<figure><img src="image_37.png" /><figcaption>**Figure 30.** Recent examples of 4D microstructures: (a) Thermo-responsive poly-NIPAM microactuators (Left panel Reproduced from [251]. CC BY 4.0. The Author(s); right panel Reproduced from [252]. CC BY 4.0. (b) Liquid crystalline 4D microstructure (Reproduced from [253]. CC BY 4.0), (c) shape memory 4D microstructures (Reproduced from [256]. CC BY 4.0. The Author(s); right panel Reproduced from [18]. CC BY 4.0 and (d) magnetic microswimmers. ([257] John Wiley & Sons. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.).</figcaption></figure>

At the technological level, new 3D printing approaches that rely on different photo-initiation mechanisms have recently emerged as alternatives to traditional two-photon processes. These mechanisms include triplet-triplet annihilation, triplet fusion up-conversion and two-step absorption processes [260–263]. Importantly, these methodologies do not require large and expensive femtosecond lasers but enable precise 3D printing using just compact and low-cost illumination sources. Although these techniques are still in their infancy, a future perspective would be their implementation in 4D printing. By designing 4D printable materials with the features discussed above, new opportunities will emerge.

## Concluding remarks

Over the past few years, exciting advancements in materials and technologies for 3D and 4D printing at small scales have been made. Despite the challenges outlined, the burgeoning

field of 4D printing at the micro- and nanoscales holds great promise. Smart and dynamic microstructures, whose properties can be precisely programmed and controlled as needed, will exert a significant impact in the very near future in several disciplines ranging from micro-robotics to optics and biomedicine.

## Acknowledgments

E. B. acknowledges funding from the Deutsche Forschungsgemeinschaft (DFG) under Germany's Excellence Strategy via the Excellence Cluster 3D Matter Made to Order (EXC-2082-390761711), and by the Carl Zeiss Foundation through the Carl-Zeiss-Focus@HEiKA. Also, E. B. thanks the Federal Ministry of Education and Research (BMBF) and the Ministry of Science Baden-Württemberg within the framework of the Excellence Strategy of the Federal and State Governments of Germany for their support.
# 19. High resolution 4D printing

Honggeng Li, Bingcong Jian and Qi Ge

Department of Mechanical and Energy Engineering, Southern
University of Science and Technology, Shenzhen 518055,
People's Republic of China

E-mail: lihg@mail.sustech.edu.cn, jianbc@sustech.edu.cn
and geq@sustech.edu.cn

## Status

4D printing is a cutting-edge manufacturing technology that integrates 3D printing with smart materials to create 3D structures that can change their shapes or functions over the fourth dimension—‘time’ in response to external stimuli such as heat, moisture, electric/magnetic field, or others. Such shape-morphing structures can be printed by various 3D printing technologies including fused deposition modeling (FDM), digital light processing (DLP), DIW, Inkjet printing, SLS, stereolithography (SLA), and TPP (figure 31(a)). Among them, the high resolution 3D printing techniques such as TPP and DLP enable high resolution 4D printing that fabricate shape-morphing 3D structures with feature size at the micro- and nanoscales [264]. As shown in figure 31(b), TPP technology can fabricate intricate 3D structures with an exceptional printing resolution ranging from 90 nm to 500 nm, relying on the two-photon absorption (TPA) theory. This process involves the simultaneous absorption of two photons from NIR light at equal low frequency (ν/2), lifting a molecule from its ground state to a higher energy level to induce polymerization in photosensitive resin [265]. Different from TPP that fabricates 3D structures by scanning the nanoscale laser spot through two photo absorption, as shown in figure 31(c), DLP technology creates 3D structures by projecting ultraviolet patterns through a digital micromirror device (DMD) to on the surface of photosensitive resin. The feature size of the projected pattern can be improved by optimizing the optical lens, and the highest resolution for DLP can be as small as 0.6 µm [266]. Both TPP and DLP can be used to achieve high resolution 4D printing by printing photopolymerizable smart materials including hydrogels [267], LCE [268], SMP [256, 269, 270], magnetic/electric responsive materials [271].

Owning to the capability of seamlessly integrating multifunctionalities into complex 3D structures with micro- or nanoscale features, high resolution 4D printing can generate intelligent microstructures and microdevices, which have found extensive applications in diverse fields including mechanical metamaterials, flexible electronics, micro-robotics and biomedicines. Shape-transformable structures [269] (figure 31(d)) and even mechanical metamaterials [270] (figure 31(e)) can be achieved through DLP printing of SMPs. By printing an ionic conductive polymer with a dielectric, flexible sensors with multimode sensing capability can be achieved [271] (figure 31(f)). Multimaterial DLP 3D printing enables multimodal mobile microrobot with piezoelectric building blocks [272] (figure 31(g)). The microrobots can be

further scaled down to micrometers, which are fabricated by TPP and used for biomedical applications [273] (figure 31(h)). Using TPP to print SMP structural colors, tunable photonic devices can be achieved [256] (figure 31(i)).

## Current and future challenges

Despite the recent rapid advances, the implementation of high resolution 4D printing into practical applications is still hindered by the following three key challenges: the conflict between printing resolution and efficiency, limited capability of printing multimaterial structures with refined features, and inadequate smart/functional materials for high resolution 3D printing.

TPP enables the fabrication of shape-morphing structures with feature sizes of 90–500 nanometers [265]. Most of these structures were fabricated on a commercial TPP 3D printer (Nanoscribe, Germany), which has the finest planar resolution of 160 nm and vertical resolution of 0.1–5 µm. Although the maximum building volume is 100 × 100 × 8 mm³, the scanning method to print 3D structures requires about 1852 d to form a bulk volume in such size at the maximum speed of 625 mm s⁻¹. Different from TPP, DLP generates 3D structures through mask projection which can quickly form a planar pattern through one shot of projection. The commercial DLP 3D printer (BMF, China) uses projection micro stereolithography to fabricate 3D structures, and its finest planar resolution is 2 µm and vertical resolution is 5 µm, but the projection area is limited to 3.84 mm × 2.16 mm. The step-repeat method extends the projection area to 50 mm × 50 mm, but the full cover of such area requires 312 repeat projections.

Additionally, the current intelligent microstructures and microdevices manufactured by high resolution 4D printing are mainly in the form of single material. This is because that both the printing process in either TPP or DLP occurs in liquid photosensitive resin, and multimaterial 3D printing requires switching of resins, which has not yet been achieved by commercial TPP and DLP printers. Despite many attempts to endow TPP [274] and DLP [275, 276] with multimaterial 3D printing capability, the current systems suffer from small building size, limited applicable materials, and low degree of structural or functional integration.

Moreover, since both TPP and DLP rely on photopolymerization to realize 3D printing, the liquid resins that are converted to the solid counterparts are required to have high photosensitivity and low viscosity. These strict requirements severely constrain the number of smart materials such as SMPs, hydrogels, ionic conductive polymers, and polymer embedded with magnetic/piezoelectric particles that can be printed by TPP or DLP.

## Advances in science and technology to meet challenges

To meet the above-mentioned challenges, significant progress for high resolution 4D printing has been achieved,
<figure><img src="image_38.png" /><figcaption>**Figure 31.** The technical characteristics and typical applications of high resolution 4D printing. (a) The diagram summarizes the printing resolution and printing area relation of TPP, DLP, SLA, DIW, inkjet, FDM as well as SLS&SLM [264]. (b)-(c). Schematic diagram of two-photon polymerization and digital light processing. (d) High resolution 4D printed shape memory polymer Eiffel Tower [269]. (e) Thermally tunable and reconfigurable microlattices [270]. (f) DLP 3D printed various architected ionotronic sensors for multi-mode sensing using polyelectrolyte elastomers with robust interfaces and without leakage [271]. (g) DLP printed piezoelectric multimodal mobile microrobot climbing obstacles driven by electric fields [272]. (h) TPP printed micro-tools eject the trapped particles as the light-controlled piston through the microbubble [273]. (i) Shape memory effect of 4D printing structural multi-colour painting [256]. Adapted from [264].

© IOP Publishing Ltd. CC BY 3.0. Adapted from [269]. CC BY 4.0. Adapted from [270] with permission from the Royal Society of Chemistry. Adapted from [271]. CC BY 4.0. From [272]. Adapted with permission from AAAS. Adapted from [273], with permission from Springer Nature. Adapted from [256]. CC BY 4.0.</figcaption></figure>

driven by three key advancements: the high-efficiency, high resolution and large-aera 3D printing, the ability of multimeral structure printing, and the development of advanced smart/functional materials for high resolution 3D printing.

The combination of multiple printing methods offers a solution to balance both printing resolution and efficiency, thereby enabling the seamless integration of high resolution, large-scale, and high-speed printing within a single
printing process. Researchers have proposed several feasible approaches to achieve this goal. Typical examples include the large area projection microstereolithography approach, which combines DLP with a coordinated optical scanning system [277], the femtosecond projection two-photon lithography technique that integrates TPP with the DMD [278], as well as integral lithography, which combines DLP with a rotational microlens array [279].

Efforts have also been made toward achieving multimaterial printing in high resolution 4D printing. Researchers have developed various multimaterial 3D printing devices to tackle the key technical obstacle of efficiently and quickly switching and removing the residual resin. Multimaterial switching can be achieved by switching multiple resin barrels [276], or dynamically controlling fluids through resin switches [275]. Particularly, an innovative DLP-based centrifugal material 3D printing via spinning technique has been reported [280], enabling the creation of large-volume heterogeneous 3D objects. Additionally, the integration of DIW with DLP technique has greatly expanded the range of available materials and improved the efficiency, versatility and complexity of printed structures [281].

The notable advancements in developing and integrating advanced materials significantly enhance the responsiveness and functionality of 4D-printed microstructures. Introducing novel molecular designs, such as double networks and intermolecular forces, into smart materials can yield robust mechanical properties [282]. The incorporation of nanoparticles into smart materials allows for finer control over their responsiveness [282]. Furthermore, the integration of process-material-structure-function design is essential for the advancement of high resolution 4D printing technology. Utilizing advanced multi-physics modeling and simulation tools has led to a deeper understanding and accurate prediction of the behavior of smart materials during 4D printing.

## Concluding remarks

In the above sections, the status, current and future challenges, as well as recent advancements in high resolution 4D printing technologies, were comprehensively reviewed. The development of high-efficiency, large-area, high resolution, multimaterial printing systems, and advanced smart materials is poised to be applied in various industries. First, as 3D printing devices advance with higher resolutions, larger print areas, and faster printing speeds, we can anticipate groundbreaking developments enabling the creation of highly detailed, large-scale 4D-printed objects with exceptional efficiency. Industries like aerospace and architecture will benefit from the capability to rapidly produce intricate, full-scale prototypes and components. Second, the achievement of multimaterial high resolution 4D printing will usher in an era of versatile and intricate 4D-printed structures. This capability will enable researchers to print materials seamlessly with diverse properties, resulting in functional, multi-modal, and highly adaptable objects. These innovations will advance biomedical devices such as customizable implants, drug delivery systems, tissue engineering, and flexible electronics with intricate, multi-material circuits. Furthermore, the potential applications will be limitless as smart materials advance, exhibiting finely tuned properties that respond to various stimuli. We can envision 4D-printed structures that autonomously self-assemble or morph in real-time in response to environmental changes. These innovations will contribute to soft robotics with intricate design, high responsiveness, and high adaptability.

## Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 12072142).
## 20. Accelerated design for 4D printing

Frédéric Demoly¹,², H Jerry Qi³ and Jean-Claude André⁴

¹ ICB UMR 6303 CNRS, Belfort-Montbéliard University of Technology, UTBM, France

² Institut universitaire de France (IUF), Paris, France

³ The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, United States of America

⁴ LRGP 7274 UMR CNRS, University of Lorraine, Nancy, France

E-mail: frederic.demoly@utbm.fr, qih@me.gatech.edu and jean-claude.andre@univ-lorraine.fr

### Status

The rapid advancement of 4D printing has primarily been fueled by researchers involved in the fields of materials science, mechanical modeling, and chemistry. Most studies focus on tuning, depositing, and stimulating active materials used in various additive manufacturing (AM) techniques. They involve mastering the creation of multifunctional objects and structures while comprehending the interactions between active materials and energy stimuli that give rise to sensing, transduction, and actuation functions [283, 284]. Expanding active material performance and deposition capabilities represents a key research strategy, essential before industry adoption. However, harnessing the potential of smart materials and AM to engineered objects capable of adapting, transforming, or deploying in response to environmental or artificial stimuli poses a significant challenge from both design and engineering perspectives [181].

Recent research efforts have been concentrated on multi-material 4D printing, a fabrication strategy that combines passive and active materials to enhance actuation performance and achieve complex shape changes [281, 285]. In this context, the successful integration of dissimilar materials within a single object necessitates advancements in the capabilities for depositing multiple materials and computational design techniques. From a design standpoint, precise material distribution becomes paramount for achieving the desired shape changes. An approach using voxel-based modeling has emerged to facilitate property and material assignment within the 3D design space, enabling forward predictions of shape change of printed structures when exposed to any energy stimuli [286]. Furthermore, significant strides have been taken in the inverse design of shape-changing structures. To determine material distribution effectively, researchers have employed a combination of genetic algorithms and machine learning (ML) techniques [128, 287, 288], even coupled with topology optimization (TO) [289], resulting in efficient computations on reduced 3D model composed of up three distinct materials (see figure 32(a)). These results provide sophisticated arrangement of materials in the 3D design space and are relevant for complex shape-changing

behaviors and shapes where engineering experience is not sufficient. However, these voxel-based multi-material structures may encounter limitations with current AM techniques. This printability issue has been addressed by combining multiple AM techniques within a single machine [157, 281, 285, 290], and more recently by introducing interlocking blocks that can be easily printed separately and then assembled. For the latter, a computational design approach has been developed to convert voxel-based material distribution into multiple interlocking blocks made of active and passive materials, leading to promising mechanical and actuation performance (see figures 32(b) and (c)) [19, 291].

### Current and future challenges

In addition to the ongoing research focusing on material distribution in the 3D design space, a systemic perspective is crucial for 4D printing design. The long-term objective is to create adaptive, deployable, and transformable systems, applicable across sectors like medicine, automotive, textiles, aerospace, space, and more. These systems must make practical sense for widespread adoption. A direct challenge lies in capturing hidden needs, stemming from the often-misunderstood nature of 4D-printed objects. Addressing this can expand potential disruptive ideas.

Designing for 4D printing involves concurrent consideration of various factors, including functions, smart materials, expertise domains, worlds, AM techniques, scales, temporal aspects, physics, and stimuli (figure 33). This comprehensive integration challenge demands increased research efforts to develop models, methods, and software that incorporate computational and reasoning capabilities for various abstraction levels. These tools are vital for rapidly exploring potential solutions (shape, structure, materials, and stimuli) and identifying optimal designs for long-term sustainability. Such challenges fall into two subfields: design for X (X representing AM, material assembly, transformation, and performance) and design with X (X representing smart materials, stimuli, and artificial intelligence—AI). In the first category, X implies an objective to ease, while in the second one, X means an opportunity for inclusion and enhancement.

The traditional design process is composed of several phases, starting with design thinking and the creative generation of ideas and concepts, followed by the embodiment and detail design stages. Therefore, it is important to support creative strategies while introducing constraints (objectives and opportunities) to converge towards a satisfactory solution. Creativity is essential for 4D printing to establish functions and solve problems at hand and could benefit greatly from biomimicry and sustainable development. Conversely, the embodiment design phase, receiving significant attention in 4D printing, requires more scientific contributions. This includes exploring material distribution at different scales, complex structures, and spatiotemporal stimuli distribution. To achieve this, the use of biomimetic computing with ML and deep learning
<figure><img src="image_39.png" /><figcaption>**Figure 32.** Inverse design strategy and computational approach to build multi-material objects and structures using voxels and interlocking blocks. (a) Voxel-based modeling for predicting smart material behaviors; determination of material distribution using genetic algorithms and ML techniques, (b) computational design of complex material distribution into interlocking blocks, and (c) printed active and passive blocks and assembly strategy towards thermally sensitive shape-changing objects.</figcaption></figure>

techniques, supported by extensive datasets, is relevant and cost-effective. However, this strategy requires explanatory capabilities. Leveraging multi-domain ontologies, knowledge graphs, and integrating physical laws, even using physics-informed neural networks for small datasets, is imperative [292, 293]. This integration aligns with neuro-symbolic AI,

applicable to forward prediction and inverse design, through voxel-based simulation, finite elements simulation, or discrete TO. To accelerate 4D printing design, another challenge is streamlining knowledge, constraints, and decisions across design stages, ensuring digital design and fabrication pipeline.
<figure><img src="image_40.png" /><figcaption>**Figure 33.** Design for 4D printing roadmap built upon knowledge, models, methods, and tools (in purple boxes) that integrate 4D printing factors (in green boxes), and dedicated reasoning layers (in orange boxes) to meet application sectors (adapted from [181]).</figcaption></figure>

## Advances in science and technology to meet challenges

The scientific challenges associated with accelerated design for 4D printing involve expanding the research domains related to this emerging technology. This expansion includes considerations of AI, industrial design, and even the utilization of nano-microscale manufacturing technologies. These research domains can be used to manage complexity and introduce novel architectural freedom. Considering the Hype Cycle that highlighted 4D printing as an innovation trigger in 2018 [294], this research field has now reached a typical phase of disillusionment. It is crucial to materialize concrete applications to reach a productivity plateau leading to market adoption. To achieve this, it is important to leverage symbolic AI techniques to expand knowledge bases related to active materials, systems comprising structure-stimuli-materials, and possibly biomimicry but not limited to. This knowledge can be effectively integrated into design and simulation models and methods to tune, justify, validate connectionist AI reasoning, and even serve as a basis for recommendation systems (materials selection, stimuli selection, mechanism selection, etc.) [295, 296].

The integration of multiple perspectives in design is challenging and cannot be addressed by a single research group. It is essential to establish scientific networks, whether through funded research programs, or relevant scientific communities in conjunction with industrial partners. From an organizational point of view and to work in a highly pragmatic manner, in the short- and mid-terms, this involves conducting bottom-up

actions (from researchers and research groups towards scientific communities and research agencies) to fuel and invigorate the creation of knowledge, materials, and technologies. It also involves top-down operations (from societies towards researchers) to structure collective intelligence and actions towards technological solutions that are beneficial for society and industry [283, 284].

## Concluding remarks

Design for 4D printing plays a crucial role for advancing the widespread adoption (society, industry) of this emerging technology. It served as the convergence point for various scientific perspectives, integrating design for X (including AM, material assembly, transformation, and performance) and design with X (including smart materials, energy stimuli, nature-inspired principles, and AI) strategies. This engineering phase requires a reimagining from a paradigmatic and computational standpoint to accelerate the exploration and discovery of innovative real-world applications and their practical usage.

## Acknowledgments

This work was supported by the IUF, a French government grant managed by the French Research Agency under the 'France 2030' initiative and the DIADEM program (ANR-22-PEXD-0013, 'ARTEMIS'), the EIPHI Graduate School (Contract ANR-17-EURE-0002), and Bourgogne Franche-Comté Region.
## 21. Pattern-controlled 4D printing

Marwan Nafea¹, Mahdi Bodaghi² and Ali Zolfagharian³

¹ Department of Electrical and Electronic Engineering, Faculty of Science and Engineering, University of Nottingham Malaysia, 43500 Semenyih, Selangor, Malaysia

² Department of Engineering, School of Science and Technology, Nottingham Trent University, Nottingham NG11 8 NS, United Kingdom

³ School of Engineering, Deakin University, Geelong, VIC 3216, Australia

E-mail: marwan.nafea@nottingham.edu.my, mahdi.bodaghi@ntu.ac.uk and a.zolfagharian@deakin.edu.au

### Status

Shape programming is a critical part of four-dimensional (4D) printing that can be achieved using multiple approaches, such as printing-process-induced programming and post-printing programming. Shape programming can be used to control the permanent or temporary shape of the 4D-printed structure, depending on the type of the programming process [297]. One of the critical factors that influence the shape-programming process is the printing patterns, leading to a diverse area of pattern-controlled 4D printing. This is because the induced strain levels in 4D-printed structures are affected by the paths of these patterns. Pattern-controlled 4D printing can be realized using nine categories of patterns that are summarized in figure 34, where each one of them offers different levels of complexity and control to the actuation process.

The most common pattern-controlled approach is achieved by manipulating the infill patterns, which are usually generated using standard three-dimensional (3D) printing slicing software [298]. The shape and density of the infill patterns influence the actuation performance of 4D-printed structures. Gradient patterns offer the ability to gradually change the thickness, size, shape, and properties of the pattern [299]. The next type is hierarchical patterns, which are made up of smaller patterns that are repeated in a specific way to create complex structures [300]. Lattice patterns consist of repeating geometric shapes that are used to create objects that can deform or change shape predictably [301]. Auxetic patterns are special types of lattice patterns that possess a negative Poisson's ratio. This means that such patterns expand transversely when longitudinally stretched while offering mechanical advantages, such as energy absorption [302]. Origami and Kirigami patterns are some of the most interesting and complex 4D printing patterns. Origami patterns rely on folding the structure, while Kirigami patterns involve folding structures that include slots as well [303]. Weaving patterns are commonly used in textile-based and hygroscopic-based 4D printing to control the stiffness of the structure at selected locations [304]. Bioinspired patterns mimic patterns that exist in nature to achieve complex actuation performance [20]. Lastly, voxel-based patterns rely on discretizing the structure into sub-blocks using multi-material printing [291, 305].

### Current and future challenges

The main challenge that currently exists in 4D printing is the incomplete understanding of the fundamentals of this technology since it is a relatively new research area. More specifically, pattern-driven 4D printing drastically increases the levels of complexity in terms of design, modeling, simulation, printing, and characterization. The challenges begin even when using the simplest pattern since it is required to perform geometrical modeling of the induced-strain levels within a single shape or component of the pattern. This step becomes more challenging when dealing with non-uniform patterns. Most reported models that aim to estimate the curvature or bending angle of 4D-printed structures rely on variations of Timoshenko's model, where the transient response can be estimated for simple structures [306]. Applying this concept to pattern-controlled structures is a complex task, especially when combined with time-varying stimulus levels or stimulus-rate-dependent responses. This issue might be addressed using finite element analysis (FEA) approaches that incorporate constitutive models [307].

To date, most researchers in this area focus on using standard computer-aided design (CAD) tools, which can be ineffective when using complex non-uniform patterns. Then, the complexity of the simulation process is affected by the type of patterns used as well as the nature of the printing process itself. Therefore, even FEA faces difficulties when simulating pattern-controlled 4D-printed structures due to the complexity of solving the induced-strain levels along the patterns' paths. Another challenge in this area is the limitations of the slicing software used to prepare the design for the printing process. Despite providing multiple infill pattern geometries, the level of control of the parameters of the patterns is still limited, especially when considering adaptive and gradient infill patterns. Moreover, the printing process suffers from limitations in terms of the dimensional accuracy, repeatability, reproducibility, and scalability of the printed structures, especially when using consumer-grade printers. Even when using industrial-grade printers, the adoption of 4D printing technology by industry is still limited since this technology is not mature enough to be implemented on a large scale without extensive research and development processes. Advancements in pattern-controlled 4D printing require collaboration between academia and industry to tackle the challenges in this area from different aspects.

### Advances in science and technology to meet challenges

It is envisioned that the future development of this area will involve four main steps, as illustrated in figure 35. The first step starts by defining the design requirements in terms of the actuation performance requirements, material properties, and the stimulus type and range used to activate the structure. The energy required to activate the structure and the self-sensing ability are factors that need to be taken into consideration. Then, the printing requirements are considered in
<figure><img src="image_41.png" /><figcaption>**Figure 34.** Main categories of pattern-controlled 4D printing, accompanied by selected sub-categories.</figcaption></figure>

<figure><img src="image_42.png" /><figcaption>**Figure 35.** Future trends in pattern-controlled 4D printing.</figcaption></figure>

terms of minimizing the use of material and reducing the cost while achieving the desired performance and printing accuracy. The next step, which is design development, starts by

selecting suitable materials from an open-access smart materials (SMs) database. It is envisioned that the development of four-axis to seven-axis printers will grow rapidly in the future
[308]. These printers will open doors for four-axis to seven-axis 4D printing, which allows complex structures and shape-programming approaches to be realized. This concept will offer the ability to print high-degree-of-freedom patterns that cannot be printed using three-axis printers. As a result, slicing tools need to adapt to these changes using parametric pattern-based slicing approaches. Artificial intelligence (AI) will play a crucial role in the development of this area in terms of AI-enhanced and generative AI design. Moreover, CAD scripting and visual programming language (VPL) design approaches [291, 309] can address the current limitations of standard CAD tools. Furthermore, the improvements in the simulation capabilities will see great improvements in terms of developing optimal FEA tools that can solve complex pattern-controlled design problems that might even rely on supercomputers.

The third step involves implementing the design based on the selected printing parameters, patterns, and shape-programming method [310]. This is followed by the assembly and integration of the structures. Lastly, the fourth step implements corrective measures to optimize the whole process. This may involve using computer vision (CV) to detect printing inaccuracy, which can be then reported to a server using cloud-connected (CC) printers. Moreover, 3D scanners can be

used during and after the printing process to verify the accuracy of the printed structures. Then, the information can be stored in a 4D printing database that can be used to optimize future designs. The actuation performance is then analyzed and compared with the design requirements, while important information is sent to the second and third steps for further improvements.

## Concluding remarks

Pattern-controlled 4D printing offers promising advantages that keep attracting the attention of researchers. Pattern-controlled design will play an essential future role in the development of 4D printing with additional manufacturing axes. The collaboration between the industry and academia is a key factor in promoting this technology, where developing new design and simulation tools is a mutual goal for both parties.

## Acknowledgments

This work was supported by the Ministry of Higher Education Malaysia under the Fundamental Research Grant Scheme (FRGS/1/2023/TK09/UNIM/02/4).
## 22. Topology optimization for 4D printing

Yun-Fei Fu<fnref n="1" /> and Bernard Rolfe<fnref n="2" />

E-mail: yfu15@ualberta.ca and bernard rolfe@deakin.edu.au

### Status

Topology optimization is a structural optimization method that has great potential to fully exploit the significant benefits provided by the increased design freedom offered by additive manufacturing or 3D printing [311–313]. 4D printing can fabricate an object that can change its color, volume, and shape under different environmental conditions [288, 314], which can provide more design freedom for topology optimization. Traditionally, the purpose of topology optimization is to obtain the lightweight structure with high stiffness. By contrast, the purpose of topology optimization for 4D printing is to find the optimal distribution of component materials or building blocks that leads to desired transformations.

Current research about topology optimization for 4D printing focuses on the design of soft active structures [289, 315, 316], and multi-material structures are designed to obtain a desired shape change as multiple combinations of materials can be generated to achieve a specific goal in comparison with single material optimization [289, 316]. The effectiveness of topologically optimized soft active structures was numerically and experimentally validated by Tian et al [316]. The topological design of a three-material soft active structure presented in figure 36 exemplifies the potential applications of current topology optimization techniques to 4D printing design. In figure 36, the environmental stimulus is the magnetic field, θ represents the magnetization direction, *p* represents the loading that is distributed on the contacting area (the black area in figure 36(a)), *B* represents the magnetic flux density, and Δ*u*<fnref n="2" /> is the least-square error with respect to the target displacement. One typical application of topology optimization to 4D printing is the design of the soft actuator for delivering delicate tasks in fragile environments, for example, food and biomedical sectors [317]. In addition, a theoretical framework of topology optimization for 4D printing was established by Garcke et al [318].

### Current and future challenges

Although the challenges and corresponding solutions concerning topology optimization for traditional 3D printing have been systematically discussed [313], 4D printing oriented topology optimization has not been widely studied yet. Some

works used the linear elastic material model for simplicity [316, 317]. However, soft active structures will generate large deformations under a certain environmental stimulus, and hence material and geometrical nonlinearities should be incorporated into topology optimization. The most challenging aspect is establishing an accurate relationship between the structural response and the corresponding environmental stimulus. If too many assumptions are made in optimization, the effects of the environmental stimulus on the structural response cannot be controlled accurately, resulting in a solution far from the actual requirements. The fabrication of topologically optimized multi-material soft active structures is challenging due to the material and geometrical complexities. The manufacturability of topologically optimized soft active structures in the literature has not been fully validated yet, and therefore most of them are conceptual designs.

Topological design of lattice structures or metamaterials for 4D printing can be regarded as the future challenge. Although 4D metamaterials with zero Poisson’s ratio, shape recovery, and energy absorption features have been studied [26], topology optimization is not used for the design of 4D metamaterials. Topological design for metamaterials requires extra computational methods such as the homogenization theory to design structural configurations with periodic boundaries and repetition of representative unit cells [319]. When it comes to 4D metamaterials, a more complicated mathematical model is required.

### Advances in science and technology to meet challenges

The existing works regarding geometrical and material nonlinearities in [320, 321] can be easily used to consider large deformations under a certain environmental stimulus for 4D printing. Feng et al [322] conducted additive manufacturing oriented multi-material topology optimization to overcome the size limitations of the 3D printer, and this work can be employed to increase the manufacturability of the optimized multi-material soft active structures by considering the dimensional constraints of each material component. Han and Wei [323] investigated multi-material topology optimization and additive manufacturing for metamaterials, which can be extended to 4D metamaterials via smart materials. Li et al [324] systematically carried out topology optimization of multi-material structures with programmable elastic responses under finite deformations, and this work can be modified to construct an accurate relationship between the structural response and environmental stimuli. Solutions to the aforementioned challenges were studied separately, and hence a proper combination of different fields is needed to obtain manufacturable topologies that are capable of responding to different environmental stimuli accurately or at least remaining an acceptable deviation.

<footnote n="1">¹ Department of Mechanical Engineering, University of Alberta, Edmonton, AB T6G 1H9, Canada</footnote>

<footnote n="2">² School of Engineering, Deakin University, Geelong, VIC 3216, Australia</footnote>
<figure><img src="image_43.png" /><figcaption>**Figure 36.** Topologically optimized three-material soft active structure with response to a magnetic field. Reprinted from [316], Copyright (2022), with permission from Elsevier.</figcaption></figure>

**Concluding remarks**

Current works mainly concentrate on the topological design of multi-material soft active structures. This research topic is still in the theoretical stage. Large deformations, manufacturability of multiple materials, and accurate

relationship between structural responses and different environmental stimuli need to be incorporated into topology optimization to yield practical solutions for 4D printing. The topological design of metamaterials for 4D printing will be a promising research direction in the future.
## 23. 4D artifacts

Ye Tao¹ and Guanyun Wang²

¹ Hangzhou City University, Hangzhou, People's Republic of China

² Zhejiang University, Hangzhou, People's Republic of China

E-mail: taoye@hzcu.edu.cn and guanyun@zju.edu.cn

### Status

4D artifacts refer to a category of objects made from programmable materials with digital manufacturing technology represented by 4D printing. Beyond three-dimensional (3D) space, a 4D artifact can transform itself into another structure under the influence of external energy input, such as temperature, light, or other environmental stimuli, and therefore achieve smart functionalities such as self-deformation [325], self-healing [326], or self-assembly [327]. The 4D concept has gained considerable and significant development across various fields, such as materials science [282], medical engineering [244], and robotics [328].

In addition to functional advancements, the consideration of human and societal impact of artifacts throughout the whole 4D process [329] (i.e. 4D manufacturing, usage, and reconfiguration) has become an ongoing topic of interest to scientists, human-computer interaction researchers, and designers. With the development of universal 3D printing and personal additive manufacturing technologies, there is a growing development in the design and manufacturing technology of democratized 4D artifacts, including in the fields of 3D printing, smart materials, programmable structures, shape-changing mechanism, etc.

Digital manufacturing technologies (see figure 37(a)), such as 3D printing, serve as the foundation for realizing 4D artifacts. Techniques like fused deposition modeling 3D printing (FDM3DP), direct ink writing (i.e. DIW, PP), and cured printing (i.e. SLA, SLS) are widely employed for fabricating 4D artifacts designed with computer-aided tools. Prominent examples are FDM3P thermoplastics (e.g. PLA, ABS, PCL, etc.) [330–337], which possess the advantages of low cost, high availability, excellent comprehensive performance, and reusability. Direct ink writing or jetting technology [338, 339] includes extrusion modeling of semi-liquid materials and inkjet modeling of liquid ink. However, due to the properties of the liquid material, the adapted printing machine usually requires customization, and the complexity of morphogenesis is limited. Cured printing technology [340] can achieve more complex and intricate three-dimensional shapes, such as suspended and stacked with the support of the powder or liquid material itself, albeit at a relatively high cost and threshold.

According to the 'smart' properties of the material (figure 37(b)), which are usually reflected in the shape-change or shape-memory properties under certain external stimulus conditions, structural design (figure 37(b)) is carried out through programming to allow for precise control over its transformation between different states (figure 37(c)).

Currently, research projects are focused on the development of customized materials, design and fabrication tools, and post-processing methods to improve shape-changing controllability and manufacturing efficiency, and on expanding shape-shifting possibilities and embedding electronics to enhance the interactivity of 4D artifacts. Beyond these, the integration of shape-changing technologies may bring about disruptive changes in the traditional manufacturing industry (figures 37(d)–(f)). For example, the exploration of flat production of 4D pasta [341], which can take shapes during cooking, can dramatically improve manufacturing efficiency, conserve storage and transportation space, improve cooking efficiency, and elevate the consumer experience. Moreover, further development on integrating 4D technology throughout the entire lifecycle of artifacts may present unique opportunities and challenges for sustainability.

### Current and future challenges

To establish 4D technology as a sustainable, consumer-grade, and industrial-scale method for 4D artifacts, the challenges can be categorized across the entire life cycle of 4D artifacts into knowledge, technological, design, humanistic, and industrial challenges.

**Knowledge challenges.** Research into the principle of material deformation is crucial in the pursuit of 4D artifacts. When confronted with unknown deformation principles and mechanisms, researchers are often required to possess inter-disciplinary knowledge integration capabilities and collaborative innovation in materials science, mechanical engineering, computer science, design, etc. Furthermore, the development of smart materials can help optimize form factors to solve practical issues, such as minimal weight, high resolution, or low cost. Consequently, the investigation of materials with unconventional functionalities has always been an enduring challenge for 4D artifacts.

**Technology challenges.** A significant challenge still exists in achieving precise control over high-resolution deformation based on smart materials. Aligned with broader computing trends, the form factor of 4D artifacts is moving from stationary to mobile, wearable, and even implantable. They are also evolving from one-way transformations to reversible, temporal, and even multi-state changes on demand. Besides investigating material properties, to realize this vision, increasing manufacturing precision and speed, enhancing actuation reliability and safety, and simplifying digital design and manufacturing technologies remain challenging to achieve highly accessible customized form factors and actuation methods.

**Design challenges.** The most substantial differences from traditional design are the form of responsive artifacts and their dynamic attributes. A crucial challenge arises when translating static forms from traditional design representations, such as sketches and prototypes, into actual 4D artifacts with temporal characteristics. Designers, in particular, will be challenged to develop 4D artifacts that are satisfying in both the form and
<figure><img src="image_44.png" /><figcaption>**Figure 37.** Schematic of the core design element of 4D artifacts including the field of (a) 3D printing, (b) smart materials, programmable structures, (c) stimulus conditions, and deformation behaviors. Examples of cutting-edge 4D artifacts include (d) 4D furniture [331], (e) shape-changing pasta [341], and (f) breathing fabrics [337].</figcaption></figure>

dynamics of interaction between artifacts and people interacting with them, as well as how to predict and verify the design at a low cost in advance.

**Humanistic challenges.** From a humanistic perspective, the viability of 4D artifacts as a reliable and useful medium for human-object interaction is underpinned by a comprehensive understanding of the user experience when using 4D artifacts. This understanding enables us to elucidate their value, identify the domains and tasks in which they offer advantages, and facilitate their design and construction. Nonetheless, there are uncertainties and challenges to formulating theories and principles regarding the acceptability of their transit interactive behaviors to the broader public, as well as how to predict and respond to users' interactions with new 4D artifacts.

**Industrial challenges.** 4D artifacts may encounter challenges in terms of short-term benefits, such as increased resource demand and higher costs of recycling and reuse, but the ultimate goal of the 4D concept is to establish a novel ecological industrial chain that spans the entire lifecycle of 4D artifacts to achieve long-term sustainability. This revolution seeks to reshape established consumption habits by realizing multiple

<figure><img src="image_45.png" /><figcaption>**Figure 38.** The challenges and opportunities of 4D artifacts in a holistic view of the vertical life-cycle chain of 4D artifacts and the horizontal relationship between humans and artifacts.</figcaption></figure>

functions within a single 4D artifact [342], such as one 4D personal computer displacing a number of mobile phones, watches, computers, laptops, etc. Therefore, the primary challenges for 4D artifacts lie in ensuring their ‘lifelong’ deformation functionality, where a new industrial standard for 4D artifacts should be established instead of adhering to a consumer-level definition.

## Advances in science and technology to meet challenges

To successfully address the current and future challenges of 4D artifacts, it is necessary to take a holistic view that considers both the vertical life-cycle chain of 4D artifacts and the horizontal relationships between humans and the artifacts (figure 38).

In tackling the challenges within the vertical life-cycle chain of 4D artifacts, the rapid and lightweight development of additive manufacturing concepts can be important. Leveraging cutting-edge materials science and nanotechnology, coupled with advanced simulation and modeling tools, holds the potential to deepen our comprehension of materials’ time-dependent properties and grant us greater control over them. This, in turn, facilitates dynamic manufacturing processes and on-demand deformations. Additionally, the enhancement of forward design capabilities and inverse
simulation computing will accelerate the development of 4D manufacturing technology, enabling engineers to predict and optimize the behavior of 4D printed objects, thereby reducing resource waste. Furthermore, the development of innovative 4D artifacts, under the guidance of new user experience requirements, is imperative for top-down guidelines for improving the vertical life cycle chain.

Confronted with the challenges in the horizontal relationship between humans and artifacts, optimizing the end-user interaction experience is critical. The integration of intelligent control systems and human-machine interfaces will enhance the practicality and usability of 4D artifacts. At the same time, addressing the safety and ethical considerations surrounding 4D artifacts is integral to its democratization. Sustainability concerns also must factor into material selection, production efficiency, and product lifespan to mitigate environmental impact and ensure the sustainable development of 4D technology.

In summary, 4D artifacts ultimately return to humans, and their development holds the promise of offering new solutions to the issues impacting humans, society, and the environment.

## Concluding remarks

Despite the fact that 4D printing remains in its early stages and there is still a long way to go before its commercialization and widespread application, as an emerging additive manufacturing technology, 4D printing is promising to become an efficient, sustainable, and personalized manufacturing method. At the same time, 4D artifacts have the potential to provide end users with adaptive, augmented, and versatile interactive experiences towards enormous applications in intelligent interactive terminal products, human-machine hybrid interaction, biomedical, and other fields.

## Acknowledgments

This work was supported by National Natural Science Foundation of China under Grant No. 62002321, and Fundamental Research Funds of Hangzhou City University (No. X-202306).
## 24. Multi-axis 4D printing

Marwan Nafea¹, Ali Zolfagharian² and Mahdi Bodaghi³

¹ Department of Electrical and Electronic Engineering, Faculty of Science and Engineering, University of Nottingham Malaysia, 43500 Semenyih, Selangor, Malaysia

² School of Engineering, Deakin University, Geelong, VIC 3216, Australia

³ Department of Engineering, School of Science and Technology, Nottingham Trent University, Nottingham NG11 8NS, United Kingdom

E-mail: marwan.nafea@nottingham.edu.my, a.zolfagharian@deakin.edu.au and mahdi.bodaghi@ntu.ac.uk

### Status

Three-dimensional (3D) printing has experienced great advancements, especially in the area of FDM printers, where many manufacturers have developed advanced types of FDM 3D printers, robotic-arm-based printers, and aerial 3D printers [343]. Most researchers use FDM 3D printers that support moving the printing head or bed along the x-, y-, and z-axes. However, the main configuration that is used by researchers is 2.5-axis 3D printing due to the incomplete control over the deposition along the z-axis. In this approach, the model is sliced into parallel planar layers that are then printed layer-by-layer using a specific increment along the z-axis. Nevertheless, researchers were able to tackle this issue by developing advanced slicing methods that support 3-axis printing [344], as well as 3D printers that support multi-axis 3D printing. This allowed achieving 3D printing of structures using multi-axis configurations, including 4-axis [345], 5-axis [346], 6-axis [347], 7-axis [348], and 8-axis [349]. These continuous, or simultaneous, multi-axis printing approaches opened the doors for sub-categories based on these approaches, which are known as positional, or indexed, configurations. Some examples include 3 + 1-axis [350], 3 + 2-axis [351, 352], and 3 + 3-axis [353].

Four-dimensional (4D) printing relies on the shape programming of structures that were 3D-printed from smart materials. This process allows these structures to change their shape, color, or function over time, which adds a fourth dimension to the 3D printing process [297]. For instance, when using FDM, the shape-programming approach is mainly carried out during the printing process along the printed lines, which is also performed using a 2.5-axis configuration [310]. Therefore, multi-axis 4D printing offers great potential for complex multi-axis shape programming, where the strain can be induced along additional printing axes. So far, multi-axis 4D printing has witnessed limited progress, where researchers have only demonstrated 6-axis 4D printing [354] and 6 + 1-axis 4D printing [355]. However, it seems that the terminology of such a process is not well-understood, where some researchers refer to this process as 5D or 6D printing [356]. These definitions might be subject to misinterpretation

since there is no additional dimension added to the printed structure when using additional printing axes. For instance, some manufacturers may refer to their printers as 5D printers, but this is a short term that refers to the degrees-of-freedom (DoF), which is different from the time-dependent behavior attributed to the fourth dimension. Therefore, we believe that there is a high need for standard terminology in multi-axis 3D and 4D printing due to the rapid development in these areas. Figure 39 presents potential advancements in multi-axis 4D printing.

### Current and future challenges

Multi-axis 3D/4D printing strategies that utilize a high number of axes, such as 5-axis 3D/4D printing, offer several structural advantages compared to 2.5-axis 3D/4D printing. This is due to the fact that the former consumes less printing material while offering the ability to produce stronger structures compared to the latter. However, increasing the number of axes used in the printing process comes with several challenges that hinder progress in this area. For instance, the complexity and cost of 3D printers and systems that support such printing methods increase significantly as the number of axes increases. In many cases, the additional printing axes are realized by adding rotational movements to the printing head or printing bed, by using a robotic arm, or by a combination of all these possibilities. This also leads to an increase in the complexity of slicing such designs, where standard slicers that support 2.5-axis 3D printing are not suitable for these approaches. This complexity is caused by the challenges associated with planning the printing path in 3D space. Moreover, such a printing process causes interference between the printing paths when printing non-uniform objects. This also leads to challenges when selecting the orientation of the printed object, as well as the orientation of the printing head along each printing path to avoid colliding with the printed part. Furthermore, multi-axis 3D and 4D printing require a long time and high energy consumption to print objects due to the constant change in orientation of the printing head and printing bed.

These challenges become more evident when developing structures for multi-axis 4D printing. The design requirements of 4D printing add more challenges to the whole printing process in terms of hardware implementation, slicing, path planning, modeling, and simulation. For example, FDM-based strain-induced shape programming faces several challenges when using this approach. The levels of induced strain in each layer and each part of the printed structure need to be precisely controlled to achieve the desired shape change after activating the structure. This means that the printing parameters need to be carefully designed to meet the additional requirements of multi-axis 4D printing. For instance, the reported modeling and simulation approaches to 4D-printed structures only consider planar layers to estimate the bending angle and shape-morphing of such structures [357]. Therefore, there is a need for advanced modeling and simulation approaches that can handle the complexity of multi-directional induced strain.
<figure><img src="image_46.png" /><figcaption>**Figure 39.** Main potential multi-axis 4D printing technologies.</figcaption></figure>

<figure><img src="image_47.png" /><figcaption>**Figure 40.** Future trends in multi-axis 4D printing.</figcaption></figure>

## Advances in science and technology to meet challenges

Currently, there is a lack of development in the area of multi-axis 4D printing since this technology is still in its early stages, where the development is mainly focused on 2.5-axis 4D printing. Therefore, most research is dedicated to tackling the challenges associated with multi-axis 3D printing without considering the requirements of 4D printing. Significant research has been undertaken to address the issues associated with slicing designs for multi-axis 3D printing, such as feature-based slicing, adaptive slicing, multidirectional slicing, and conformal slicing. Moreover, path planning has been one of the main focus areas in multi-axis 3D printing, which is performed after the slicing process to generate the printing toolpaths. This process can be realized using several approaches, such as online and offline collision detection and avoidance, contour-parallel

printing path generation, continuous spatial path generation, gradient infill generation, as well as multi-robot path planning.

It is expected that multi-axis 4D printing will experience great advancements in the near future. This is caused by the rapid development of slicing and path-planning methods, which offer a high level of control over the paths of the induced strain. In addition, the current trend of increased quality in multi-axis 3D printers and robots indicates that 4D printing technology will have the required tools to meet the complexity of shape programming in 3D space. One of the promising areas that might see great investigation in the future is the use of teams of robotic arms in the 4D printing process, which offers great advantages in terms of increasing the DoF of the printing process. This will also open doors to creating large-scale 4D-printed structures that are not limited to the size of 3D printers. Moreover, 4D printing might benefit from the great flexibility of aerial robotics, where a drone
or a swarm of drones can 4D-print structures at remote locations. Meanwhile, these advancements will also require crucial support from other technologies, such as artificial intelligence (AI), which can be used in several 4D printing areas, such as AI-enhanced design, generative AI design, and AI-based slicing and path planning. Lastly, the combined advantages of AI and finite element analysis (FEA) can be used to model the complex actuation performance of multi-axis 4D-printed structures, which may require using supercomputers to handle such complexity. A summary of the future trends in multi-axis 4D printing is presented in figure 40.

## Concluding remarks

Multi-axis 4D printing offers promising advantages that can broaden the horizons of 4D printing. This technology will play a key role in the future development of 4D printing. There is a high need for collaboration between academia and industry to develop the tools required to advance this technology. Moreover, the terminology used in this research area requires further standardization and careful consideration. The authors propose the terminology of *n*-axis 3D/4D printing to differentiate products fabricated using a range of printers with modified axes, either as conventional 3D or time-responsive 4D constructs.

## Acknowledgments

This work was supported by the Ministry of Higher Education Malaysia under the Fundamental Research Grant Scheme (FRGS/1/2023/TK09/UNIM/02/4).

## Data availability statement

All data that support the findings of this study are included within the article (and any supplementary files).

## ORCID iDs

Mahdi Bodaghi https://orcid.org/0000-0002-0707-944X

Yanju Liu https://orcid.org/0000-0001-8269-1594

Jinsong Leng https://orcid.org/0000-0001-5098-9871

Ruizhe Xing https://orcid.org/0000-0002-3651-376X

Michael D Dickey https://orcid.org/0000-0003-1251-1871

Katarina Winands https://orcid.org/0000-0002-3114-8476

Saqlain Zaman https://orcid.org/0000-0002-9003-9712

Hesam Soleimanzadeh https://orcid.org/0000-0002-9452-9532

Tibor Barši Palmić https://orcid.org/0000-0001-6403-8233

Janko Slavič https://orcid.org/0000-0002-5982-8377

Yonas Tadesse https://orcid.org/0000-0001-6606-7089

Qinglei Ji https://orcid.org/0000-0001-9221-0918

Chun Zhao https://orcid.org/0000-0003-4925-8793

Leonid Ionov https://orcid.org/0000-0002-0770-6140

A M Sousa https://orcid.org/0000-0003-0256-0119

J Henriques https://orcid.org/0000-0001-8016-4846

A P Piedade https://orcid.org/0000-0002-1588-0640

Qi Ge https://orcid.org/0000-0002-8666-8532

Frédéric Demoly https://orcid.org/0000-0002-5825-6573

H Jerry Qi https://orcid.org/0000-0002-3212-5284

Marwan Nafea https://orcid.org/0000-0001-6123-5100

Yun-Fei Fu https://orcid.org/0009-0005-1083-8389

Ye Tao https://orcid.org/0000-0002-9152-7793

Guanyun Wang https://orcid.org/0000-0002-7904-1504

Ali Zolfagharian https://orcid.org/0000-0001-5302-360X

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