scholarly journals Dual Graded Lattice Structures: Generation Framework and Mechanical Properties Characterization

Polymers ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1528
Author(s):  
Khaled G. Mostafa ◽  
Guilherme A. Momesso ◽  
Xiuhui Li ◽  
David S. Nobes ◽  
Ahmed J. Qureshi
Keyword(s):  
Mechanical Properties ◽  
Relative Density ◽  
Lattice Structure ◽  
Cell Types ◽  
Functionally Graded ◽  
Unit Cell ◽  
Lattice Structures ◽  
Unit Cells ◽  
Mechanical Properties Characterization ◽  
Graded Lattice

Additive manufacturing (AM) enables the production of complex structured parts with tailored properties. Instead of manufacturing parts as fully solid, they can be infilled with lattice structures to optimize mechanical, thermal, and other functional properties. A lattice structure is formed by the repetition of a particular unit cell based on a defined pattern. The unit cell’s geometry, relative density, and size dictate the lattice structure’s properties. Where certain domains of the part require denser infill compared to other domains, the functionally graded lattice structure allows for further part optimization. This manuscript consists of two main sections. In the first section, we discussed the dual graded lattice structure (DGLS) generation framework. This framework can grade both the size and the relative density or porosity of standard and custom unit cells simultaneously as a function of the structure spatial coordinates. Popular benchmark parts from different fields were used to test the framework’s efficiency against different unit cell types and grading equations. In the second part, we investigated the effect of lattice structure dual grading on mechanical properties. It was found that combining both relative density and size grading fine-tunes the compressive strength, modulus of elasticity, absorbed energy, and fracture behavior of the lattice structure.

scholarly journals Design Optimization of Lattice Structures under Compression: Study of Unit Cell Types and Cell Arrangements

Materials ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 97
Author(s):  
Kwang-Min Park ◽  
Kyung-Sung Min ◽  
Young-Sook Roh
Keyword(s):  
Mechanical Properties ◽  
Compressive Strength ◽  
Relative Density ◽  
Lattice Structure ◽  
Density Ratio ◽  
Cell Types ◽  
Unit Cell ◽  
Structure Characterization ◽  
Optimized Design ◽  
Lattice Structures

Additive manufacturing enables innovative structural design for industrial applications, which allows the fabrication of lattice structures with enhanced mechanical properties, including a high strength-to-relative-density ratio. However, to commercialize lattice structures, it is necessary to define the designability of lattice geometries and characterize the associated mechanical responses, including the compressive strength. The objective of this study was to provide an optimized design process for lattice structures and develop a lattice structure characterization database that can be used to differentiate unit cell topologies and guide the unit cell selection for compression-dominated structures. Linear static finite element analysis (FEA), nonlinear FEA, and experimental tests were performed on 11 types of unit cell-based lattice structures with dimensions of 20 mm × 20 mm × 20 mm. Consequently, under the same relative density conditions, simple cubic, octahedron, truncated cube, and truncated octahedron-based lattice structures with a 3 × 3 × 3 array pattern showed the best axial compressive strength properties. Correlations among the unit cell types, lattice structure topologies, relative densities, unit cell array patterns, and mechanical properties were identified, indicating their influence in describing and predicting the behaviors of lattice structures.

A Novel Design Method for Nonuniform Lattice Structures Based on Topology Optimization

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
Yafeng Han ◽  
Wen Feng Lu
Keyword(s):  
Mechanical Properties ◽  
Topology Optimization ◽  
Relative Density ◽  
Common Ground ◽  
Lattice Structure ◽  
Design Method ◽  
Lattice Structures ◽  
Structural Wall ◽  
Unit Cells ◽  
The Common

Lattice structures are broadly used in lightweight structure designs and multifunctional applications. Especially, with the unprecedented capabilities of additive manufacturing (AM) technologies and computational optimization methods, design of nonuniform lattice structures has recently attracted great research interests. To eliminate constraints of the common “ground structure approaches” (GSAs), a novel topology optimization-based method is proposed in this paper. Particularly, the structural wall thickness in the proposed design method was set as uniform for better manufacturability. As a solution to carry out the optimized material distribution for the lattice structure, geometrical size of each unit cell was set as design variable. The relative density model, which can be obtained from the solid isotropic microstructure with penalization (SIMP)-based topology optimization method, was mapped into a nonuniform lattice structure with different size cells. Finite element analysis (FEA)-based homogenization method was applied to obtain the mechanical properties of these different size gradient unit cells. With similar mechanical properties, elements with different “relative density” were translated into unit cells with different size. Consequently, the common topology optimization result can be mapped into a nonuniform lattice structure. This proposed method was computationally and experimentally validated by two different load-support design cases. Taking advantage of the changeable surface-to-volume ratio through manipulating the cell size, this method was also applied to design a heat sink with optimum heat dissipation efficiency. Most importantly, this design method provides a new perspective to design nonuniform lattice structures with enhanced functionality and manufacturability.

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.

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.

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.

scholarly journals Compressive Properties of Al-Si Alloy Lattice Structures with Three Different Unit Cells Fabricated via Laser Powder Bed Fusion

Materials ◽  
2020 ◽  
Vol 13 (13) ◽  
pp. 2902 ◽  
Author(s):  
Xiaoyang Liu ◽  
Keito Sekizawa ◽  
Asuka Suzuki ◽  
Naoki Takata ◽  
Makoto Kobashi ◽  
...  
Keyword(s):  
Strain Rate ◽  
Lattice Structure ◽  
Unit Cell ◽  
Lattice Structures ◽  
Powder Bed Fusion ◽  
Laser Powder Bed Fusion ◽  
Compressive Properties ◽  
Powder Bed ◽  
Unit Cells ◽  
Indentation Tests

In the present study, in order to elucidate geometrical features dominating deformation behaviors and their associated compressive properties of lattice structures, AlSi10Mg lattice structures with three different unit cells were fabricated by laser powder bed fusion. Compressive properties were examined by compression and indentation tests, micro X-ray computed tomography (CT), together with finite element analysis. The truncated octahedron- unit cell (TO) lattice structures exhibited highest stiffness and plateau stress among the studied lattice structures. The body centered cubic-unit cell (BCC) and TO lattice structures experienced the formation of shear bands with stress drops, while the hexagon-unit cell (Hexa) lattice structure behaved in a continuous deformation and flat plateau region. The Hexa lattice structure densified at a smaller strain than the BCC and TO lattice structures, due to high density of the struts in the compressive direction. Static and high-speed indentation tests revealed that the TO and Hexa exhibited slight strain rate dependence of the compressive strength, whereas the BCC lattice structure showed a large strain rate dependence. Among the lattice structures in the present study, the TO lattice exhibited the highest energy absorption capacity comparable to previously reported titanium alloy lattice structures.

Compressive Behavior and Deformation Characteristic of Al-Based Auxetic Lattice Structure Filled with Silicate Rubber

2018 ◽  
Vol 933 ◽  
pp. 240-245
Author(s):  
Ying Ying Xue ◽  
Xing Fu Wang ◽  
Xin Fu Wang ◽  
Fu Sheng Han
Keyword(s):  
Mechanical Properties ◽  
Relative Density ◽  
Composite Structures ◽  
Lattice Structure ◽  
Deformation Characteristic ◽  
Damage Mechanism ◽  
Lattice Structures ◽  
Compressive Behavior ◽  
Plateau Region ◽  
Pressure Infiltration

The composites composed of Al-based auxetic lattice structures and silicate rubbers were fabricated by pressure infiltration technology. The compressive behavior and deformation characteristic of the composites were investigated related with the relative densities of the auxetic lattice structures. We found that the composites exhibit a longer plateau region than the non-filled Al-based auxetic lattice structures, and the relative density of the auxetic lattice structures play an important role in the compressive mechanical properties, the higher the relative density, the higher flow stress. It is also noticing that, the composite structures show different deformation and damage mechanism due to the filled incompressible silicate rubber. It is expected that the study may provide useful information for the applications of composite structure.

Multiphase Thermomechanical Topology Optimization of Functionally Graded Lattice Injection Molds

2016 ◽  
Author(s):  
Tong Wu ◽  
Kai Liu ◽  
Andres Tovar
Keyword(s):  
Topology Optimization ◽  
Heat Conduction ◽  
Mechanical Performance ◽  
Lattice Structure ◽  
Functionally Graded ◽  
Unit Cell ◽  
Design Approach ◽  
Stiffness Reduction ◽  
Lattice Unit ◽  
Graded Lattice

This work presents a design methodology of lightweight, thermally efficient injection molds with functionally graded lattice structure using multiphase thermomechanical topology optimization. The aim of this methodology is to increase or maintain thermal and mechanical performance as well as to lower the cost of thermomechanical components such as injection molds when these are fabricated using additive manufacturing technologies. The proposed design approach makes use of thermal and mechanical finite element analyses to evaluate the components stiffness and heat conduction in two length scales: mesoscale and macroscale. The mesoscale contains the structural features of the lattice unit cell. Mesoscale homogenized properties are implemented in the macroscale model, which contains the components boundary conditions including the external mechanical loads as well as the heat sources and heat sinks. The macroscale design problem addressed in this work is to find the optimal distribution of given number of lattice unit cell phases within the component so its mass is minimized, while satisfying stiffness and heat conduction constraints of the overall component and the specific regions. This problem is solved through two steps: conceptual design generation and multiphase material distribution. In the first step, the mass is minimized subject to constraints of mechanical compliance and thermal cost function. In the second step, a given number of lattice material are optimally distributed subjected to nonlinear thermal and mechanical constraints, e.g., maximum nodal temperature, maximum nodal displacement. The proposed design approach is demonstrated through 2D and 3D examples including the optimal design of the core of an injection mold. The results demonstrate that a small reduction in mechanical and thermal performance allows for significant mass savings: the second example shows that 3.5% heat conduction reduction and 8.7% stiffness reduction results in 30.3% mass reduction.

Multiobjective optimization of a newly developed additively manufactured functionally graded anisotropic porous lattice structure

2020 ◽  
Vol 234 (11) ◽  
pp. 2233-2255
Author(s):  
Mahshid Mahbod ◽  
Masoud Asgari
Keyword(s):  
Elastic Modulus ◽  
Analytical Solution ◽  
Multiobjective Optimization ◽  
Relative Density ◽  
Elastic Moduli ◽  
Lattice Structure ◽  
Functionally Graded ◽  
Elastic Behavior ◽  
Average Error ◽  
Lattice Structures

In this paper, the elastic behavior of uniform and functionally graded porous lattice structures made by a double pyramid dodecahedron unit cell is investigated. Analytical solutions are derived in order to estimate the elastic moduli of the proposed structures in two directions. The analytical solution is validated by finite element simulations and experimental tests while the results show good agreement in general. The average difference between the numerical and analytical values of elastic modulus is under 14.44%, while the average error of experimental test and analytical solution is 15.69%. A comprehensive optimization is performed by considering elastic moduli in two different directions as objective functions. Various uniform lattice structures with different relative densities are optimized using NSGA-II algorithm as well as lattice structures with graded distribution of porosity. A variety of optimal designs are achieved by multiobjective optimization algorithm and the best point of the Pareto front is selected by the TOPSIS method. Furthermore, the functionally graded lattice structures are optimized by considering desirable relative densities in each layer and applying constructive constraints. Different distribution patterns of relative density are considered in layers in order to present the flexible design capability of the developed structure. The obtained results show that the elastic modulus is significantly dependent on the relative density of each layer as well as cell configuration. Also, different lattice structures could be achieved by applying desirable prescribed distribution of properties. A comparison between optimized and base model indicated that elastic moduli was considerably improved in optimized models. In optimization of uniform models, [Formula: see text] was increased by 115%, 89%, and 69% in optimized structures for relative densities of 10%, 30%, and 50%, respectively. Moreover, [Formula: see text] was improved in optimized models by 27%, 24%, and 18% for relative densities of 10%, 30%, and 50%, respectively.

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