intrinsic curvature generated by through-thickness shrinkage mismatch. These measured actuation descriptors are then assigned to members of closed quadrilateral grid structures. The mechanics of such grids is governed not by the free bending of individual strips, but by closed-loop compatibility, which redistributes axial stretching, out-of-plane bending, in-plane bending, torsion, and nodal rotations throughout the structure. To predict this coupled response, a semi-analytical energy-minimisation model is developed with geometrically exact strain measures and finite-size nodal blocks. The model is verified against nonlinear shell finite element simulations and validated using structured-light measurements of thermally activated single-cell and multicell grids. The results demonstrate that layerwise temperature-programmed shrinkage can provide a practical and mechanics-guided route for 4D shape forming of single-material thermoplastic grid structures.