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### Guest Editorial

J. Mech. Des. 2018;140(11):110301-110301-2. doi:10.1115/1.4041254.
FREE TO VIEW

The design of engineered materials and structures is a growing and increasingly impactful field of research that intersects materials science, engineering design, engineering mechanics, manufacturing, and data science. The overarching goal is to accelerate the discovery of new materials for engineering applications. The approach compliments a traditionally empirical, trial-and-error approach to materials discovery with an inverse, requirements-driven approach that strategically leverages material databases, simulations, and engineering design algorithms and methods to synthesize new materials and structures.

Topics: Design , Optimization
Commentary by Dr. Valentin Fuster

### Review Article

J. Mech. Des. 2018;140(11):110801-110801-9. doi:10.1115/1.4041177.

We present the results from a workshop on interdisciplinary research on design of engineering material systems, sponsored by the National Science Foundation. The workshop was prompted by the need to foster a culture of interdisciplinary collaboration between the engineering design and materials communities. The workshop addressed the following: (i) conceptual barriers between materials and engineering design research communities; (ii) research questions that the interdisciplinary field of materials design should focus on; (iii) processes and metrics to be used to validate research activities and outcomes on materials design; and (iv) strategies to sustain and grow the interdisciplinary field. This contribution presents a summary of the state of the field—elicited through extensive guided discussions between representatives of both communities—and a snapshot of research activities that have emerged since the workshop. Based on the increasing level of sophistication of interdisciplinary research programs on design of materials it is apparent that the field is growing and has great potential to play a key role in a vibrant interdisciplinary materials innovation ecosystem. Sustaining such efforts will contribute significantly to the advancement of technologies that will impact many industries and will enhance society-wide health, security, and economic well-being.

Commentary by Dr. Valentin Fuster

### Research Papers: Design Automation

J. Mech. Des. 2018;140(11):111401-111401-11. doi:10.1115/1.4040624.

We present a new method for the simultaneous topology optimization and material selection of structures made by the union of discrete geometric components, where each component is made of one of multiple available materials. Our approach is based on the geometry projection method, whereby an analytical description of the geometric components is smoothly mapped onto a density field on a fixed analysis grid. In addition to the parameters that dictate the dimensions, position, and orientation of the component, a size variable per available material is ascribed to each component. A size variable value of unity indicates that the component is made of the corresponding material. Moreover, all size variables can be zero, signifying the component is entirely removed from the design. We penalize intermediate values of the size variables via an aggregate constraint in the optimization. We also introduce a mutual material exclusion constraint that ensures that at most one material has a unity size variable in each geometric component. In addition to these constraints, we propose a novel aggregation scheme to perform the union of geometric components with dissimilar materials. These ingredients facilitate treatment of the multi-material case. Our formulation can be readily extended to any number of materials. We demonstrate our method with several numerical examples.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111402-111402-9. doi:10.1115/1.4040881.

Microstructures are stochastic by their nature. These aleatoric uncertainties can alter the expected material performance substantially and thus they must be considered when designing materials. One safe approach would be assuming the worst case scenario of uncertainties in design. However, design under the worst case conditions can lead to over-conservative solutions that provide less effective material properties. Here, a more powerful design approach can be developed by implementing reliability constraints into the optimization problem to achieve superior material properties while satisfying the prescribed design criteria. This is known as reliability-based design optimization (RBDO), and it has not been studied for microstructure design before. In this work, an analytical formulation that models the propagation of microstructural uncertainties to the material properties is utilized to compute the probability of failure. Next, the analytical uncertainty solution is integrated into the optimization problem to define the reliability constraints. The presented optimization under uncertainty scheme is exercised to maximize the yield stress of α-Titanium and magnetostriction of Galfenol, respectively.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111403-111403-17. doi:10.1115/1.4041050.

A material's design revolution is underway with a focus to design the material microstructure and processing paths to achieve certain performance requirements of products. A host of manufacturing processes are involved in producing a product. The processing carried out in each process influences its final properties. To couple the material processing-structure-property-performance (PSPP) spaces, models of specific manufacturing processes must be enhanced and integrated using multiscale modeling techniques (vertical integration) and then the input and output of the various manufacturing processes must be integrated to facilitate the flow of information from one process to another (horizontal integration). Together vertical and horizontal integration allows for the decision-based design exploration of the manufacturing process chain in an inverse manner to realize the end product. In this paper, we present an inverse method to achieve the integrated design exploration of materials, products, and manufacturing processes through the vertical and horizontal integration of models. The method is supported by the concept exploration framework (CEF) to systematically explore design alternatives and generate satisficing design solutions. The efficacy of the method is illustrated for a hot rod rolling (HRR) and cooling process chain problem by exploring the processing paths and microstructure in an inverse manner to produce a rod with specific mechanical properties. The proposed method and the exploration framework are generic and support the integrated decision-based design exploration of a process chain to realize an end product by tailoring material microstructures and processing paths.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111404-111404-12. doi:10.1115/1.4041052.

Stiffened structures are widely used in industry. However, how to optimally distribute the stiffening ribs on a given base plate remains a challenging issue, partially because the topology and geometry of stiffening ribs are often represented in a geometrically implicit way in traditional approaches. This implicit treatment may lead to problems such as high computational cost (caused by the large number of design variables, geometry constraints in optimization, and large degrees-of-freedom (DOF) in finite element analysis (FEA)) and the issue of manufacturability. This paper presents a moving morphable component (MMC)-based approach for topology optimization of rib-stiffened structures, where the topology and the geometry of stiffening ribs are explicitly described. The proposed approach displays several prominent advantages, such as (1) both the numbers of design variables and DOF in FEA are reduced substantially; (2) the proper manufacture-related geometry requirements of stiffening ribs can be readily satisfied without introducing any additional constraint. The effectiveness of the proposed approach is further demonstrated with numerical examples on topology optimization of rib-stiffened structures with buckling constraints.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111405-111405-10. doi:10.1115/1.4041170.

A great deal of engineering effort is focused on changing mechanical material properties by creating microstructural architectures instead of modifying chemical composition. This results in meta-materials, which can exhibit properties not found in natural materials and can be tuned to the needs of the user. To change Poisson's ratio and Young's modulus, many current designs exploit mechanisms and hinges to obtain the desired behavior. However, this can lead to nonlinear material properties and anisotropy, especially for large strains. In this work, we propose a new material design that makes use of curved leaf springs in a planar lattice. First, analytical ideal springs are employed to establish sufficient conditions for linear elasticity, isotropy, and a zero Poisson's ratio. Additionally, Young's modulus is directly related to the spring stiffness. Second, a design method from the literature is employed to obtain a spring, closely matching the desired properties. Next, numerical simulations of larger lattices show that the expectations hold, and a feasible material design is presented with an in-plane Young's modulus error of only 2% and Poisson's ratio of $2.78×10−3$. These properties are isotropic and linear up to compressive and tensile strains of 0.12. The manufacturability and validity of the numerical model is shown by a prototype.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111406-111406-13. doi:10.1115/1.4041208.

Even in a well-functioning total hip replacement, significant peri-implant bone resorption can occur secondary to stress shielding. Stress shielding is caused by an undesired mismatch of elastic modulus between the stiffer implant and the adjacent bone tissue. To address this problem, we present here a microarchitected hip implant that consists of a three-dimensional (3D) graded lattice material with properties that are mechanically biocompatible with those of the femoral bone. Asymptotic homogenization (AH) is used to numerically determine the mechanical and fatigue properties of the implant, and a gradient-free scheme of topology optimization is used to find the optimized relative density distribution of the porous implant under multiple constraints dictated by implant micromotion, pore size, porosity, and minimum manufacturable thickness of the cell elements. Obtained for a 38-year-old patient femur, bone resorption is assessed by the difference in strain energy between the implanted bone and the intact bone in the postoperative conditions. The numerical results suggest that bone loss for the optimized porous implant is only 42% of that of a fully solid implant, here taken as benchmark, and 79% of that of a porous implant with uniform density. The architected hip implant presented in this work shows clinical promise in reducing bone loss while preventing implant micromotion, thereby contributing to reduce the risk of periprosthetic fracture and the probability of revision surgery.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111407-111407-12. doi:10.1115/1.4040984.

Design optimization of composite structures is a challenging task due to the large dimensionality of the design space. In addition to the geometric variables (e.g., thickness of each component), the composite layup (the fiber orientation of each layer) also needs to be considered as design variables in optimization. However, the existing optimization methods are inefficient when applied to the multicomponent, multilayer composite structures. The low efficiency is caused by the high dimensionality of the design space and the inherent shortcomings in the existing design representation methods. In this work, two existing composite layup representation methods are investigated to discuss the root cause of the low efficiency. Furthermore, a new structural equation modeling (SEM)-based strategy is proposed to reduce the dimensionality of the design space. This strategy also helps the designers identify the loading mode of each component of the structural system. This strategy is tested in two scenarios of engineering optimization: (1) the direct multidisciplinary design optimization (DMDO), and (2) the metamodeling-based optimization. The proposed methods are compared with the traditional methods on two engineering design problems. It is observed that the design representation methods have a strong impact on the optimization results. The two case studies also demonstrate the effectiveness of the proposed strategy. Furthermore, recommendations are made on the selection of optimization methods for the design of composite structures.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111408-111408-14. doi:10.1115/1.4040912.

Organic photovoltaic cells (OPVCs), having received significant attention over the last decade, are yet to be established as viable alternatives to conventional solar cells due to their low power conversion efficiency (PCE). Complex interactions of several phenomena coupled with the lack of understanding regarding the influence of fabrication conditions and nanostructure morphology have been major barriers to realizing higher PCE. To this end, we propose a computational microstructure design framework for designing the active layer of P3HT:PCBM based OPVCs conforming to the bulk heterojunction (BHJ) architecture. The framework pivots around the spectral density function (SDF), a frequency space microstructure characterization, and reconstruction methodology, for microstructure design representation. We validate the applicability of SDF for representing the active layer morphology in OPVCs using images of the nanostructure obtained by cross-sectional scanning tunneling microscopy and spectroscopy (XSTM/S). SDF enables a low-dimensional microstructural representation that is crucial in formulating a parametric-based microstructure optimization scheme. A level-cut Gaussian random field (GRF, governed by SDF) technique is used to generate reconstructions that serve as representative volume elements (RVEs) for structure–performance simulations. A novel structure–performance (SP) simulation approach is developed using a physics-based performance metric, incident photon to converted electron (IPCE) ratio, to account for the impact of microstructural features on OPVC performance. Finally, a SDF-based computational IPCE optimization study incorporating only three design variables results in 36.75% increase in IPCE, underlining the efficacy of the proposed design framework.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111409-111409-14. doi:10.1115/1.4041034.

Integrated Computational Materials Engineering (ICME) calls for the integration of computational tools into the materials and parts development cycle, while the Materials Genome Initiative (MGI) calls for the acceleration of the materials development cycle through the combination of experiments, simulation, and data. As they stand, both ICME and MGI do not prescribe how to achieve the necessary tool integration or how to efficiently exploit the computational tools, in combination with experiments, to accelerate the development of new materials and materials systems. This paper addresses the first issue by putting forward a framework for the fusion of information that exploits correlations among sources/models and between the sources and “ground truth.” The second issue is addressed through a multi-information source optimization framework that identifies, given current knowledge, the next best information source to query and where in the input space to query it via a novel value-gradient policy. The querying decision takes into account the ability to learn correlations between information sources, the resource cost of querying an information source, and what a query is expected to provide in terms of improvement over the current state. The framework is demonstrated on the optimization of a dual-phase steel to maximize its strength-normalized strain hardening rate. The ground truth is represented by a microstructure-based finite element model while three low fidelity information sources—i.e., reduced order models—based on different homogenization assumptions—isostrain, isostress, and isowork—are used to efficiently and optimally query the materials design space.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111410-111410-9. doi:10.1115/1.4040816.

Additive manufacturing (AM) has enabled the creation of a near infinite set of functionally graded materials (FGMs). One limitation on the manufacturability and usefulness of these materials is the presence of undesirable phases along the gradient path. For example, such phases may increase brittleness, diminish corrosion resistance, or severely compromise the printability of the part altogether. In the current work, a design methodology is proposed to plan an FGM gradient path for any number of elements that avoids undesirable phases at a range of temperatures. Gradient paths can also be optimized for a cost function. A case study is shown to demonstrate the effectiveness of the methodology in the Fe–Ni–Cr system. Paths were successfully planned from 316 L Stainless Steel (316 L SS) to pure Cr that either minimize path length or maximize separation from undesirable phases. Examinations on the stochastic variability, parameter dependency, and computational efficiency of the method are also presented. Several avenues of future research are proposed that could improve the manufacturability, utility, and performance of FGMs through gradient path design.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111411-111411-8. doi:10.1115/1.4040788.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111412-111412-10. doi:10.1115/1.4040960.

The objective of this work is to establish a cluster-based optimization method for the optimal design of cellular materials and structures for crashworthiness, which involves the use of nonlinear, dynamic finite element models. The proposed method uses a cluster-based structural optimization approach consisting of four steps: conceptual design generation, clustering, metamodel-based global optimization, and cellular material design. The conceptual design is generated using structural optimization methods. K-means clustering is applied to the conceptual design to reduce the dimensional of the design space as well as define the internal architectures of the multimaterial structure. With reduced dimension space, global optimization aims to improve the crashworthiness of the structure can be performed efficiently. The cellular material design incorporates two homogenization methods, namely, energy-based homogenization for linear and nonlinear elastic material models and mean-field homogenization for (fully) nonlinear material models. The proposed methodology is demonstrated using three designs for crashworthiness that include linear, geometrically nonlinear, and nonlinear models.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111413-111413-8. doi:10.1115/1.4041220.

In this paper, the application of orthotropic material orientation optimization for controlling heat flow in electric car power trains is presented. The design process is applied to a case model, which conducts heat while storing heat-sensitive electronic components. The core of the case is designed using a low thermal conductivity material on order to focus the heat flow into the surface layer, which is designed using a high thermal conductivity material. Material orthotropy is achieved in the surface layer of the case by removing the material at points determined by the optimization analysis. For this purpose, an orthotropic material orientation optimization method was extended to calculate optimal material distribution. This is achieved by transforming the initially obtained optimal orientation vector field into a scalar field through the use of coupled time-dependent nonisotropic Helmholtz equations. Multiple parameters allow the control of the scalar field and therefore the control over material distribution in accordance to the optimal orientation. This allows the material distribution pattern to be scaled depending on the desired manufacturing method. The analysis method is applied to divert heat flow from a specific section of the model while focusing the heat flow to another section. The results are shown for a model with a 0.1 mm thick surface layer of copper and are compared to those results from several other materials and layer thicknesses. Finally, the manufactured design is presented.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111414-111414-13. doi:10.1115/1.4040704.

Many engineering applications utilize periodic lattice structures to take advantage of their favorable and tailorable mechanical properties. However, manufacturing the structures and evaluating their mechanical properties are still challenging. Additive manufacturing (AM) processes offer an alternative method to fabricate periodic lattice structures but the processes only approximate bounding part surfaces. Periodic lattice structures generally have two important geometrical characteristics, large bounding surfaces, and a large number of joints. Since geometric approximation errors on large bounding surfaces critically affect mechanical properties of the structures, designers and engineers should incorporate this degradation into mechanical property estimation procedures. In addition, the effects of joints should be analyzed in the estimation process, because joints reduce struts lengths, and as a result, they add stiffness to lattice structures. This paper presents a new homogenization approach to estimate mechanical properties of additively manufactured periodic lattice structures that is based on semirigid joint frame elements, and it takes into account effects of geometric approximation errors and joint stiffening. Effective structural parameters of a semirigid joint frame element are calculated from an as-fabricated voxel model to incorporate the geometric approximation errors. The semirigid joint frame element is integrated into a discrete homogenization process to evaluate joint stiffening effects. This paper reports results of parametric studies that investigate effects of AM process and joint properties on periodic lattice structures fabricated by material extrusion. This paper also compares estimates from the proposed approach and conventional homogenization approaches with test results. The comparison shows that the proposed method provides estimates that are more accurate.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111415-111415-14. doi:10.1115/1.4041251.

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.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111416-111416-10. doi:10.1115/1.4041371.

Identifying the key microstructure representations is crucial for computational materials design (CMD). However, existing microstructure characterization and reconstruction (MCR) techniques have limitations to be applied for microstructural materials design. Some MCR approaches are not applicable for microstructural materials design because no parameters are available to serve as design variables, while others introduce significant information loss in either microstructure representation and/or dimensionality reduction. In this work, we present a deep adversarial learning methodology that overcomes the limitations of existing MCR techniques. In the proposed methodology, generative adversarial networks (GAN) are trained to learn the mapping between latent variables and microstructures. Thereafter, the low-dimensional latent variables serve as design variables, and a Bayesian optimization framework is applied to obtain microstructures with desired material property. Due to the special design of the network architecture, the proposed methodology is able to identify the latent (design) variables with desired dimensionality, as well as capturing complex material microstructural characteristics. The validity of the proposed methodology is tested numerically on a synthetic microstructure dataset and its effectiveness for microstructural materials design is evaluated through a case study of optimizing optical performance for energy absorption. Additional features, such as scalability and transferability, are also demonstrated in this work. In essence, the proposed methodology provides an end-to-end solution for microstructural materials design, in which GAN reduces information loss and preserves more microstructural characteristics, and the GP-Hedge optimization improves the efficiency of design exploration.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2018;140(11):111417-111417-12. doi:10.1115/1.4041176.

With the rapid developments of advanced manufacturing and its ability to manufacture microscale features, architected materials are receiving ever increasing attention in many physics fields. Such a design problem can be treated in topology optimization as architected material with repeated unit cells using the homogenization theory with the periodic boundary condition. When multiple architected materials with spatial variations in a structure are considered, a challenge arises in topological solutions, which may not be connected between adjacent material architecture. This paper introduces a new measure, connectivity index (CI), to quantify the topological connectivity, and adds it as a constraint in multiscale topology optimization to achieve connected architected materials. Numerical investigations reveal that the additional constraints lead to microstructural topologies, which are well connected and do not substantially compromise their optimalities.

Commentary by Dr. Valentin Fuster

J. Mech. Des. 2018;140(11):113501-113501-8. doi:10.1115/1.4039104.

For a number of emerging mechatronics applications, dielectric elastomers (DEs) appear as a more energy efficient, lightweight, and low-cost solution with respect to established actuation technologies based, e.g., on solenoids or pneumatic cylinders. In addition to large strain, low power consumption, and high flexibility, DE actuators (DEA) are also highly scalable. Since DE membranes can be easily manufactured in different sizes and shapes, an effective approach to scale their performance is based on properly designing the material geometry. Clearly, to perform an optimal scaling the relation between material geometry and performance has to be properly investigated. In this paper, performance scaling by means of geometry is studied for circular out-of-plane (COP) DEAs. Such actuators consist of a silicone elastomer membrane sandwiched between two electrodes (carbon black silicone mixture). DEAs with six different geometries are manufactured, and a model-based strategy is used to find an experimental relationship between geometry and electro-mechanical behavior. In addition, an effective and computationally efficient method for predicting force–displacement characteristics of different geometries is presented. The proposed method allows to easily adapt DEAs to different applications in terms of stroke and force requirement, while minimizing at the same time both characterization and prototyping effort.

Commentary by Dr. Valentin Fuster

### Technical Brief

J. Mech. Des. 2018;140(11):114501-114501-5. doi:10.1115/1.4040911.

The structure of pomelo peel arouses research interest in recent years because of the outstanding damping and energy dissipating performance of the pomelo peel. Researchers found that pomelo peel has varying pore size through the peel thickness; the pore size gradient is one of the key reasons leading to superior energy dissipation performance of pomelo peel. In this paper, we introduce a method to model pomelo peel bioinspired foams with nonuniform pore distribution. We generate the skeletal open cell structure of the bioinspired foams using Voronoi tessellation. The skeleton of the bioinspired foams is built as three-dimension (3D) beam elements in a full-scale finite element model. The quasi-static and dynamic mechanical behaviors of the pomelo peel bioinspired foams could be derived through a finite element analysis (FEA). We illustrate our method using a case study of pomelo peel bioinspired aluminum foams under quasi-static compression and free fall impact circumstances. The case study results validate our method and demonstrate the superior impact resistance and damping behavior of bioinspired foam with gradient porosity for designers.

Commentary by Dr. Valentin Fuster