Research Papers: Design Automation

Design Exploration of Reliably Manufacturable Materials and Structures With Applications to Negative Stiffness Metamaterials and Microstereolithography1

[+] Author and Article Information
Clinton Morris, Carolyn C. Seepersad

Mechanical Engineering Department,
The University of Texas at Austin,
Austin, TX 78712

Logan Bekker

Lawrence Livermore National Laboratory,
Livermore, CA 94550

Michael R. Haberman

Mechanical Engineering Department
and Applied Research Laboratories,
The University of Texas at Austin,
Austin, TX 78712

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 2, 2018; final manuscript received August 7, 2018; published online September 12, 2018. Assoc. Editor: James K. Guest.

J. Mech. Des 140(11), 111415 (Sep 12, 2018) (14 pages) Paper No: MD-18-1286; doi: 10.1115/1.4041251 History: Received April 02, 2018; Revised August 07, 2018

One of the challenges in designing metamaterials for additive manufacturing (AM) is accounting for the differences between as-designed and as-built geometries and material properties. From a designer's perspective, these differences can lead to degradation of part and metamaterial performance, which is especially difficult to accommodate in small-lot or one-of-a-kind production. In this context, each part is unique, and therefore, extensive iteration is costly. Designers need a means of exploring the design space while simultaneously considering the reliability of additively manufacturing particular candidate designs. In this work, a design exploration approach, based on Bayesian network classifiers (BNC), is extended to incorporate manufacturing variation into the design exploration process and identify designs that reliably meet performance requirements when this variation is taken into account. The example application is the design of negative stiffness (NS) metamaterials, in which small volume fractions of NS inclusions are embedded within a host material. The resulting metamaterial or composite exhibits macroscopic mechanical stiffness and loss properties that exceed those of the base matrix material. The inclusions are fabricated with microstereolithography with features on the scale of tens of microns, but variability is observed in material properties and dimensions from specimen to specimen. This variability is measured and modeled via design, fabrication, and characterization of metrology parts. The quantified manufacturing variability is incorporated into the BNC approach as a manufacturability classifier to identify candidate designs that achieve performance targets reliably, even when manufacturing variability is taken into account.

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Fig. 1

Illustration of the BNC approach partitioning design spaces into regions of satisfactory and unsatisfactory design for a multilevel design problem

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Fig. 2

Classified satisfactory and unsatisfactory training data generate posterior class probabilities

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Fig. 3

Comparing the posterior class probabilities identifies regions of satisfactory or unsatisfactory design

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Fig. 4

Kernel density estimate from random distribution of bivariate data

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Fig. 5

Flowchart illustrating the workflow of incorporating manufacturing variability in the BNC approach

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Fig. 6

Flowchart describing classification scheme for incorporating manufacturing variation

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Fig. 7

Illustration of the geometric interpretation of the relationship between the manufacturing variation and BNC satisfactory region. The manufacturing variation distribution is formed via Monte Carlo sampling from the multivariate manufacturing distribution centered on the candidate point. If the hyper volume of the manufacturing distribution bounded by the BNC decision boundary is greater than a manufacturability threshold specified by the designer, the candidate point is considered reliably manufacturable.

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Fig. 8

Proposed geometry for a NS inclusion (top right) with associated force–displacement curve for a loaded beam

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Fig. 9

Schematic illustrating the multilevel nature of the design of negative stiffness metamaterials (top). Flowchart illustrating the connectivity of the design and performance spaces (bottom).

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Fig. 10

Negative stiffness inclusion geometry parameterized by design variables

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Fig. 11

Classification of the macroscale performance space (top) propagated to the microscale design space (bottom)

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Fig. 12

Decision boundary of the microscale design space formed by the BNC approach (top) and 2D projection of design space to highlight the shape of the classification boundary (bottom)

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Fig. 13

Decision boundary of the microscale design space (left) with two unsatisfactory designs highlighted and a projection of the satisfactory designs and two selected unsatisfactory designs into the mesoscale performance space (right), indicating that the satisfactory designs exhibit a linear relationship between C11Inc and C12Inc that is not provided by the unsatisfactory designs

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Fig. 14

Scanning electron microscope images of a NS inclusion (bottom) in which a cubic spline is fit to the boundary of a NS beam. Arrows indicate the normal direction used to measure beam thickness (top).

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Fig. 15

Illustration of a cubic spline fit to the boundary of a NS beam that can be used to determine the apex height of the beam

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Fig. 16

Kernel density estimates generated from beam thickness measurements

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Fig. 17

Plot illustrating that sufficient samples have been obtained for thickness and apex height measurements to converge to a stable thickness variation distribution

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Fig. 18

Mappings of the satisfactory decision boundaries for the microscale design space

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Fig. 19

Mappings of the reliably manufacturable decision boundaries illustrating the impact of varying the reliability threshold

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Fig. 20

Mappings of the performance space predicting satisfactory and attainable performance for the highlighted performance requirement

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Fig. 21

Visual workflow illustrating the complete incorporation of manufacturing variation into the BNC approach for a NS metamaterials design problem

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Fig. 22

Kernel density estimates generated from beam thickness measurements of new design (left) compared to original distribution (right)



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