Advances in high-resolution, high-throughput measurement techniques, coupled with powerful recent developments in computational modeling, simulation, and artificial intelligence (AI), have enabled breakthroughs in rapid discovery and testing of novel materials. These possibilities raise new questions pertaining to the credibility of the underlying models for real-world use, especially when these models are adopted to inform engineering or regulatory decisions in applications that deal with human safety and life. We present a risk-informed credibility assessment framework, that has been applied in adjacent domains to support engineering and regulatory decision-making based on the use of computational (including AI) models, and demonstrate its application in the context of rapid discovery and testing of metallic alloys. The framework consists of a number of steps and best practices to define a question of interest, establish a context of use, assess the model risk, develop and execute a plan to validate and verify the model's credibility within that context, document the results and deviations from the plan, determine adequacy of the models based on such results, and iterate over these steps until the required adequacy is achieved. We present a few case studies using a number of models developed to support rapid discovery and testing of novel metallic alloys in DARPA METALS. We highlight challenges, gaps, and opportunities for future directions that are generalizable to broader engineering applications.

The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop-on-demand (DoD) microfluidic devices that eject liquid metal droplets, where accurate knowledge of the damping rates for the least-damped oscillation modes following droplet ejection is paramount for assessing jetting stability at higher jetting frequencies, as ejection from a nonquiescent meniscus can result in deviations from nominal droplet properties. Computational fluid dynamics (CFD) simulations often struggle to accurately predict meniscus damping unless very fine discretizations are adopted, so calculations are slow and computationally expensive. The faster alternative we adopt here is to compute the damping rate directly from the eigenvalues of the linearized problem. The presence of a surface tension term in Stokes or sloshing problems requires approximation of the meniscus displacements as well, which introduces additional complexity in their numerical solution. In this paper, we consider the combined effects of viscosity and surface tension, approximate the meniscus displacements, and construct a finite element method to compute the fluid's oscillation modes. We prove that if the finite element spaces satisfy a typical inf-sup condition, and the space of the meniscus displacements is a subset of the set of normal traces of the space of velocities, then the method is free of spurious modes with zero or positive damping rates. To construct numerical examples, we implement the method with Taylor-Hood elements for the velocity and pressure fields, and with continuous piecewise quadratic elements for the displacement of the meniscus. We verify the numerical convergence of the method by reproducing the solution to an analytical benchmark problem and two more complex examples with axisymmetric geometry. Remarkably, the spatial shape and temporal evolution (angular frequency and damping rate) of the set of least-damped oscillation modes are obtained in a matter of minutes, compared to days for a CFD simulation. The method's ability to quickly generate accurate estimates of fluid oscillation damping rates makes it suitable for integration into design loops for prototyping microfluidic nozzles.

In this paper, we propose PATO-a producibility-aware topology optimization (TO) framework to help efficiently explore the design space of components fabricated using metal additive manufacturing (AM), while ensuring manufacturability with respect to cracking. Specifically, parts fabricated through Laser Powder Bed Fusion are prone to defects such as warpage or cracking due to high residual stress values generated from the steep thermal gradients produced during the build process. Maturing the design for such parts and planning their fabrication can span months to years, often involving multiple handoffs between design and manufacturing engineers. PATO is based on the a priori discovery of crack-free designs, so that the optimized part can be built defect-free at the outset. To ensure that the design is crack free during optimization, producibility is explicitly encoded within the standard formulation of TO, using a crack index. Multiple crack indices are explored and using experimental validation, maximum shear strain index (MSSI) is shown to be an accurate crack index. Simulating the build process is a coupled, multi-physics computation and incorporating it in the TO loop can be computationally prohibitive. We leverage the current advances in deep convolutional neural networks and present a high-fidelity surrogate model based on an Attention-based U-Net architecture to predict the MSSI values as a spatially varying field over the part's domain. Further, we employ automatic differentiation to directly compute the gradient of maximum MSSI with respect to the input design variables and augment it with the performance-based sensitivity field to optimize the design while considering the trade-off between weight, manufacturability, and functionality. We demonstrate the effectiveness of the proposed method through benchmark studies in 3D as well as experimental validation.

One of the main concerns in design and process planning for multi-axis additive and subtractive manufacturing is collision avoidance between moving objects (e.g., tool assemblies) and stationary objects (e.g., part unified with fixtures). The collision measure for various pairs of relative rigid translations and rotations between the two pointsets can be conceptualized by a compactly supported scalar field over the 6D non-Euclidean configuration space. Explicit representation and computation of this field is costly in both time and space. If we fix O(m) sparsely sampled rotations (e.g., tool orientations), computation of the collision measure field as a convolution of indicator functions of the 3D pointsets over a uniform grid (i.e., voxelized geometry) of resolution O(n3) via fast Fourier transforms (FFTs) scales as in O(mn3logn) in time and O(mn3) in space. In this paper, we develop an implicit representation of the collision measure field via deep neural networks (DNNs). We show that our approach is able to accurately interpolate the collision measure from a sparse sampling of rotations, and can represent the collision measure field with a small memory footprint. Moreover, we show that this representation can be efficiently updated through fine-tuning to more efficiently train the network on multi-resolution data, as well as accommodate incremental changes to the geometry (such as might occur in iterative processes such as topology optimization of the part subject to CNC tool accessibility constraints).

Engineering design often involves representation in at least two levels of abstraction: the system-level, represented by lumped parameter models (LPMs), and the geometric-level, represented by distributed parameter models (DPMs). Functional design innovation commonly occurs at the system-level, followed by a geometric-level realization of functional LPM components. However, comparing these two levels in terms of behavioral outcomes can be challenging and time-consuming, leading to delays in design translations between system and mechanical engineers. In this paper, we propose a simulation-free scheme that compares LPMs and spatially-discretized DPMs based on their model specifications and behaviors of interest, regardless of modeling languages and numerical methods. We adopt a model order reduction (MOR) technique that a priori guarantees accuracy, stability, and convergence to improve the computational efficiency of large-scale models. Our approach is demonstrated through the model consistency analysis of several mechanical designs, showing its validity, efficiency, and generality. Our method provides a systematic way to compare system-level and geometric-level designs, improving reliability and facilitating design translation.

A major challenge in developing accurate and robust numerical solutions to multi-physics problems is to correctly model evolving discontinuities in field quantities. These manifest themselves as interfaces between different phases in multi-phase flows, or as shock and contact discontinuities in (either single- or multi-phase) compressible flows. A plethora of bespoke discretization schemes have been developed to capture both types of discontinuities in physics-based simulations. However, when a quick response is required to rapidly emerging challenges such as the need to design novel hypersonic vehicles, the complexity of such implementations impedes a swift transition from problem formulation to computation. This is exacerbated by the need to compose multiple interacting physics, which may cause specialized schemes to break unexpectedly as governing equations need to be changed and/or added. We introduce “inverse asymptotic treatment” (IAT) as a unified framework for capturing discontinuities in fluid flows that enables building directly computable models based on standard, off-the-shelf numerics. By capturing discontinuities through modifications at the level of the governing equations, rather than via reliance on specialized discretization schemes, IAT can seemlessly handle additional physics and thus makes it easier for novice end users to quickly obtain numerical results for a variety of multi-physics scenarios. This strategy also facilitates the use of a “multi-physics” compiler that automates the conversion of the modified PDEs to numerical source code readable by popular computational frameworks like OpenFOAM. We outline IAT in the context of phase-field modeling of two-phase incompressible flows, and then demonstrate its generality by showing how localized artificial diffusivity (LAD) methods for single-phase compressible flows can be viewed as instances of IAT. Through the real-world example of a laminar hypersonic compression corner, we illustrate IAT’s ability to, within a span of just a few months, generate a directly computable model whose wall metrics predictions for sufficiently small corner angles come close to that of NASA’s state-of-the-art VULCAN-CFD solver. Finally, we propose a novel LAD approach via “reverse-engineered” PDE modifications, inspired by total variation diminishing (TVD) flux limiters, to eliminate the problem-dependent parameter tuning that plagues traditional LAD. Through canonical numerical tests, we demonstrate that this “limiter-inspired” LAD approach, when combined with second-order central differencing, can robustly and accurately model compressible flows.

Accurate analytical and numerical modeling of multiscale systems is a daunting task. The need to properly resolve spatial and temporal scales spanning multiple orders of magnitude pushes the limits of both our theoretical models as well as our computational capabilities. Rigorous upscaling techniques enable efficient computation while bounding/tracking errors and helping to make informed cost-accuracy tradeoffs. The biggest challenges arise when the applicability conditions of upscaled models break down. Here, we present a non-intrusive two-way (iterative bottom-up top-down) coupled hybrid model, applied to thermal runaway in battery packs, that combines fine-scale and upscaled equations in the same numerical simulation to achieve predictive accuracy while limiting computational costs. First, we develop two methods with different orders of accuracy to enforce continuity at the coupling boundary. Then, we derive weak (i.e., variational) formulations of the fine-scale and upscaled governing equations for finite element (FE) discretization and numerical implementation in FEniCS. We demonstrate that hybrid simulations can accurately predict the average temperature fields within error bounds determined a priori by homogenization theory. Finally, we demonstrate the computational efficiency of the hybrid algorithm against fine-scale simulations.

In this paper, we present a topology optimization (TO) framework to simultaneously optimize the matrix topology and fiber distribution of functionally graded continuous fiber-reinforced composites (FRC). Current approaches in density-based TO for FRC use the underlying finite element mesh both for analysis and design representation. This poses several limitations while enforcing sub-element fiber spacing and generating high-resolution continuous fibers. In contrast, we propose a mesh-independent representation based on a neural network (NN) both to capture the matrix topology and fiber distribution. The implicit NN-based representation enables geometric and material queries at a higher resolution than a mesh discretization. This leads to the accurate extraction of functionally-graded continuous fibers. Further, by integrating the finite element simulations into the NN computational framework, we can leverage automatic differentiation for end-to-end automated sensitivity analysis, i.e., we no longer need to manually derive cumbersome sensitivity expressions. We demonstrate the effectiveness and computational efficiency of the proposed method through several numerical examples involving various objective functions. We also show that the optimized continuous fiber reinforced composites can be directly fabricated at high resolution using additive manufacturing.

Design requirements for moving parts in mechanical assemblies are typically specified in terms of interactions with other parts. Some are purely kinematic (e.g., pairwise collision avoidance) while others depend on physics and material properties (e.g., deformation under loads). Kinematic design methods and physics-based shape/topology optimization (SO/TO) deal separately with these requirements. They rarely talk to each other as the former uses set algebra and group theory while the latter requires discretizing and solving differential equations. Hence, optimizing a moving part based on physics typically relies on either neglecting or pruning kinematic constraints in advance, e.g., by restricting the design domain to a collision-free space using an unsweep operation. In this paper, we show that TO can be used to co-design two or more parts in relative motion to simultaneously satisfy physics-based criteria and collision avoidance. We restrict our attention to maximizing linear-elastic stiffness while penalizing collision measures aggregated in time. We couple the TO loops for two parts in relative motion so that the evolution of each part’s shape is accounted for when penalizing collision for the other part. The collision measures are computed by a correlation functional that can be discretized by left- and right-multiplying the shape design variables by a pre-computed matrix that depends solely on the motion. This decoupling is key to making the computations scalable for TO iterations. We demonstrate the effectiveness of the approach with 2D and 3D examples.

Despite the availability of advanced numerical capabilities and computational power, complex multi-physical, multiscale systems continue to challenge modeling efforts due to their elusive behaviors and nontrivial couplings. High-fidelity simulations have paved the way for simulating such systems, but the associated computational costs prohibit such tools from being used in iterative routines for engineering design and optimization. While numerical strategies for accelerating complex at-scale multi-physical simulations exist, they often concede predictive accuracy and lack rigorous justification. Alternatively, methods for developing rigorous multiscale models (e.g., upscaling techniques) offer a priori modeling error guarantees, but are primarily used in academic settings due to their requirements in time and specialized expertise for handling analytically intractable derivations. In our previous work, we developed an automated upscaling engine, Symbolica, that uses symbolic computation to avoid these overheads and rapidly develop multiscale models via rigorous homogenization theory. In this work, we extend Symbolica’s model development capabilities to accommodate multi-domain structures and demonstrate Symbolica’s generality in model development by applying it to a real-world problem; namely, to analyze thermal runaway in Li-ion battery modules. We obtain homogenized models that capture the sharp spatiotemporal gradients associated with thermal runaway to within the guaranteed modeling error. Upon numerically validating the models, we demonstrate how Symbolica can be used to reduce the level of effort in rigorous multiscale modeling and model implementation for real-world applications.

Predicting part quality for additive manufacturing (AM) processes requires high-fidelity numerical simulation of partial differential equations (PDEs) governing process multiphysics on a scale of minimum manufacturable features. This makes part-scale predictions computationally demanding, especially when they require many small-scale simulations. We consider drop-on-demand liquid metal jetting (LMJ) as an illustrative example of such computational complexity. A model describing droplet coalescence for LMJ may include coupled incompressible fluid flow, heat transfer, and phase change equations. Numerically solving these equations becomes prohibitively expensive when simulating the build process for a full part consisting of thousands to millions of droplets. Reduced-order models (ROMs) based on neural networks (NN) or k-nearest neighbor (kNN) algorithms have been built to replace the original physics-based solver and are computationally tractable for part-level simulations. However, their quick inference capabilities often come at the expense of accuracy, robustness, and generalizability. We apply an operator learning (OL) approach to learn a mapping between initial and final states of the droplet coalescence process for enabling rapid and accurate part-scale build simulation. Preliminary results suggest that OL requires order-of-magnitude fewer data points than a kNN approach and is generalizable beyond the training set while achieving similar prediction error.

Additive manufacturing (AM) is a class of advanced manufacturing technologies that facilitates fabrication of geometrically complex, high-performance functional parts. AM processes often produce a “near-net” shape comprising the intended design and sacrificial support structures to be removed in postprocessing. The amount of extra material in the near-net shape directly increases fabrication cost and clean-up time. This paper presents a shape modification method for AM parts to minimize the need for sacrificial material in the near-net shape. Given an existing triangulated boundary representation of the part, we formulate the problem as a generic shape optimization that minimizes the changes made to the original geometry by locally modifying vertex coordinates while both maintaining the manifold nature of the representation and satisfying the overhang angle constraints, when possible. Specifically, we augment a pseudo-energy regularization term to our primary objective function for self-supporting to ensure that the optimized shape is valid and suitable for AM. We propose two mesh regularization methods, using virtual springs and sphere packing, and provide differentiable expressions of the objective function and constraints to enable efficient gradient-based optimization. We show that the sphere packing is more robust and retains the quality of the mesh during optimization. Finally, we demonstrate the effectiveness and efficiency of our method in modifying realistic models in 3D.

Metal additive manufacturing (AM) processes often fabricate a near-net shape that includes the as-designed part as well as the sacrificial support structures that need to be machined away by subtractive manufacturing (SM), for instance multi-axis machining. Thus, although AM is capable of generating highly complex parts, the limitations of SM due to possible collision between the milling tool and the workpiece can render an optimized part non-manufacturable. We present a systematic approach to topology optimization (TO) of parts for AM followed by SM to ensure removability of support structures, while optimizing the part’s performance. A central idea is to express the producibility of the part from the near-net shape in terms of accessibility of every support structure point using a given set of cutting tool assemblies and fixturing orientations. Our approach does not impose any artificial constraints on geometric complexity of the part, support structures, machining tools, and fixturing devices. We extend the notion of inaccessibility measure field (IMF) to support structures to identify the inaccessible points and capture their contributions to non-manufacturability by a continuous spatial field. IMF is then augmented to the sensitivity field to guide the TO towards a manufacturable design. The approach enables efficient and effective design space exploration by finding nontrivial complex designs whose near-net shape can be 3D printed and post-processed for support removal by machining with a custom set of tools and fixtures. We demonstrate the efficacy of our approach on nontrivial examples in 2D and 3D.

Mechanical assemblies can exhibit complex relative motions, during which collisions between moving parts and their surroundings must be avoided. To define feasible design spaces for each part’s shape, “maximal” collision-free pointsets can be computed using configuration space modeling techniques such as Minkowski operations and sweep/unsweep. For example, for a pair of parts undergoing a given relative motion, to make the problem well-posed, the geometry of one part (chosen arbitrarily) must be fixed to compute the maximal shape of the other part by an unsweep operation. Making such arbitrary choices in a multi-component assembly can place unnecessary restrictions on the design space. A broader family of collision-free pairs of parts can be explored, if fixing the geometry of a component is not required. In this paper, we formalize this family of collision-free shapes and introduce a generic method for generating a broad subset of them. Our procedure, which is an extension of the unsweep, allows for co-generation of a pair of geometries which are modified incrementally and simultaneously to avoid collision. We demonstrate the effectiveness and scalability of our procedure in both 2D and 3D by generating a variety of collision-free shapes. Notably, we show that our approach can automatically generate freeform cam and follower profiles, gear teeth, and screw threads, starting from colliding blocks of materials, solely from a specification of relative motion and without the use of any feature-informed heuristics. Moreover, our approach provides continuous measures of collision that can be incorporated into standard gradient-descent design optimization, allowing for simultaneous collision-free and physics-informed co-design of mechanical parts for assembly.

The properties of rechargeable lithium-ion batteries are determined by the electrochemical and kinetic properties of their constituent materials as well as by their underlying microstructure. Microstructural design can be leveraged to achieve a leap in performance and durability. Here we investigate a porous electrode structure, as a strategy to increase the surface area, and provide structural stability for Li-metal anodes. The porous architecture consists of a mixed electron/ion conductor that function as a scaffold for lithium metal deposition. A new finite element model was developed to simulate the large topological changes associated with Li plating/stripping. This model is used to predict the current density distribution as a function of material and structural properties. A dimensionless quantity that combines Li-ion conductivity, surface impedance and average pore size is shown to be a good indicator to predict the peak current density. Preventing current localization at the separator reduces the risk of cell shorting. The analyses show that the peak current scales as ( hG ) 1/2 , where h is the ratio between surface and bulk conductivity and G is the average pore size. Stability analyses suggest that the growth is morphologically stable, and that confining Li-plating into pores can enable high-energy density solid-state batteries.

Hybrid manufacturing (HM) technologies combine additive and subtractive manufacturing (AM/SM) capabilities in multi-modal process plans that leverage the strengths of each. Despite the growing interest in HM technologies, software tools for process planning have not caught up with advances in hardware and typically impose restrictions that limit the design and manufacturing engineers' ability to systematically explore the full design and process planning spaces. We present a general framework for identifying AM/SM actions that make up an HM process plan based on accessibility and support requirements, using morphological operations that allow for arbitrary part and tool geometries to be considered. To take advantage of multi-modality, we define the actions to allow for temporary excessive material deposition or removal, with an understanding that subsequent actions can correct for them, unlike the case in unimodal (AM-only or SM-only) process plans that are monotonic. We use this framework to generate a combinatorial space of valid, potentially non-monotonic, process plans for a given part of arbitrary shape, a collection of AM/SM tools of arbitrary shapes, and a set of relative rotations (fixed for each action) between them, representing build/fixturing directions on 3-axis machines. Finally, we define a simple objective function quantifying the cost of materials and operating time in terms of deposition/removal volumes and use a search algorithm to explore the exponentially large space of valid process plans to find "cost-optimal" solutions. We demonstrate the effectiveness of our method on 3D examples.

Parts fabricated by additive manufacturing (AM) are often fabricated first as a near-net shape, a combination of intended nominal geometry and sacrificial support structures, which need to be removed in a subsequent post-processing stage using subtractive manufacturing (SM). In this paper, we present a framework for optimizing the build orientation with respect to removability of support structures. In particular, given a general multi-axis machining setup and sampled build orientations, we define a Pareto-optimality criterion based on the total support volume and the "secluded" support volume defined as the support volume that is not accessible by a given set of machining tools. Since total support volume mainly depends on the build orientation and the secluded volume is dictated by the machining setup, in many cases the two objectives are competing and their trade-off needs to be taken into account. The accessibility analysis relies on the inaccessibility measure field (IMF), which is a continuous field in the Euclidean space that quantifies the inaccessibility of each point given a collection of tools and fixturing devices. The value of IMF at each point indicates the minimum possible volumetric collision between objects in relative motion including the part, fixtures, and the tools, over all possible tool orientations and sharp points on the tool. We also propose an automated support removal planning algorithm based on IMF, where a sequence of actions are provided in terms of the fixturing devices, cutting tools, and tool orientation at each step. In our approach, each step is chosen based on the maximal removable volume to iteratively remove accessible supports. The effectiveness of the proposed approach is demonstrated through benchmark examples in 2D and realistic examples in 3D.

Macroscopic differential equations that accurately account for microscopic phenomena can be systematically generated using rigorous upscaling methods. However, such methods are time-consuming, prone to error, and become quickly intractable for complex systems with tens or hundreds of equations. To ease these complications, we propose a method of automatic upscaling through symbolic computation. By streamlining the upscaling procedure and derivation of applicability conditions to just a few minutes, the potential for democratization and broad utilization of upscaling methods in real-world applications emerges. We demonstrate the ability of our software prototype, Symbolica, by reproducing homogenized advective–diffusive–reactive (ADR) systems from earlier studies and homogenizing a large ADR system deemed impractical for manual homogenization. Novel upscaling scenarios previously restricted by unnecessarily conservative assumptions are discovered, and numerical validation of the models derived by Symbolica is provided.

Artificial intelligence (AI) has been increasingly applied in scientific activities for decades; however, it is still far from an insightful and trustworthy collaborator in the scientific process. Most existing AI methods are either too simplistic to be useful in real problems faced by scientists or too domain-specialized (even dogmatized), stifling transformative discoveries or paradigm shifts. We present an AI research associate for early-stage scientific discovery based on (a) a novel minimally-biased ontology for physics-based modeling that is context-aware, interpretable, and generalizable across classical and relativistic physics; (b) automatic search for viable and parsimonious hypotheses, represented at a high-level (via domain-agnostic constructs) with built-in invariants, e.g., postulated forms of conservation principles implied by a presupposed spacetime topology; and (c) automatic compilation of the enumerated hypotheses to domain-specific, interpretable, and trainable/testable tensor-based computation graphs to learn phenomenological relations, e.g., constitutive or material laws, from sparse (and possibly noisy) data sets.

In this paper, we present a topology optimization (TO) framework to enable automated design of mechanical components while ensuring the result can be manufactured using multi-axis machining. Although TO improves the part’s performance, the as-designed model is often geometrically too complex to be machined and the as-manufactured model can significantly vary due to machining constraints that are not accounted for during TO. In other words, many of the optimized design features cannot be accessed by a machine tool without colliding with the part (or fixtures). The subsequent post-processing to make the part machinable with the given setup requires trial-and-error without guarantees on preserving the optimized performance. Our proposed approach is based on the well-established accessibility analysis formulation using convolutions in configuration space that is extensively used in spatial planning and robotics. We define an inaccessibility measure field (IMF) over the design domain to identify non-manufacturable features and quantify their contribution to non-manufacturability. The IMF is used to penalize the sensitivity field of performance objectives and constraints to prevent formation of inaccessible regions. Unlike existing discrete formulations, our IMF provides a continuous spatial field that is desirable for TO convergence. Our approach applies to arbitrary geometric complexity of the part, tools, and fixtures, and is highly parallelizable on multi-core architecture. We demonstrate the effectiveness of our framework on benchmark and realistic examples in 2D and 3D. We also show that it is possible to directly construct manufacturing plans for the optimized designs based on the accessibility information.