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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Additive Manufacturing Skills in Practice.
- Sprache: Englisch
Concise, practical guide presenting skills to integrate porous structure design with additive manufacturing requirements
Part of Wiley’s Additive Manufacturing Skills in Practice series and written with the industry practitioner in mind, Advanced Techniques in Porous Structure Design for Additive Manufacturing addresses the growing integration of porous structures and additive manufacturing, essential for applications in the biomedical, aerospace, and automotive fields in which porous structures are crucial due to their ability to deliver top-notch performance alongside lightweight characteristics.
This book covers all areas of the subject and concludes with a series of specialized chapters devoted to simulation software, case studies, and future trends and emerging technologies. Each chapter features a design problem that presents an open-ended scenario to prompt readers to think through the real-world applications of the concepts and theories discussed and connect them to their own job roles.
Topics discussed in Advanced Techniques in Porous Structure Design for Additive Manufacturing include:
- Fundamentals of additive manufacturing, covering processes, materials, and design considerations
- Mathematical modeling, covering optimization techniques and the finite element method
- Multiscale topology optimization, shape optimization methods, and post-processing techniques
- Software utilization in porous structure design, with information on how to program simulations
- Porous structures in soft robotics, porous heat sinks, porous plates, and porous mechanical support structures
With a blend of theoretical understanding and hands-on expertise in an emerging domain, Advanced Techniques in Porous Structure Design for Additive Manufacturing is an essential reference for industry professionals, researchers, and postgraduate students in universities, particularly those specializing in mechanical design and additive manufacturing.
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Veröffentlichungsjahr: 2025
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Table of Contents
Cover
Table of Contents
Additive Manufacturing Skills in Practice
Title Page
Copyright
Dedication
Preface
Chapter 1: Introduction to Porous Structures and Additive Manufacturing
1.1 INTRODUCTION
1.2 WHY DESIGNING POROUS STRUCTURES
1.3 TYPES OF CELLS
1.4 CHALLENGES IN THE DESIGN AND FABRICATION OF POROUS STRUCTURES
REFERENCES
Chapter 2: Fundamentals of Additive Manufacturing
2.1 INTRODUCTION
2.2 METALLIC MATERIALS
2.3 METALLIC ADDITIVE MANUFACTURING
2.4 PLASTICS
2.5 PLASTIC 3D PRINTING
2.6 CERAMICS
2.7 CERAMIC 3D PRINTING
2.8 THE PRODUCTION CYCLE OF 3D PRINTING
2.9 CHALLENGES FACING ADDITIVE MANUFACTURING
2.10 EMERGING TECHNIQUES IN ADDITIVE MANUFACTURING
REFERENCES
Chapter 3: Mathematical Modeling for the Calculation of Porous Structure Properties: Techniques and Applications
3.1 INTRODUCTION
3.2 OVERVIEW OF COMPUTATIONAL ASSESSMENTS OF PHYSICAL PROPERTIES OF MATERIALS
3.3 MECHANICAL PROPERTIES OF MICROSTRUCTURE
3.4 EFFECTIVE ELASTICITY TENSOR FOR POROUS STRUCTURES USING FEM FORMULATION
REFERENCES
Chapter 4: Advanced Techniques in Porous Structure Design
4.1 INTRODUCTION
4.2 PARAMETRIC OPTIMIZATION
4.3 NON‐PARAMETRIC OPTIMIZATION
4.4 MULTIPHYSICS TOPOLOGY OPTIMIZATION FUNDAMENTALS
4.5 TOPOLOGY OPTIMIZATION METHODOLOGIES
4.6 SHAPE OPTIMIZATION
4.7 POROUS STRUCTURAL DESIGN
REFERENCES
Chapter 5: Practical Examples and Case Studies
5.1 INTRODUCTION
5.2 POROUS HEAT SINK DESIGNS WITH NON‐PARAMETRIC OPTIMIZATION
5.3 APPLICATION OF ROBOTICS
REFERENCES
Chapter 6: Advanced Software Utilization for Designing and Analyzing Porous Structures
6.1 INTRODUCTION
6.2 COMMERCIAL SOFTWARE
6.3 CODING‐BASED COMMERCIAL SOFTWARE DESIGN OF POROUS STRUCTURES
REFERENCES
Chapter 7: Emerging Trends and Directions in Advanced Porous Structures
7.1 INTRODUCTION
7.2 ADVANCED MANUFACTURING
7.3 APPLICATIONS OF ADVANCED POROUS STRUCTURES
7.4 CHALLENGES AND FUTURE DIRECTIONS
References
Index
End User License Agreement
List of Tables
Chapter 5
Table 5.1 The outcomes of concurrent multi‐scale topology optimization for 3...
Table 5.2 A comparative analysis of the performance of different microstruct...
Table 5.3 Effect of sub‐design domain configurations on heat conductivity ma...
Table 5.4 The best results of multi‐scale optimization on the Pareto front o...
Table 5.5 Single macroscale design of the heat‐activated displacement actuat...
Table 5.6 Multi‐scale design of the heat‐activated displacement actuator wit...
Table 5.7 A single macroscale heat‐activated gripper design that reduces wei...
Table 5.8 A single macroscale heat‐activated gripper design that reduces wei...
Table 5.9 Heat‐activated gripper design on many scales with different heat c...
List of Illustrations
Chapter 1
Figure 1.1 The effect of material distribution on material properties, with ...
Figure 1.2 Common porous structure categorization.
Chapter 2
Figure 2.1 Lattice structure examples.
Figure 2.2 Metallic grains and boundaries: (a) Microscopic and (b) atomic.
Figure 2.3 Metallic grain orientation: (a) Random and (b) preferred.
Figure 2.4 3D printing with powder bed fusion.
Figure 2.5 The cycle of additive manufacturing.
Figure 2.6 Porous microstructure exhibiting a negative Poisson's ratio and n...
Figure 2.7 Internal voids within a solid 3D‐printed structure.
Figure 2.8 The three progressive stages of solid‐state sintering: (a) Initia...
Chapter 3
Figure 3.1 Analytical logic for composite material spatial configuration.
Figure 3.2 The stress–strain relations for composite configurations: (a) Iso...
Figure 3.3 Classical Voigt–Reuss upper and lower bounds.
Figure 3.4 The Hashin–Shtrikman bounds.
Figure 3.5 Same volume fraction with different topological distribution comp...
Figure 3.6 Asymptotic homogenization problem.
Figure 3.7 The finite element discretization of the microstructure.
Figure 3.8 The oscillatory behavior of periodic boundary conditions.
Figure 3.9 The three modes of mechanical deformation in a 2D RVE [3].
Figure 3.10 A multi‐scale structure incorporating both macro‐ and microlevel...
Figure 3.11 Representation of the homogenized thermal properties of the micr...
Figure 3.12 Periodic RVE model [5].
Chapter 4
Figure 4.1 The cantilever beam's thickness versus deflection under constant ...
Figure 4.2 Optimizing cantilever beam deflection: finding the ideal thicknes...
Figure 4.3 The topology optimization designing process for the heat maximiza...
Figure 4.4 Functional example of convexity.
Figure 4.5 Mathematical optimization with multiple minima.
Figure 4.6 Multi‐objective function optimization.
Figure 4.7 Level‐set representations of the boundary for a single function....
Figure 4.8 Biologically inspired microstructure process.
Figure 4.9 Examples of the TPMS model.
Chapter 5
Figure 5.1 Design domain in (a) macro‐ and (b) microscale.
Figure 5.2 Optimization for (a) a 50% volume fraction at the macroscale, (b)...
Figure 5.3 Optimization for (a) a fully distributed initial design domain, (...
Figure 5.4 The multi‐scale design domains of the 3D cases (a) Central point ...
Figure 5.5 Iteration histories of the normalized heat compliance of 3D case ...
Figure 5.6 The final multi‐scale design of case (c) [20].
Figure 5.7 The ABS‐printed specimen of the 3D multi‐scale optimized case (c)...
Figure 5.8 Simultaneous optimization of design domains: (a) a square macro d...
Figure 5.9 The influence of microstructure design on the performance of heat...
Figure 5.10 Flowchart of concurrent multi‐scale heat and stiffness optimizat...
Figure 5.11 The spatial layout of numerical examples: (a) mechanical loading...
Figure 5.12 Pareto front of the concurrent multiphysics optimization of exam...
Figure 5.13 The multi‐objective history of the concurrent optimization for e...
Figure 5.14 Pareto front of the concurrent multiphysics optimization of the ...
Figure 5.15 The design challenge of the soft robotic gripper mechanism: (a) ...
Figure 5.16 A case study on concurrent multi‐scale hybrid design for soft gr...
Figure 5.17 The number of iterations for (a) the hybrid topology optimizatio...
Figure 5.18 Comparison of output displacement between (a) the SIMP method an...
Figure 5.19 Concurrent multi‐scale, multi‐material design using hybrid SIMP‐...
Figure 5.20 Objective function history.
Figure 5.21 Macro and micro design domains in a multi‐scale structure.
Figure 5.22 Heat transfer modeling of conduction–convection problem.
Figure 5.23 Thermo‐elastic compliant mechanism design problem for the therma...
Figure 5.24 Finite element modeling of the coupled multi‐scale and multiphys...
Figure 5.25 Multi‐scale design problem: (a) macrostructure; (b) periodic cel...
Figure 5.26 Single‐scale macromodel of the heat‐activated displacement actua...
Figure 5.27 Normalized objective function of the single‐scale heat‐activated...
Figure 5.28 Heat map and deformation of the displacement inverter design for...
Figure 5.29 Multi‐scale design domain of the heat‐activated displacement act...
Figure 5.30 Porous design of the heat‐activated displacement actuator [73] /...
Figure 5.31 Performance of the 50% weight reduction solid, 75% weight reduct...
Figure 5.32 Design domain of a heat‐activated gripper [73].
Figure 5.33 Normalized objective function of the single‐scale heat‐activated...
Figure 5.34 Multi‐scale design domain of the heat‐activated gripper as (a) t...
Figure 5.35 Porous design of the heat‐activated gripper design as (a) the ma...
Figure 5.36 Performance comparison of the 50% weight reduction solid, 75% we...
Figure 5.37 The heat‐activated gripper's multi‐scale design domain consists ...
Figure 5.38 Optimization results of (a) four‐sectioned heat‐activated grippe...
Figure 5.39 Multi‐scale design domain for the heat‐activated gripper of eigh...
Figure 5.40 Optimization results of (a) the eight sections of the heat‐activ...
Figure 5.41 Performance comparison of heat‐activated gripper designs.
Figure 5.42 Multi‐scale design domain of the heat‐activated gripper with a n...
Figure 5.43 Heat‐activated gripper optimization results for four parts with ...
Figure 5.44 Heat‐activated gripper optimization results for eight parts with...
Figure 5.45 Heat‐activated gripper multi‐sectioned design with and without c...
Chapter 6
Figure 6.1 COMOSL‐MATLAB microstructure design examples.
Figure 6.2 Porous plate design using Nastran‐C++ program. Shimoda et al., (2...
Figure 6.3 MATLAB code flow for multiphysics concurrent topology optimizatio...
Figure 6.4 The input data section of MATLAB main code (Concurrent_MOO.m) [18...
Figure 6.5 Bilinear quadratic element used [18].
Figure 6.6 Mechanical finite element section of MATLAB main code of the main...
Figure 6.7 Node definition and degree of freedom for mechanical analysis.
Figure 6.8 Mechanical finite element section of MATLAB main code of the main...
Figure 6.9 Nadir and utopia points for mechanical compliance of the main fun...
Figure 6.10 Nadir and utopia points for heat compliance of the main function...
Figure 6.11 Initial design domains of (a) the micro‐ and (b) macrostructures...
Figure 6.12 The calculation of macro and micro objective functions and sensi...
Figure 6.13 Finite element model example of 25 elements [18].
Figure 6.14 The mesh independency filtering scheme [18].
Figure 6.15 The mesh independency filter within the optimizer function [18] ...
Figure 6.16 The GUI of concurrent multi‐scale optimization software.
Figure 6.17 The program while optimizing.
Figure 6.18 The error message of non‐sufficient data.
Figure 6.19 The output of the concurrent multi‐scale program.
Guide
Cover Page
Table of Contents
Additive Manufacturing Skills in Practice
Title Page
Copyright
Dedication
Advanced Techniques in Porous Structure Design for Additive Manufacturing
Preface
Begin Reading
Index
End User License Agreement
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Additive Manufacturing Skills in Practice
Fundamentals of Additive Manufacturing for the Practitioner by Sheku Kamara and Kathy Faggiani
3D Scanning for Advanced Manufacturing. Design, and Construction by Gary C. Confalone, John Smits, and Thomas Kinnare
ADVANCED TECHNIQUES IN POROUS STRUCTURE DESIGN FOR ADDITIVE MANUFACTURING
FIRST EDITION
MUSADDIQ AL ALI
Toyota Technological Institute
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To Reiko
Rigorous scientific investigation may necessitate a departure from established and conventional views. Therefore, anyone encountering findings that contradict their prior understanding should refrain from immediate dismissal, as such haste would be imprudent. Indeed, some widely rejected concepts may prove factual, while some familiar and widely accepted notions may be erroneous. After all, the essence of the fact stands on its own merit, independent of what people say about it.
Ibn Al‐Nafis
Preface
Porous structures have become essential in modern engineering due to their unique ability to combine lightweight properties with high functionality. These structures are integral in applications where reducing weight is critical, such as in aerospace, automotive, and energy‐efficient technologies. By reducing mass without compromising strength or performance, porous materials contribute significantly to energy savings, improved fuel efficiency, and enhanced system performance. The ability to tailor the porosity of a material opens up opportunities for optimizing various properties, such as thermal conductivity, mechanical stiffness, and fluid flow, making them ideal for a wide range of applications, from heat dissipation systems to biomedical implants.
This book provides a structured approach to the design of porous structures for additive manufacturing, a field that has revolutionized the production of complex geometries with precise control over material distribution. It is intended for students, engineers, and researchers in mechanical and manufacturing engineering. This book integrates theoretical concepts with practical applications, offering readers the tools needed to understand and implement porous structure designs effectively.
The chapters cover a wide range of topics, beginning with an introduction to porous structures and additive manufacturing methods. The discussion progresses to mathematical modeling, optimization techniques, and numerical methods for evaluating porous structures. Advanced design methods, including parametric and nonparametric optimization, are explored, with applications demonstrated through practical examples. To support learning, educational resources such as codes and numerical tools are included, enabling readers to apply the formulations and techniques to their own designs.
The relationship between material properties and manufacturing methods is addressed, providing insights into process selection for metallic, polymeric, and ceramic materials. Additionally, the book discusses software tools used in porous structure design and highlights emerging trends and challenges in the field.
This book is intended to provide readers with both the theoretical foundation and practical tools necessary to engage with the design of porous structures for additive manufacturing.
Chapter 1Introduction to Porous Structures and Additive Manufacturing
1.1 INTRODUCTION
Porous structures, from a physical standpoint, can be viewed as composites comprising base materials that confer porosity and the surrounding media that fill the interstitial spaces. In the context of this discourse, we will refer to the individual pores as “cells” and the spaces they create as “voids.” The concept of porous structures finds its inspiration in nature, where numerous natural constructs, such as bones and cork, inherently exhibit porosity. This characteristic arises from the biological process of constructing these structures through the growth of single cells. These natural constructs exhibit a wide spectrum of properties, enabling them to adapt to applications.
For example, nature employs porosity to optimize the structure and function of various organisms. In avian biology, bird bones exhibit a unique porous structure, combining strength with weight reduction, essential for aerial locomotion. This intricate network of interconnected pores within the bone matrix not only minimizes weight but also enhances the bone's overall strength. The porous architecture distributes stress evenly, preventing fractures and maximizing the bone's load‐bearing capacity [1, 2].
For plant structure, porosity plays a crucial role in the efficient transport of water and minerals throughout the plant body. Trees, in particular, rely on a complex porous structure of xylem vessels, which are characterized by their porous structure. These vessels, composed of dead, hollow cells, facilitate the upward movement of water from the roots to the leaves. The porous nature of the xylem vessels allows for capillary action, enabling water molecules to adhere to the vessel walls and be drawn upward against gravity. Additionally, the porosity of the xylem vessels provides a large surface area for the absorption of water and minerals, ensuring adequate nutrient supply to the entire plant.
Although the existence of porous structures dates back to ancient times, they have recently garnered significant attention, leading to the development of a novel class of materials in contemporary engineering. These materials offer a unique opportunity for achieving high performance relative to their weight, a characteristic highly sought after in advanced structural and other engineering applications.
By selectively designing the pore structure, it is possible to derive new desired properties from a base material that lacks such properties in its bulk form. This selective design essentially creates a composite of voids and solid materials. For instance, by manipulating the porosity, one can achieve materials with properties such as negative thermal expansion and apparent negative thermal conductivity. These properties can be tailored to specific applications, such as high‐efficiency energy absorption [3, 4] and thermal insulation [5, 6].
Historically, the mastery of metals has significantly shaped human civilization, marking distinct epochs such as the Bronze Age and the Iron Age. The development and utilization of porous metal structures continue this legacy, presenting a modern frontier in material science and engineering.
As such, porous metals, in particular, represent a fascinating class of materials characterized by high surface area, high permeability, and tunable pore size and distribution. These attributes make them suitable for a diverse array of applications, including catalysis, filtration, energy storage, and biomedical engineering. Compared to polymers, porous metals exhibit superior mechanical stability, are lightweight, and have additional physical properties such as good electrical and thermal conductivities.
On the other hand, the high surface area of porous metals facilitates a greater number of chemical reactions at active sites, rendering them ideal for catalytic applications. In filtration, such as gas separation and water purification, the ability to tune pore size and distribution allows for the efficient separation of particles of different sizes. In energy storage, porous metals are used in batteries and supercapacitors due to their ability to provide high surface area and permeability, enhancing ion transport and storage capacity.
In biomedical applications, porous metals are employed for bone implants because their structure can promote bone tissue regeneration and integration.
How can porous materials exhibit extraordinary properties and characteristics that are absent in their bulk base materials? To address this question, it is essential to investigate the unique microstructural features of porous materials, including their geometry, connectivity, and distribution, which govern their ability to achieve such remarkable functionalities. Porous structures exhibit a hierarchical organization that spans multiple length scales, from the atomic to the macroscopic. At the atomic level, the arrangement of atoms and the types of chemical bonds play a crucial role in determining the intrinsic properties of the material. Moving to the microscale, the size, shape, and distribution of the pores significantly influence the mechanical, thermal, and transport properties. Macroscale considerations include the overall geometry and connectivity of the porous network, which can produce a new collective property.
The phenomenal properties of porous materials may include materials with a negative Poisson's ratio, also known as auxetic materials, which expand laterally when stretched, a behavior opposite to that of conventional materials. This property can be engineered by designing the pore structure according to a specific function, leading to applications in protective gear, medical devices, and flexible electronics.
Recently, the development of materials with the capacity to exhibit anomalous thermal behavior, such as apparent negative thermal conductivity, represents a significant advancement in the field of thermal management. These materials are engineered to manipulate heat flow in unconventional manners, allowing them to redirect thermal energy in ways that are not typically achievable with conventional materials. The redirection and dissipation of heat enable these materials to enhance the efficiency of cooling systems in electronic devices, ensuring that they operate within safe temperature ranges. Furthermore, these materials hold great potential for providing superior thermal insulation in extreme environments, such as space exploration or deep‐sea applications, where traditional insulation methods may fall short.
The true industrial and engineering potential of porous metals began to be recognized in the early 20th century. The first commercially available porous metals were produced using sintered powder technology. This process involves compacting and heating metal powders to a temperature just below their melting point, allowing the particles to coalesce and form a solid mass with a network of interconnected pores. The unique properties of these sintered metals, including their high surface area and permeability, made them ideal for applications such as filters, batteries, and self‐lubricating bearings. These early applications demonstrated the potential of porous metals to enhance performance in high‐volume industrial processes, a promise that continues to be realized today in various fields.
Historically, the concept of porous metals is not a modern invention. The earliest known reference to man‐made porous metals can be traced back to the work of Pliny the Elder in 77 AD, who documented a process known as granulation. This technique was notably used by Etruscan goldsmiths, who applied it to create intricate patterns and textures on jewelry, a process that involved the creation of fine, porous structures on the surface of metals [7, 8]. Although these early applications were primarily esthetic, serving decorative purposes in jewelry and religious artifacts, they laid the foundation for the understanding of porous metals and their potential applications 9..
The concept of metallic foams, which involves creating a metal structure with high porosity through the introduction of gas bubbles or other foaming agents, was first formally introduced in a French patent in 1925. Metallic foams offer a distinct combination of lightweight, high strength, and excellent energy absorption characteristics, making them suitable for applications ranging from lightweight structural components to impact protection and thermal insulation. However, despite the early conceptualization, the commercialization of metallic foams did not begin in earnest until the late 1950s in the United States. This delay was primarily due to the need for extensive research and development to understand and optimize the foaming processes and to tailor the properties of the foams to specific applications [10, 11].
During the initial wave of research and development that started extensively from the 1950s, significant efforts were made to explore the potential applications of metallic foams across various industries [12, 13]. This period saw the development of foaming techniques for different metals and alloys, as well as the investigation of their mechanical and thermal properties. The versatility of metallic foams became apparent, leading to their adoption in a range of applications, including lightweight panels for aerospace structures, energy‐absorbing layers in automotive crash protection systems, and high‐efficiency heat exchangers.
Moreover, porous metals were created using electrochemical deposition. Historically, this was started as a series of studies to understand this “undesirable” feature in metal plating. However, it has found useful applications, such as in the creation of heat exchanger channels for space rocket engines [14–17].
The fabrication of metal foams presents a significant challenge due to the difficulty in achieving precise topological control of the cellular spatial configuration. To address this issue, various advanced manufacturing techniques have emerged to produce metal cellular structures with detailed and controlled cell architectures. The methods for producing porous metals are diverse and include powder metallurgy, foaming, chemical vapor deposition (CVD), electrodeposition, and chemical etching.
In powder metallurgy, a blend of metal powder and a sacrificial filler material is sintered, and the filler is subsequently removed to create pores. This technique allows for precise control over the pore size and distribution. Foaming involves the creation of a metallic foam by mixing a molten metal with a blowing agent, which generates gas bubbles within the metal, followed by rapid cooling to solidify the porous structure. This method is advantageous for producing lightweight materials with a high strength‐to‐weight ratio.
CVD is a process in which metal atoms are deposited onto a substrate from a vapor phase, forming a porous structure. This technique is highly effective in producing thin films and coatings with controlled porosity.
These methods have limitations, such as the requirement for specialized equipment, slow processing speeds, and incompatibility with large surface areas. Additionally, the mechanical strength of the resulting porous metals may be limited.
Alternatively, chemical and physical etching involves treating a metal piece with an etchant solvent to selectively remove materials and create pores. This technique allows for the processing of large surface areas using relatively low‐cost resources. Chemical etching is effective for producing nano‐ and microlattice structures, making it suitable for highly specialized applications such as sensors and microelectromechanical systems (MEMS).
Despite the high surface quality and accurate spatial configuration of the pores achieved through these methods, they are limited to certain types of metallic alloys. Moreover, achieving consistent results requires meticulous control over the processing parameters. The scalability of these techniques is also restricted, making them less suitable for producing large components and mass manufacturing.
Recent advancements in manufacturing technologies are fundamentally transforming the design and production landscape, addressing long‐standing limitations inherent to conventional fabrication methods. Among these, additive manufacturing (AM), commonly referred to as three‐dimensional printing, has emerged as a pivotal technology enabling unprecedented precision in the creation of geometrically complex and hierarchically porous structures. By leveraging layer‐by‐layer deposition techniques, AM provides unparalleled control over the topology and morphology of manufactured components, allowing for the meticulous customization of mechanical, thermal, and fluidic properties at both micro‐ and macroscales.
The defining capability of AM lies in its capacity to fabricate structures that were previously unattainable through traditional manufacturing methods, such as casting, machining, or injection molding. In particular, the ability to engineer controlled porosity is of immense interest due to the critical role it plays in optimizing material properties for specific applications. For instance, porous structures can be tailored to exhibit superior strength‐to‐weight ratios, enhanced thermal conductivity, and improved acoustic damping characteristics, attributes that are crucial for aerospace and automotive industries striving for high‐performance, lightweight designs.
The versatility of AM extends to its capability to produce components with gradient porosity, where the distribution of pore sizes and densities varies spatially within a single structure. Such designs are particularly valuable in applications requiring multifunctional materials. For example, aerospace components can be engineered with denser regions for load‐bearing purposes and more porous zones for thermal insulation. Similarly, in the automotive industry, gradient porosity can be utilized to optimize both crashworthiness and weight reduction in vehicle components.
Moreover, AM's potential for scalability and integration with computational design tools, such as topology optimization and generative design algorithms, has further augmented its impact. These tools enable the design of porous structures that are not only optimized for specific functional requirements but also manufacturable with minimal material wastage, aligning with sustainability goals. By seamlessly coupling advanced computational methods with AM, researchers can iterate rapidly between design and fabrication, significantly reducing development cycles and costs.
Despite these remarkable capabilities, challenges remain in standardizing the properties and reliability of AM‐fabricated porous structures, particularly for load‐bearing applications. Ongoing research is focused on improving material consistency, surface finish, and structural integrity to ensure broader adoption across industries. Nonetheless, AM continues to unlock transformative opportunities, pushing the boundaries of what is achievable in engineering design and solidifying its role as a cornerstone of modern manufacturing.
Furthermore, hybrid manufacturing techniques that combine traditional methods with modern technologies are being developed to enhance the efficiency and scalability of porous metal production. These innovations hold the promise of creating robust, high‐performance materials suitable for a wide range of engineering applications, from structural components to advanced functional materials.
1.2 WHY DESIGNING POROUS STRUCTURES
Porous structures present a remarkable potential for achieving a high performance‐to‐weight ratio, offering the capability to attain high stiffness with low weight. This unique characteristic arises from the inherent porosity within these materials, which provides a complex network of voids and solid regions. These voids can significantly reduce the overall density of the material, thus lowering its weight, while the solid regions maintain structural integrity and stiffness. Consequently, porous structures are highly desirable in applications requiring materials that are both lightweight and strong.
One of the significant advantages of porous materials is their ability to facilitate multiphysics phenomena, for example porous heat exchangers, such that the interconnected pores allow for fluid flow through the material, enhancing convective heat transfer. This feature is especially beneficial in systems such as internal combustion engines, where the material can bear mechanical loads while simultaneously aiding in cooling. The pores provide pathways for the coolant to pass through, effectively dissipating the heat generated during combustion processes and maintaining the structural integrity of the engine components.
Furthermore, porous materials exhibit high surface area‐to‐volume ratios, which are advantageous in thermal, chemical, and biological processes. The extensive surface area allows for more significant interactions with surrounding environments, enhancing reaction rates in various applications. In thermal processes, this can lead to more efficient heat exchange. In chemical processes, it can increase the rate of reactions, making porous materials ideal for use in catalysts and reactors. In biological processes, the high surface area can support cell attachment and growth, making these materials suitable for biomedical applications such as tissue engineering.
These benefits, however, only scratch the surface of the potential advantages offered by porous structures. One of the most critical aspects determining the structural behavior of these materials is their spatial configuration or the material distribution within the domain. This aspect profoundly influences the physical properties and functionality of the structure. To illustrate this concept, consider a 10‐g mass of iron.
If this mass of iron is shaped into a cube, it behaves as a rigid body, capable of withstanding considerable compressive loads. However, if the same mass is formed into a long wire, it becomes easily bendable due to its high aspect ratio and slender geometry. When shaped into a helical spring, the iron mass exhibits elasticity, capable of storing and releasing mechanical energy efficiently.
This variability in behavior is solely due to the different shapes and configurations given to the same mass of iron. By altering the spatial arrangement of the material, we can achieve a wide range of physical properties and functionalities beyond the scope of bulk materials in a similar manner to have a new material. This principle is equally applicable to porous structures. The distribution and connectivity of the pores within the material can be engineered to optimize specific properties, such as stiffness, strength, thermal conductivity, and band gap photonics, that depend on the intended application.
Designing bulk materials as cellular structures allows for precise control over their mechanical behavior. Consider iron shaped into a small plate with a honeycomb structure. This configuration results in a lightweight plate with orthotropic mechanical properties, meaning its behavior differs along different directions. The Poisson's ratio, a measure of the material's ability to expand laterally when stretched longitudinally, is positive in this case and is influenced by the intrinsic properties of the constitutive iron material.
Consider redesigning the honeycomb structure (as illustrated in Figure 1.1), where we can achieve even more remarkable behaviors. If we invert the upper triangular sections of the honeycomb so that the upper base becomes the lower and the two lower links become the upper, we create what is known as a re‐entrant auxetic structure. This re‐entrant design fundamentally changes the mechanical response of the material, giving it a negative Poisson's ratio. As a result, the structure expands laterally when stretched, contrary to the behavior of most materials.
Figure 1.1 The effect of material distribution on material properties, with a positive‐to‐negative Poisson ratio.
This negative Poisson's ratio is due to the unique geometry of the re‐entrant auxetic cells, which causes the structure to deform in a manner that increases its cross‐sectional area under tension. This auxetic behavior has several practical advantages, including enhanced energy absorption, increased shear resistance, and improved fracture toughness.
1.3 TYPES OF CELLS
Cellular materials can be classified in multiple ways, including by topology and design methodology, with particular emphasis on volume occupation aspects. These classifications are vital in understanding the functional behavior of the materials in various applications. The primary classifications in terms of topology are closed‐cell and open‐cell structures.
Closed‐cell structures are characterized by cells that are entirely encapsulated by their walls, forming discrete, impermeable units akin to bubbles. This encapsulation means that the internal volume of each cell is isolated from its surroundings, making the material impenetrable to environmental factors such as moisture or air. The impermeability of closed‐cell structures leads to their widespread use in applications where water resistance and buoyancy are critical. For instance, closed‐cell foams are used in flotation devices, life vests, and watercraft where buoyancy and the ability to remain dry are paramount. Their dense structure also provides excellent thermal insulation, making them ideal for use in environments where thermal management is essential, such as in the construction of refrigerated units and insulated shipping containers.
Conversely, open‐cell structures feature cells that are not fully enclosed, with walls that have openings or are interconnected with other cells. This interconnectedness allows for the passage of fluids, air, or other substances through the material, leading to a range of unique properties. Open‐cell materials excel in applications requiring compression set resistance and force relaxation, such as cushioning and shock absorption. The ability of these materials to absorb and gradually release air or moisture is beneficial in applications where gradual dissipation of absorbed substances is desired, such as in filters or moisture‐wicking materials.
However, the open structure of these cells also means that they are less effective at preventing water absorption when uncompressed. In certain situations, such as when a high level of compression is applied, the small openings in the cell walls can close off, creating an effective seal. This characteristic makes open‐cell foams suitable for dynamic environments where materials are subjected to varying pressures. In addition to cushioning and acoustic absorption, open‐cell structures are used in chemical reactors, where their ability to allow fluid flow is crucial, as well as in biomedical scaffolds, where the porous structure supports tissue growth and nutrient transport.
Beyond the basic classification into closed‐ and open‐cell structures, modern engineering and material science have advanced to include the design and application of mathematically generated or “typical” cells (as illustrated in Figure 1.2). These are geometric shapes that form the building blocks of regular cellular structures and can be designed with specific mechanical or thermal properties in mind. Examples of such shapes include the cube, G7, diamond, truncated cuboctahedron, rhombic dodecahedron, and gyroid. Each of these shapes confers distinct mechanical properties to the resulting cellular material. For instance, the gyroid structure, known for its minimal surface area configuration, offers excellent mechanical strength and stiffness while minimizing material usage. This makes it an attractive option for lightweight structural components in aerospace and automotive industries. The rhombic dodecahedron and truncated cuboctahedron, with their high degree of symmetry, are favored in applications requiring isotropic mechanical properties, where uniform strength in all directions is necessary.
Figure 1.2 Common porous structure categorization.
The application of these mathematically generated cells extends into various high‐performance fields. In biomedical engineering, for example, the gyroid structure has been employed to design implants that mimic the porosity of natural bone, promoting osseointegration and reducing implant weight.
The integration of computational design tools and advanced manufacturing techniques, such as AM, has further expanded the possibilities for designing and fabricating cellular materials with tailored properties. Engineers can now optimize cellular structures at multiple scales, from the overall material geometry down to the microscopic cell configuration, to achieve the desired performance characteristics. This capability is particularly important in applications such as energy absorption, where the material must deform predictably under impact, or in lightweight strategies, where the material is removed strategically without compromising structural integrity.
Moreover, the field of non‐parametric optimization, where the material distribution within a given design space is optimized to meet specified performance criteria, has seen significant advancements through the use of cellular materials. By incorporating closed‐ or open‐cell structures into topology‐optimized designs, engineers can create components that are not only lightweight but also exhibit superior mechanical properties compared to traditional solid materials.
Recently, many commercial software offer cellular structural design scale such as nTopology®, Abaqus®, ANSYS®, COMSOL®, and OptiStrct® solver, which have integrated specialized capabilities for creating porous structures. These tools are widely adopted in various industries due to their effectiveness in optimizing lightweight, high‐strength materials. However, a notable limitation of these predefined structures is their fixed mechanical properties, which may not always meet the diverse demands of a specific application. To address this, engineers can vary the thickness of the members and links within the cellular structure. This variation, when guided by an empirically driven predictive model of mechanical properties, enables the creation of a wide array of porous designs with enhanced robustness and for a specific application.
The field of natural inspiration, particularly in the context of material design, has gained significant attention due to technological advances in capturing the intricate details of cellular structures and modeling their mechanical properties. Most materials in nature, especially those utilized in engineering applications, are inherently heterogeneous. This heterogeneity arises from both structural and compositional variations, which are often random and complex, making it challenging to predict the material's overall response accurately. Nature‐inspired materials aim to replicate the intricate structures or functionalities observed in natural materials, offering a blueprint for designing advanced engineering materials [18–22].
