Estimation of the compressive and shear responses of three-dimensional micro-lattice structures

Ushijima, Kazuo; Cantwell, W.J.; Chen, D. H.

doi:10.1016/j.proeng.2011.04.402

Cited by 12 publications

(26 citation statements)

References 2 publications

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“…For example, SC is considered stretch dominated because it is usually loaded vertically, which only creates axial loads in the vertical struts. If loaded in another direction, such as [111] using Miller indices, the Gibson Ashby curve would be close to other bending dominated curves. The opposite occurs with the BCC structure, commonly regarded as bending dominated.…”

Section: Quasi-static Mechanical Propertiesmentioning

confidence: 90%

“…Timoshenko beam theory considers shear deformation of the struts, in contrast to Euler beams, which makes the Timoshenko beam more accurate for higher relative densities, when struts are not as slender [110]. Analytical models were developed for a wide range of structures: the BCC structure [111], diamond unit cell [67], rhombic dodecahedron [112], truncated cuboctahedron [113] and truncated cube [114]. Furthermore, Zadpoor and Hedayati collected many of the models for different structures in a review article [110], which also includes buckling analysis, and these models are depicted in Figure 1.20.…”

Section: Analytical Modelsmentioning

confidence: 99%

“…The beam models can be implemented as-designed, with increased thickness at the nodes or including the aforementioned manufacturing imperfections. The accuracy of as-designed beam models (see Figure 1.21a) varies across different works: while in some studies the numerical models agree with the experimental data [119,67], in others the experimental stiffness and strength are below the numerical values [114,113,120], or even the opposite [111].…”

Section: Finite Element Modelsmentioning

confidence: 99%

“…Fig. 1 defines the orthogonal directions used as subscripts of the stiffness matrix, together with some important directions defined with the Miller indices [100], [110], [101], [111] and [001], and the isotropic 1-2 plane. Eq.…”

Section: Semi-analytical Model 211 Elastic Behaviormentioning

confidence: 99%

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Design, modeling and characterization of lattice structures for orthopedic implant applications

Alaña¹

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Interest in lattice structures has soared in recent years thanks to the advances in the field of additive manufacturing, which has led to increasingly complex designs and the production of parts which was impossible up to not long ago. These advances enabled to create lattice structures that mimic the cellular solids of nature, which attracted broad attention due to its applicability in the aerospace and biomedical industries. These structures can be designed to have predefined stiffness and strength values, which enables the production of parts with engineered mechanical properties. One problem of traditional implants made of monolithic parts of Ti6Al4V, CoCr, pure Ti, etc., is the mismatch between the stiffness of the host bone and the metallic implant, which creates the so-called stress shielding. Stress shielding occurs when the bone adjacent to the implant does not have to withstand the main physiological loads because the much stiffer implant bears them in its place. Bone is a living tissue, which is created or resorbed (diluted in blood) depending on the loads to optimize its functionality. Thus, the stiffness mismatch between bone and the implant leads to the bone resorption due to the lack of mechanical stimuli on the host bone. The bone surrounding the implant loses density and weakens, which causes pain to the patient, affects implant stability, and may lead to the loosening of the implant. Lattice structures offer the possibility to create porous implants with tailored mechanical properties to match the stiffness of the surrounding bone, thus avoiding stress shielding and subsequent bone loss. Furthermore, lattice structures form porous parts with high surface to volume ratios, and this porosity enables the bone ingrowth within the implant, improving its fixation and long-term stability. This work is devoted to the development of tools to design lattice structures with controlled mechanical properties, as well as to deepen into the factors that affect such properties. Thus, the main purpose of this dissertation is to create lattice structures that mimic bone stiffness and could be implemented in orthopedic implants to avoid the stress shielding. In addition, orthopedic implants must withstand millions of load cycles throughout the lifetime of the patients, thus the fatigue behavior of the structures was also studied in this thesis. Finally, the small feature sizes required to implement such structures in orthopedic implants requires to reach the manufacturing limits of current additive manufacturing technologies, which induces important deviations from the actually designed geometry and in turn the mechanical properties. Another goal of this work is to understand the impact of such manufacturing deviations on the stiffness of the structures. The obtained results show that there are different possibilities to design structures with stiffness levels comparable to bone. The developed analytical or semi-analytical models predict and enable to design the mechanical properties of the structures for different topologies. These models can be used with personalized bone data to mimic the bone stiffness of each patient. Furthermore, the anisotropy of the structures can also be controlled to adapt it to the complex loads that arise in various anatomical sites. Regarding dynamic loads, fatigue life prediction tools in literature were compared and adapted to improve their applicability, and a fatigue failure surface was developed to easily predict the fatigue life of the structures. Moreover, it was concluded that hot isostatic pressing enhanced the fatigue strength of the structures. Finally, the manufacturing deviations were studied, developing a methodology to consider the proximity to the nodes in the analysis of the imperfection level, and to include such imperfections in a numerical model that predicts the change of anisotropy in the structure.

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Section: Quasi-static Mechanical Propertiesmentioning

confidence: 90%

Section: Analytical Modelsmentioning

confidence: 99%

Section: Finite Element Modelsmentioning

confidence: 99%

Section: Semi-analytical Model 211 Elastic Behaviormentioning

confidence: 99%

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Design, modeling and characterization of lattice structures for orthopedic implant applications

Alaña¹

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“…To obtain a graded lattice structure from the micro-struts; the beams are assumed to follow classical Euler-Bernoulli beam theory [162]. Mechanical properties for micro-lattice structures have been studied extensively with FEM simulations closely modeling classical beam theory [162,163,164].…”

Section: Lattice Beam Optimizationsmentioning

confidence: 99%

Numerical and Experimental Optimization for Specific Fatigue Life Maximization of Additively Manufactured Ti-6Al-4V Aerospace Components

Trudel¹

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Developing scaling laws to predict compressive mechanical properties and determine geometrical parameters of modified BCC lattice structures

Abdulhadi

Fadeel

Alwattar

et al. 2022

Engineering Reports

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The objective of this study is to develop generalized empirical closed‐form equations to predict the compressive mechanical properties and determine geometrical parameters. To achieve that, 117 models are built and analyzed using ABAQUS/CAE 2016 to provide two types of reliable data: one for lattice mechanical properties based on finite element method and the other for geometrical parameters using the measurements of ABAQUS diagnostic tool. All the models are created by modifying the basic feature of body‐centered cubic lattice structure based on a range of strut angles, a set of relative densities, and two design sets. Also, the influence of lattice cell tessellations and material distribution at strut intersections are considered within these models to provide accurate results. The first data set is fitted with the scaling laws, relating relative elastic modulus and stress with the relative density, to determine Gibson and Ashby's coefficients. The second type of data regarding lattice geometries is correlated with the relative density to estimate actual lattice volume, strut radius, aspect ratio, and overall lattice volume. By this way, these equations can be used to predict directly the lattice characteristics and geometrical parameters without the need for ABAQUS. The results show that the generalized empirical closed‐form equations can predict well both the lattice characteristics and geometries. In addition, the relative stresses and elastic modulus increase with increasing the strut angles since the main deformation mechanisms move toward stretch‐dominated rather than bending. Besides, Gibson and Ashby's coefficients along with the geometrical factors of aspect ratios are found to be approximately similar for both generations. This study contributes to developing efficient equations to provide the researchers with a preliminary insight about the best lattice design and its compatibility in a certain application before starting the fabrication process.

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Estimation of the compressive and shear responses of three-dimensional micro-lattice structures

Cited by 12 publications

References 2 publications

Design, modeling and characterization of lattice structures for orthopedic implant applications

Design, modeling and characterization of lattice structures for orthopedic implant applications

Numerical and Experimental Optimization for Specific Fatigue Life Maximization of Additively Manufactured Ti-6Al-4V Aerospace Components

Developing scaling laws to predict compressive mechanical properties and determine geometrical parameters of modified BCC lattice structures

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