图  1  基于不同维度前驱结构驱动的4D打印：(a) 一维直线图案转换为二维平面或三维立体结构^[8-10]；(b) 二维平面图案转换为三维立体结构^[12-14]；(c) 三维立体结构重构^[15-17]

Figure  1.  4D printing driven by different dimensions of precursor structures: (a) One-dimensional linear patterns transfer to two-dimensional or three-dimensional structures^[8-10]; (b) Two-dimensional planar patterns transfer to three-dimensional structures^[12-14]; (c) Reconstruction of three-dimensional structures^[15-17]

图  2  基于一维线性前驱结构驱动的4D打印^{[8, 17, 42]}：(a) 一维线条转换为一维或二维图案；(b) 一维线条转换为二维平面图案；(c) 一维直线棒转换为三维结构

ML—Machine learning; EA—Evolutionary algorithms; CV—Computer vision

Figure  2.  4D printing driven by linear precursor structure^{[8, 17, 42]}: (a) One-dimensional lines transfer to one-dimensional or two-dimensional patterns; (b) One-dimensional lines transfer to two-dimensional flat patterns; (c) A one-dimensional straight rod transfers to a three-dimensional structure

图  3  多材料喷墨打印的基于二维平面前驱结构驱动的4D打印^{[11, 45-46]}：(a) 嵌有一种纤维的平面前驱结构的弯曲变形；(b) 嵌有一种纤维结合排布模式的平面前驱结构的自折叠折纸结构；(c) 嵌有两种纤维的前驱结构驱动的多形状转换

σ—Stress; T_H—High temperature (60℃) above glass transition temperature (35℃); T_L—Low temperature (15℃) below glass transition temperature (35℃); F—Fiber; M—Matrix; ε₀—Strain applied along the printing direction; L—Length of strip; w—Width of strip; h—Height of strip; t₁—Dimensions of fiber 1; t₂—Dimensions of fiber 2

Figure  3.  4D printing driven by a two-dimensional planar precursor structure via multi-material inkjet printing method^{[11, 45-46]}: (a) Bending deformation of a simple planar precursor structure embedded with a fiber; (b) A self-folding origami structure with a planar precursor structure embedded with a combination of fibers and different layout patterns; (c) Multi-shape conversion driven by precursor structure embedded with two types of fibers

图  4  熔融沉积成型技术(FDM)打印的基于二维平面前驱结构驱动的4D打印^[47-48]：(a) 以不同打印方向调控层间的应变失配；(b) 以不同打印速度调控层间的应变失配

T—Temperature; T_g—Glass transition temperature; h—Total thickness of deformation unit; d—Thickness of single layer of deformation unit; n—Representative porosity; σ—Standard deviation; t—Time; L—Original length; L₀—Length after heating expansion; ∆L—Length change before and after heating

Figure  4.  4D printing driven by a two-dimensional planar precursor structure via fused deposition modeling (FDM) printing method^[47-48]: (a) Strain mismatch was adjusted by different printing directions between printing layers; (b) Strain mismatch was adjusted by different printing speeds between different layers

图  5  数字光处理(DLP)打印的基于二维平面前驱结构驱动的4D打印^{[51- 52]}：(a) 以曝光时间调控材料交联度使溶胀率不同驱动形状变化；(b) 不同材料吸水溶胀率时不同驱动形状变化

PEGDA—Poly(ethylene glycol) diacrylate; PPGDMA—Poly(propylene glycol) dimethacrylate; r—Radius of in-plane circle; R—Excircle radius of plane; r'—Geometric radius after deformation; H—Geometric height after deformation

Figure  5.  4D printing driven by a two-dimensional planar precursor structure via digital light processing (DLP) printing method^{[51- 52]}: (a) Adjusted crosslinking degree of materials with different exposure time results in different swelling rates and various shape changes; (b) Different materials with different water absorption and swelling rates drive shape changes

图  6  墨水直书写(DIW)打印的基于二维平面前驱结构驱动的4D打印^{[34, 53]}：(a) 加热脱除溶剂驱动变形；(b) 热水-Ca²⁺溶液双重刺激驱动变形

L—Longitudinal; T—Transversal; PCLDMA—Polycaprolactone dimethylacetamide; SAMA—Sodium alginate methacrylate; θ—Tilt angle; PCL-MA—Polycaprolactone methacrylate

Figure  6.  4D printing driven by 2D planar precursor structure via direct ink writing (DIW) printing method^{[34, 53]}: (a) Solvent removal by heating drives shape changes; (b) Hot water-Ca²⁺solvent double stimulation drive shape changes

图  7  基于三维立体前驱结构驱动的4D打印^{[12, 37]}：(a) 具有多曲率及高刚度结构的变形；(b) 具有中空管状结构的变形

l—Length; t—Thickness; d₂—The displacement of joints determined from the temperature-induced elongation skew; θ, λ—Angle; E_c and E_f—Axial elastic modulus of the core and frame trusses; α_c and α_f—Coefficient of thermal expansion of the core and frame trusses; k—Curvature; α—The number of passive layers; β—The amount of the programmed out-of-plane actuation; Compr.—Compress; Lens.—Tension; EXP—Experiment; FEA—Finite element analysis

Figure  7.  4D printing driven by a three-dimensional precursor structure^{[12, 37]}: (a) Deformation of structures with multiple curvatures and high stiffness; (b) Deformation of structures with hollow tubular patterning

图  8  基于4D打印以非对称层合板结构开发的柔性机翼^[54]

Figure  8.  4D printed flexible wings with asymmetric laminated plates^[54]

图  9  基于理论计算模型的双层弯曲结构辅助设计^[58-60]：(a) 对折叠结构的建模；(b) 热驱动双层结构的建模

t—Time; ε—Strain; α—Coefficient of thermal expansion; d—Thickness; k—Thickness ratio; θ—Temperature change; ∆ε^T—The average strain of bilayer structure; n—Ratio of modulus; m—Ratio of thickness; h_total—Sum of thickness; E—Elastic modulus; a—Thickness; P—Axial tensile forces; κ—Curvature; I—Moment of inertia;

Figure  9.  Aided design of double-layer bending structures based on theoretical calculation models^[58-60]: (a) Modeling of folding structures; (b) Modeling of double layer structure by heating

图  10  模拟仿真辅助4D打印结构设计^[63-65]：(a) 温度驱动双层结构的变形仿真；(b) 复杂可逆变形结构仿真

Figure  10.  Simulation-assisted 4D printing structure design^[63-65]: (a) Deformation simulation of temperature-driven double-layer structures; (b) Simulation of complex reversible deformation structures

图  11  逆几何方法辅助设计前驱结构^{[10, 68-69]}：(a) 基于共形曲面投影的前驱结构设计；(b) 基于智能材料体素化分布的前驱结构设计；(c) 基于智能材料拓扑优化的前驱结构设计

L—Length of per-rib; R⁻¹—Curvature

Figure  11.  Inverse geometry method aided design of precursor structure^{[10, 68-69]}: (a) Design of precursor structure based on conformal surface projection; (b) Design of precursor structures based on voxel distribution of intelligent materials; (c) Topology optimization design of precursor structure based on intelligent materials