Compression behavior of three-dimensional printed polymer lattice structures

2018 ◽  
Vol 233 (8) ◽  
pp. 1574-1584 ◽  
Author(s):  
Mohammed Al Rifaie ◽  
Ahsan Mian ◽  
Raghavan Srinivasan
Keyword(s):  
Energy Absorption ◽  
Lattice Structure ◽  
Three Dimensional ◽  
Unit Cell ◽  
The Body ◽  
Basic Unit ◽  
Lattice Structures ◽  
Body Centered Cubic ◽  
Static Compression ◽  
Compression Behavior

This paper focuses on the compression behavior of additively manufactured or three-dimensional printed polymer lattice structures of different configurations. The body-centered cubic lattice unit cell, which has been extensively investigated for energy absorption applications, is the starting point for this research. In this study, the lattice structure based on the body-centered cubic unit cell was modified by adding vertical struts in different arrangements to create three additional configurations. Four lattice structure designs were selected for comparison: the basic unit cell (body centered cubic), body centered cubic with vertical struts added to all nodes in the lattice, body centered cubic with vertical struts added to alternate nodes in the lattice, and body centered cubic with gradient in the number of vertical bars in the lattice. Samples of all four designs were prepared using acrylonitrile–butadiene–styrene polymer by three-dimensional printing. The stiffness, failure loads, and energy absorption behaviors of all four configurations were determined under quasi-static compression loading. Specific properties were calculated by normalizing the test properties by the sample mass. It is observed from experimental data that selective placement of vertical support struts in the unit cell influences both the absolute and specific mechanical properties of lattice structures.

scholarly journals Energy Absorption and Mechanical Performance of Functionally Graded Soft–Hard Lattice Structures

Materials ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1366 ◽  
Author(s):  
Hafizur Rahman ◽  
Ebrahim Yarali ◽  
Ali Zolfagharian ◽  
Ahmad Serjouei ◽  
Mahdi Bodaghi
Keyword(s):  
Cell Size ◽  
Energy Absorption ◽  
Mechanical Performance ◽  
Lattice Structure ◽  
Unit Cell ◽  
Lattice Structures ◽  
Hard Materials ◽  
Unit Cell Size ◽  
Rational Combination ◽  
Dual Material

Today, the rational combination of materials and design has enabled the development of bio-inspired lattice structures with unprecedented properties to mimic biological features. The present study aims to investigate the mechanical performance and energy absorption capacity of such sophisticated hybrid soft–hard structures with gradient lattices. The structures are designed based on the diversity of materials and graded size of the unit cells. By changing the unit cell size and arrangement, five different graded lattice structures with various relative densities made of soft and hard materials are numerically investigated. The simulations are implemented using ANSYS finite element modeling (FEM) (2020 R1, 2020, ANSYS Inc., Canonsburg, PA, USA) considering elastic-plastic and the hardening behavior of the materials and geometrical non-linearity. The numerical results are validated against experimental data on three-dimensional (3D)-printed lattices revealing the high accuracy of the FEM. Then, by combination of the dissimilar soft and hard polymeric materials in a homogenous hexagonal lattice structure, two dual-material mechanical lattice statures are designed, and their mechanical performance and energy absorption are studied. The results reveal that not only gradual changes in the unit cell size provide more energy absorption and improve mechanical performance, but also the rational combination of soft and hard materials make the lattice structure with the maximum energy absorption and stiffness, in comparison to those structures with a single material, interesting for multi-functional applications.

scholarly journals A Comparison of Miniature Lattice Structures Produced by Material Extrusion and Vat Photopolymerization Additive Manufacturing

Polymers ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 2163
Author(s):  
Rafael Guerra Silva ◽  
María Josefina Torres ◽  
Jorge Zahr Viñuela
Keyword(s):  
Additive Manufacturing ◽  
Energy Absorption ◽  
Lattice Structure ◽  
Solid Material ◽  
Unit Cell ◽  
Lattice Structures ◽  
Compression Tests ◽  
Material Extrusion ◽  
Lower Accuracy ◽  
Manufacturing Methods

In this paper, we study the capabilities of two additive manufacturing technologies for the production of lattice structures, namely material extrusion and vat photopolymerization additive manufacturing. A set of polymer lattice structures with diverse unit cell types were built using these additive manufacturing methods and tested under compression. Lattice structures built using material extrusion had lower accuracy and a lower relative density caused by the air gaps between layers, but had higher elastic moduli and larger energy absorption capacities, as a consequence of both the thicker struts and the relatively larger strength of the feedstock material. Additionally, the deformation process in lattices was analyzed using sequential photographs taken during the compression tests, evidencing larger differences according to the manufacturing process and unit-cell type. Both additive manufacturing methods produced miniature lattice structures with similar mechanical properties, but vat polymerization should be the preferred option when high geometrical accuracy is required. Nevertheless, as the solid material determines the compressive response of the lattice structure, the broader availability of feedstock materials gives an advantage to material extrusion in applications requiring stiffer structures or with higher energy absorption capabilities.

scholarly journals Dynamic crushing behavior of closed-cell aluminum foams based on different space-filling unit cells

2021 ◽  
Vol 21 (3) ◽  
Author(s):  
S. Talebi ◽  
R. Hedayati ◽  
M. Sadighi
Keyword(s):  
Surface Area ◽  
Dynamic Behavior ◽  
Energy Absorption ◽  
Peak Stress ◽  
Absorption Capacity ◽  
Unit Cell ◽  
Lattice Structures ◽  
Energy Absorption Capacity ◽  
Closed Cell ◽  
Unit Cells

AbstractClosed-cell metal foams are cellular solids that show unique properties such as high strength to weight ratio, high energy absorption capacity, and low thermal conductivity. Due to being computation and cost effective, modeling the behavior of closed-cell foams using regular unit cells has attracted a lot of attention in this regard. Recent developments in additive manufacturing techniques which have made the production of rationally designed porous structures feasible has also contributed to recent increasing interest in studying the mechanical behavior of regular lattice structures. In this study, five different topologies namely Kelvin, Weaire–Phelan, rhombicuboctahedron, octahedral, and truncated cube are considered for constructing lattice structures. The effects of foam density and impact velocity on the stress–strain curves, first peak stress, and energy absorption capacity are investigated. The results showed that unit cell topology has a very significant effect on the stiffness, first peak stress, failure mode, and energy absorption capacity. Among all the unit cell types, the Kelvin unit cell demonstrated the most similar behavior to experimental test results. The Weaire–Phelan unit cell, while showing promising results in low and medium densities, demonstrated unstable behavior at high impact velocity. The lattice structures with high fractions of vertical walls (truncated cube and rhombicuboctahedron) showed higher stiffness and first peak stress values as compared to lattice structures with high ratio of oblique walls (Weaire–Phelan and Kelvin). However, as for the energy absorption capacity, other factors were important. The lattice structures with high cell wall surface area had higher energy absorption capacities as compared to lattice structures with low surface area. The results of this study are not only beneficial in determining the proper unit cell type in numerical modeling of dynamic behavior of closed-cell foams, but they are also advantageous in studying the dynamic behavior of additively manufactured lattice structures with different topologies.

Determination of Optimal Unit-Cell Size of Homogeneous Conformal Unit-Cell Lattice Structure Using Solid Shape Matching

2016 ◽  
Author(s):  
Mahmoud A. Alzahrani ◽  
Seung-Kyum Choi
Keyword(s):  
Cell Size ◽  
Solid Body ◽  
Strain Energy ◽  
Lattice Structure ◽  
Weight Ratio ◽  
Unit Cell ◽  
Optimal Size ◽  
Lattice Structures ◽  
Unit Cell Size ◽  
Unit Cells

With rapid developments and advances in additive manufacturing technology, lattice structures have gained considerable attention. Lattice structures are capable of providing parts with a high strength to weight ratio. Most work done to reduce computational complexity is concerned with determining the optimal size of each strut within the lattice unit-cells but not with the size of the unit-cell itself. The objective of this paper is to develop a method to determine the optimal unit-cell size for homogenous periodic and conformal lattice structures based on the strain energy of a given structure. The method utilizes solid body finite element analysis (FEA) of a solid counter-part with a similar shape as the desired lattice structure. The displacement vector of the lattice structure is then matched to the solid body FEA displacement results to predict the structure’s strain energy. This process significantly reduces the computational costs of determining the optimal size of the unit cell since it eliminates FEA on the actual lattice structure. Furthermore, the method can provide the measurement of relative performances from different types of unit-cells. The developed examples clearly demonstrate how we can determine the optimal size of the unit-cell based on the strain energy. Moreover, the computational cost efficacy is also clearly demonstrated through comparison with the FEA and the proposed method.

scholarly journals Phase transition induced by an external field in a three-dimensional isotropic Heisenberg antiferromagnet

2018 ◽  
Vol 32 (32) ◽  
pp. 1850390
Author(s):  
Minos A. Neto ◽  
J. Roberto Viana ◽  
Octavio D. R. Salmon ◽  
E. Bublitz Filho ◽  
José Ricardo de Sousa
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Three Dimensional ◽  
Effective Field ◽  
The Body ◽  
Bravais Lattice ◽  
Body Centered Cubic ◽  
Cubic Lattice ◽  
Cubic Lattices ◽  
Simple Cubic

The critical frontier of the isotropic antiferromagnetic Heisenberg model in a magnetic field along the z-axis has been studied by mean-field and effective-field renormalization group calculations. These methods, abbreviated as MFRG and EFRG, are based on the comparison of two clusters of different sizes, each of them trying to mimic a specific Bravais lattice. The frontier line in the plane of temperature versus magnetic field was obtained for the simple cubic and the body-centered cubic lattices. Spin clusters with sizes N = 1, 2, 4 were used so as to implement MFRG-12, EFRG-12 and EFRG-24 numerical equations. For the simple cubic lattice, the MFRG frontier exhibits a notorious re-entrant behavior. This problem is improved by the EFRG technique. However, both methods agree at lower fields. For the body-centered cubic lattice, the MFRG method did not work. As in the cubic lattice, all the EFRG results agree at lower fields. Nevertheless, the EFRG-12 approach gave no solution for very low temperatures. Comparisons with other methods have been discussed.

Stress-Constrained Design of Functionally Graded Lattice Structures With Spline-Based Dimensionality Reduction

2019 ◽  
Author(s):  
Jenmy Zimi Zhang ◽  
Conner Sharpe ◽  
Carolyn Conner Seepersad
Keyword(s):  
Three Dimensional ◽  
Surrogate Models ◽  
Functionally Graded ◽  
Unit Cell ◽  
Cell Stiffness ◽  
Stress Constraint ◽  
Compact Representation ◽  
Lattice Structures ◽  
Worst Case ◽  
Graded Lattice

Abstract This paper presents a computationally tractable approach for designing lattice structures for stiffness and strength. Yielding in the mesostructure is determined by a worst-case stress analysis of the homogenization simulation data. This provides a physically meaningful, generalizable, and conservative way to estimate structural failure in three-dimensional functionally graded lattice structures composed of any unit cell architectures. Computational efficiency of the design framework is ensured by developing surrogate models for the unit cell stiffness and strength as a function of density. The surrogate models are then used in the coarse-scale analysis and synthesis. The proposed methodology further uses a compact representation of the material distribution via B-splines, which reduces the size of the design parameter space while ensuring a smooth density variation that is desirable for manufacturing. The proposed method is demonstrated in compliance minimization studies using two types of unit cells with distinct mechanical properties. The effects of B-spline mesh refinement and the presence of a stress constraint on the optimization results are also investigated.

Design and Analysis of Lattice Structures for Additive Manufacturing

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Christiane Beyer ◽  
Dustin Figueroa
Keyword(s):  
Additive Manufacturing ◽  
Lattice Structure ◽  
Cost Savings ◽  
Unit Cell ◽  
Cnc Machining ◽  
Numerical Control ◽  
Full Potential ◽  
Lattice Structures ◽  
Cell Structures ◽  
Bending Load

Additive manufacturing (AM) enables time and cost savings in the product development process. It has great potential in the manufacturing of lighter parts or tools by the embedding of cellular/lattice structures that consume less material while still distributing the necessary strength. Less weight and less material consumption can lead to enormous energy and cost savings. Although AM has come a long way over the past 25–30 years since the first technology was invented, the design of parts and tools that capitalize on the technology do not yet encompass its full potential. Designing for AM requires departing from traditional design guidelines and adopting new design considerations and thought structures. Where previous manufacturing techniques (computer numerical control (CNC) machining, casting, etc.) often necessitated solid parts, AM allows for complex parts with cellular and lattice structure implementation. The lattice structure geometry can be manipulated to deliver the level of performance required of the part. The development and research of different cell and lattice structures for lightweight design is of significant interest for realizing the full potential of AM technologies. The research not only includes analysis of existing software tools to design and optimize cell structures, but it also involves design consideration of different unit cell structures. This paper gives a solid foundation of an experimental analysis of additive manufactured parts with diverse unit cell structures in compression and flexural tests. Although the research also includes theoretical finite element analysis (FEA) of the models, the results are not considered here. As an introduction, the paper briefly explains the basics of stress and strain relationship and summarizes the test procedure and methods. The tests concentrate primarily on the analysis of 3D printed polymer parts manufactured using PolyJet technology. The results show the behavior of test specimens with different cell structures under compression and bending load. However, the research has been extended and is still ongoing with an analysis of selective laser melted test specimens in aluminum alloy AlSi10Mg.

scholarly journals Stress-Constrained Design of Functionally Graded Lattice Structures With Spline-Based Dimensionality Reduction

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Jenmy Zimi Zhang ◽  
Conner Sharpe ◽  
Carolyn Conner Seepersad
Keyword(s):  
Three Dimensional ◽  
Surrogate Models ◽  
Functionally Graded ◽  
Unit Cell ◽  
Cell Stiffness ◽  
Stress Constraint ◽  
Compact Representation ◽  
Lattice Structures ◽  
Worst Case ◽  
Graded Lattice

Abstract This paper presents a computationally tractable approach for designing lattice structures for stiffness and strength. Yielding in the mesostructure is determined by a worst-case stress analysis of the homogenization simulation data. This provides a physically meaningful, generalizable, and conservative way to estimate structural failure in three-dimensional functionally graded lattice structures composed of any unit cell architectures. Computational efficiency of the design framework is ensured by developing surrogate models for the unit cell stiffness and strength as a function of density. The surrogate models are then used in the coarse-scale analysis and synthesis. The proposed methodology further uses a compact representation of the material distribution via B-splines, which reduces the size of the design parameter space while ensuring a smooth density variation that is desirable for manufacturing. The proposed method is demonstrated in compliance with minimization studies using two types of unit cells with distinct mechanical properties. The effects of B-spline mesh refinement and the presence of a stress constraint on the optimization results are also investigated.

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