Stiffness and yield strength of architectured foams based on the Schwarz Primitive triply periodic minimal surface

Lee, Dong‐Wook; Khan, Kamran A.; Al‐Rub, Rashid K. Abu

doi:10.1016/j.ijplas.2017.03.005

Cited by 139 publications

(36 citation statements)

References 42 publications

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“…In the FE unit cell model, a Young's modulus of 1.0 MPa and a Poisson's ratio of 0.45 [41] were defined for the void domain to facilitate the definition of periodic boundary condition, because in some unit cell models, the scaffold solid phase finished at one exterior surface and there were no corresponding elements in the opposite surface. Using the FE unit cell model, the effective elasticity tensor for each scaffold was first derived by solving the material constitutive equations, established by defining three individual loading, i.e., ε x = 0.01, ε y = 0.01, ε xy = 0.01 [42,43]. The reason for defining three individual loading is that all the scaffolds investigated have three nonzero constants in the elasticity matrix and can be regarded as the structure with a cubic symmetry [42].…”

Section: Plos Onementioning

confidence: 99%

Relationship between the morphological, mechanical and permeability properties of porous bone scaffolds and the underlying microstructure

et al. 2020

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Bone scaffolds are widely used as one of the main bone substitute materials. However, many bone scaffold microstructure topologies exist and it is still unclear which topology to use when designing scaffold for a specific application. The aim of the present study was to reveal the mechanism of the microstructure-driven performance of bone scaffold and thus to provide guideline on scaffold design. Finite element (FE) models of five TPMS (Diamond, Gyroid, Schwarz P, Fischer-Koch S and F-RD) and three traditional (Cube, FD-Cube and Octa) scaffolds were generated. The effective compressive and shear moduli of scaffolds were calculated from the mechanical analysis using the FE unit cell models with the periodic boundary condition. The scaffold permeability was calculated from the computational fluid dynamics (CFD) analysis using the 4×4×4 FE models. It is revealed that the surface-to-volume ratio of the Fischer-Koch S-based scaffold is the highest among the scaffolds investigated. The mechanical analysis revealed that the bending deformation dominated structures (e.g., the Diamond, the Gyroid, the Schwarz P) have higher effective shear moduli. The stretching deformation dominated structures (e.g., the Schwarz P, the Cube) have higher effective compressive moduli. For all the scaffolds, when the same amount of change in scaffold porosity is made, the corresponding change in the scaffold relative shear modulus is larger than that in the relative compressive modulus. The CFD analysis revealed that the structures with the simple and straight pores (e.g., Cube) have higher permeability than the structures with the complex pores (e.g., Fischer-Koch S). The main contribution of the present study is that the relationship between scaffold properties and the underlying microstructure is systematically investigated and thus some guidelines on the design of bone scaffolds are provided, for example, in the scenario where a high surface-to-volume ratio is required, it is suggested to use the Fischer-Koch S based scaffold.

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Section: Plos Onementioning

confidence: 99%

Relationship between the morphological, mechanical and permeability properties of porous bone scaffolds and the underlying microstructure

et al. 2020

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“…Young's modulus and yield strength) of these topologies. Compared with finite element method, which is more common in terms of computer simulation, FVM is faster and more efficient with respect to the simulations of these complicated porous materials [21][22][23][24][25][26][27][28].…”

Section: Finite Volume Methods Simulationmentioning

confidence: 99%

Mechanical behavior of TPMS-based scaffolds: a comparison between minimal surfaces and their lattice structures

et al. 2019

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Triply periodic minimal surfaces (TPMS) have drawn widespread attention out of their biomimetic features. This work compares skeletal-TPMS lattices with of strut-TPMS lattices in terms of their geometric and mechanical properties. Skeletal-TPMS lattices consist of continually smooth surfaces, while their counterparts, strut-TPMS lattices, are composed of cylindrical beams. These lattices derived from four kinds of TPMS, namely Gyroid (G), Schwarz Diamond (D), Schwarz Primitive (P), and iWp (W), having incremental nodal connectivity of 3, 4, 6, and 8, respectively. The scaling laws of Young's modulus and yield strength are determined as power functions of volume fraction according to finite volume method (FVM) simulations. Their uniaxial compression behaviors are characterized by FVM simulations and are experimentally validated using additive manufacturing and uniaxial compression tests, showing that skeletal-TPMS lattices exhibit more homogeneous stress distribution. This work would not only broaden the material space for scaffolds, but shed light on the design criteria for tissue engineering.

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“…Although they have been discovered for a long time, their realization as a three-dimensional structure was not an easy task due to their structural complexity. However, recent advances in fabrication techniques facilitated this task and many recent studies have successfully fabricated and tested these topologies in different engineering disciplines such as water treatment, 9,10,16 lightweight materials, [19][20][21][22][23] and composites. [24][25][26][27] A minimal surface can be converted into a cellular material with a defined volume using two main approaches as explained by Kapfer et al 28 and shown in Figure 2B.…”

Section: Introductionmentioning

confidence: 99%

Additive manufacturing of architected catalytic ceramic substrates based on triply periodic minimal surfaces

et al. 2019

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The exhibited geometry of catalytic substrates can have a significant influence on the chemical activity and efficiency. Controlling their geometry can be challenging using the traditional techniques. In this work, we propose new and novel catalytic substrates with architected and controllable topologies based on the minimal surfaces framework. A novel design approach and an additive manufacturing (AM) technique were proposed to manufacture the catalytic substrates using ceramic materials. After 3D printing, their mechanical and flow properties were investigated experimentally. An elastic‐plastic‐damage coupled model was employed to investigate the underlying deformation mechanism of the investigated substrates. Results showed that the CLP substrate exhibited the highest mechanical properties as well as the least pressure drop among the tested substrates. Also, numerical simulations showed that the strut‐based substrates exhibit stress localization which leads to faster failure, while stress is distributed more homogeneously in the sheet‐based substrates. While the model showed to have a good agreement in the experimental and simulation stress‐strain responses, the damage mechanism was not fully captured by the numerical simulations. This was attributed mainly to the process‐induced defects in the form of microcracks and microvoids that can alter the nature of deformation and damage.

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Stiffness and yield strength of architectured foams based on the Schwarz Primitive triply periodic minimal surface

Cited by 139 publications

References 42 publications

Relationship between the morphological, mechanical and permeability properties of porous bone scaffolds and the underlying microstructure

Relationship between the morphological, mechanical and permeability properties of porous bone scaffolds and the underlying microstructure

Mechanical behavior of TPMS-based scaffolds: a comparison between minimal surfaces and their lattice structures

Additive manufacturing of architected catalytic ceramic substrates based on triply periodic minimal surfaces

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