This work develops a model-order reduction framework for the meshless weakly-compressible smoothed-particle hydrodynamics (SPH) method. The proposed framework introduces the concept of modal reference spaces to overcome the challenges of discovering low-dimensional subspaces from unstructured, dynamic, and mixing numerical topology that occurs in SPH simulations. These modal reference spaces enable a low-dimensional projection of the SPH field equations while maintaining their inherent meshless qualities. Modal reference spaces are constructed by projecting SPH snapshot data onto a reference space where low-dimensionality of field quantities can be discovered via traditional modal decomposition techniques (e.g., the proper orthogonal decomposition (POD)). Scattered data interpolation is then used to represent the low-dimensional embedding in a meshless sense, which is leveraged during the online predictive stage. The proposed model-order reduction framework is cast into the meshless Galerkin POD (GPOD) and the Adjoint Petrov–Galerkin (APG) projection model-order reduction (PMOR) formulation. The PMORs are tested on three numerical experiments: 1) the Taylor–Green vortex; 2) the lid-driven cavity; and 3) the flow past an open cavity. Results show good agreement in reconstructed and predictive velocity fields, which showcase the ability of this framework to evolve the field equations in a low-dimensional subspace that originate from approximations in an unstructured, dynamic, and mixing numerical topology. Results also show that the pressure field is sensitive to the projection error due to the stiff weakly-compressible assumption made in the current SPH framework. However, there is evidence that this sensitivity can be alleviated through adjoint stabilization of the APG approach, though formal proof remains to be identified. Finally, the proposed meshless model-order reduction framework reports a dimensionality compression factor of up to 54,000 ×  within 10, % error in quantities of interest. While no hyper-reduction is incorporated to reduce costs in wall-clock time and memory, the present work marks a first step toward cost reduction in SPH simulations via a generalizable intrusive PMOR architecture.

The present work describes the early steps in creating a digital twin to predict aging for multi-material adhesive step lap joints (ASLJs), considering simultaneous mechanical and environmental influences. It begins by defining the digital twin context and its specific architecture known as the data-driven digital twin (D3T). For a D3T to work, a theoretical and computational framework must be established to understand how the properties of materials in ASLJs degrade due to environmental damage. The developed framework describes a thermodynamics-based theory for predicting material degradation. The computational implementation of the framework and its performance are evaluated using two models of multi-material ASLJs. The first model contains a single-step ASLJ made of titanium Ti-6Al-4V and carbon epoxy composite with FM-300K adhesive, featuring three variations to show different levels of homogenization. Studies on this model assess the impact of various parameters such as the finite element order, mesh density, damage parameters, and inclusion of damage models for the participating domains. The validation of this model is also provided against experimental data. The second model addresses a multistep ASLJ using the same materials. Predictions from this model are compared favorably with experimental results under two different environmental conditions to gain insights into the aging and performance degradation of the ASLJs. Finally, conclusions and plans close the present paper.

The present paper is concerned with deep learning techniques applied to detection and localization of damage in a thin aluminum plate. We used data collected on a tabletop apparatus by mounting to the plate four piezoelectric transducers, each of which took turns to generate a Lamb wave that then traversed the region of interest before being received by the remaining three sensors. Upon training a neural network to analyze time-series data of the material response, which displayed damage-reflective features whenever the plate-guided waves interacted with a contact load, we achieved a model that detected with >99% accuracy in addition to a model that localized with 2.58 ± 0.12 mm mean distance error. For each task, the best-performing model was designed according to the inductive bias that our transducers were both similar and arranged in a square pattern on a nearly uniform plate.

We present the initial steps towards formulating a multiphysics-based digital twin for predicting aging for multi-material adhesive step lap joints (ASLJs) that accounts for mechanical and environmental generalized loading. Initially, we provide a definition of the digital twin context and the particular digital twin architecture considered associated with the data-driven digital twin flavor. Subsequently, focus is given to establishing and exercising a theoretical and computational framework accounting for the degradation of properties for materials participating in ASLJs due to environmentally-aided damage accumulation. A thermodynamics-based theory is derived as a first step. An initial computational implementation of it is developed and applied to two models of multi-material ASLJs involving a titanium Ti-6Al-4V alloy and carbon epoxy composite adherent and an FM-300K adhesive. Several studies have been performed to identify the effect of parameters related to the choice of element order, mesh density, damage parameters and inclusion of damage models for the participating domains. Finally, the predictions obtained from the framework are compared with experimental results to establish the necessary validation for two environmental conditions of room and elevated temperatures at low ambient humidity. These results provide an initial insight into the characteristics of the aging degradation of ASLJ performance when both the adhesive and the composite material adherent are accumulating damage and contribute to aging of the respective materials.

In this work we are introducing a Machine Intelligence (MI) concept that belongs to the set of approaches that emphasize data over artificial intelligence model. The development of the concept was motivated by the need to eliminate training as the means to enable fast or perpetual system adaptation and update, and also vastly reduce pre-processing times. This characteristic can be extremely valuable in situations when new data are regularly becoming available and utilized to increase the MI accuracy with minimal delay, or when the represented system changes with time. A characteristic of the proposed data-defined MI approach is that of introspection; it can be queried to locally estimate the system error at any data point that is part of its data set and potentially act accordingly. To provide evidence of the validity and performance of the approach, we first demonstrate on classical hand-writing classification of numerical digits. We then apply it to a challenging problem of identifying the properties of bi-linear elastoplastic material using a single full-field strain tensor image of a synthetic experiment. The validation test is performed for many untrained instances, and the histogram, mean and maximum errors are discussed. We also discuss several interesting capabilities that a data-defined concept enables.

While working on the implementation of hygro-thermo-structural models for composite materials like those used in aircraft, we started noticing discontinuities in the fringe plots of the validation tests. This led us down a time-consuming path of debugging the implementation, that indicated that there were no problems with our numerical code. After further investigation we established the the issue emanated from the non-uniform nature of the colormap used to map the field variables. In researching the matter further we identified several contemporary attempts in establishing metric to judge the perceptual non-uniformity of colormaps. In this work we extend these attempts to encompass objective functions that allow for the automated generation of colormaps that minimize non-uniformity with the goal to reduce visual bias to the extent allowed by modern color theory and color standards. The objective functions are formulates on the basis of lightness, chromaticity, gamut completion, and desired color in both explicit and implict forms. We present several application examples and illustrate them based on typical benchmark data. We furthermore demonstrate the appearance of colormaps for the three types of color vision deficiency using simulated mapping. These studies are a precursor of refinement of the proposed framework towards more universal colormaps.

The work presented in this paper estimates the spectral radiance emitted from plasma induced by the interaction of hypervelocity moving structural/material systems with the atmosphere. The motivation for this effort originates from the need to compute the radiative heat fluxes imparted to hypersonic vehicles to facilitate their design, control, and maintenance. In response to this need, a computational framework was established to predict the fluid dynamics fields around a hypervelocity vehicle that in turn is coupled with the plasma physics that enables the calculation of the plasma fields and species dynamics. This framework implements a one-way coupling between fluid dynamics and plasma physics models. The framework solves the fluid dynamics partial differential equations representing the conservation of mass, momentum, and energy. The computed pressure, velocity, and temperature fields are subsequently utilized to drive the plasma physics PDEs describing the mass transport and energetics of all the nitrogen-oxygen 11 species present according to the socalled Dunn plasma model. An application of this framework for a spherical body for a wide range of velocities is presented as a verification of the framework's functionality. Typical distributions of the fluid and plasma dynamics are presented. Finally, the plasma radiance spectra are produced by employing statistical mechanics principles.

The continuous progress of additive manufacturing techniques has enabled engineers and designers to build complex geometries at various length scales with minimal setup time, reduced need for skilled labor, and minimal material waste. One important subset of structures endowed with complex geometrical features is formed by periodic and non-periodic metamaterials that enable engineering applications where certain combinations of performance features are desirable. For example, these structures could be used in naval engineering applications where light-weight, large surface area, energy absorption, heat dissipation, and acoustic bandgaps are critical. Nevertheless, to deploy these complex geometry structures, their multiphysics response must be well understood and characterized. The current effort aims to describe an initial approach for designing and deploying graded triply periodic minimal surface (TPMS) architectures. The work focuses on three TPMS systems: (a) Neovius, (b) Schoen's gyroid, and (c) Schoen's F-RD made of Ti-6Al-4V alloy. These three geometries are enhanced using variable wall thickness to obtain the so-called graded TPMS. Three problems are explored: (1) evaluation of the elastic equivalent material properties of various unit cells with graded thickness; (2) investigation of acoustics dispersion properties of three cells and (3) a thermo-structural response of a complex geometry made of twelve graded representative volume elements (RVE). Finite element results of the relevant thermo-structural partial differential equations for the case of a gyroid triply periodic cylindrical sandwich structure are presented.

The use of topology optimization algorithms for engineering design has become widespread. Motivated by the objective of producing lightweight, high-performance components, a wide variety of approaches have emerged, and many alternatives now exist for every stage of the associated computing pipeline. The present work introduces a generalized topology optimization framework for use in the area of additive manufacturing (AM), with a focus on naval applications. The development of this framework is outlined, with particular attention paid to the development of an anisotropic experimental data-driven material constitutive model. Additionally, methods for handling arbitrary numbers of objectives, design constraints imposed by additive manufacturing process physics, and boundary conditions particular to naval applications are explored. Steps for post-processing and refining the optimizer output in order to produce manufacturing-ready files are also discussed. The approach is demonstrated on a pair of test cases. The first is the design of an optimized "conformal" pressure vessel, which departs from the typical sphere / cylinder forms and allows for increased storage capacity by occupying a non-convex envelope space. The second application problem is the design of an optimized propulsor intended to be produced using large-scale AM. This propulsor is optimized for inertial and hydrodynamic loads, and a parametric study of the effect of outer shell thickness is performed.

This study presents a method, along with its algorithmic and computational framework implementation, and performance verification for dynamical system identification. The approach incorporates insights from phase space structures, such as attractors and their basins. By understanding these structures, we have improved training and testing strategies for operator learning and system identification. Our method uses time delay and non-linear maps rather than embeddings, enabling the assessment of algorithmic accuracy and expressibility, particularly in systems exhibiting multiple attractors. This method, along with its associated algorithm and computational framework, offers broad applicability across various scientific and engineering domains, providing a useful tool for data-driven characterization of systems with complex nonlinear system dynamics.

We propose a formulation of the Shifted Boundary Method, an immersed/embedded/unfitted boundary method, for transient thermo-elasticity problems characterized by very complex geometries. With an extensive set of numerical experiments, we demonstrate that the SBM performs accurately and robustly, even when the geometry is represented in stereolithography format (STL, or Standard Tessellation Language) with gaps and overlaps. We conclude with a thermoelastic analysis of an advanced fluid tank design, obtained with topology optimization methodologies and a candidate for additive manufacturing processes. This final example represents what is foreseen as the typical application of the SBM in the context of the simulation of additively manufactured components.

Materials science requires the collection and analysis of great quantities of data. These data almost invariably require various post-acquisition computation to remove noise, classify observations, fit parametric models, or perform other operations. Recently developed machine-learning (ML) algorithms have demonstrated great capability for performing many of these operations, and often produce higher quality output than traditional methods. However, it has been widely observed that such algorithms often suffer from issues such as limited generalizability and the tendency to "over fit" to the input data. In order to address such issues, this work introduces a metacomputing framework capable of systematically selecting, tuning, and training the best available machine-learning model in order to process an input dataset. In addition, a unique "cross-training" methodology is used to incorporate underlying physics or multiphysics relationships into the structure of the resultant ML model. This metacomputing approach is demonstrated on four example problems: repairing "gaps" in a multiphysics dataset, improving the output of electron back-scatter detection crystallographic measurements, removing spurious artifacts from X-ray microtomography data, and identifying material constitutive relationships from tensile test data. The performance of the metacomputing framework on these disparate problems is discussed, as are future plans for further deploying metacomputing technologies in the context of materials science and mechanical engineering.

Volumetric material manufacturing involves forming a solid shape within a precursor powder volume as a whole instead of the traditional layer by layer technique used for most additive manufacturing methodologies. This work presents an inverse technique for designing masking parameters in order to generate a predetermined shape within the precursor powder volume. The model utilizes a microwave cavity for inducing heat in BaTiO3 precursor powder via Joule heating. Material sintering and microwave propagation is modeled by coupling electromagnetics and heat conduction using finite element discretization. This interaction is complicated by the nonlinear thermal dependence of dielectric properties of BaTiO3 (i.e. density, specific heat, dielectric constant and loss tangent), which are considered here. Heat can be localized within the powder volume using one or multiple conductive masks that modulate incident energy. Utilizing both 3D and 2D models, it is demonstrated that an arbitrary nonuniform mask can create nonuniform heating in the powder volume. An experimental framework is then established to conduct a forward experiment parameterized with five masking and cavity design variables causing different powder heating patterns. Then an inverse problem is solved by specifying a desired shape and outputting a mask and cavity design capable of generating said shape. It is demonstrated that mask parameters can be optimized in order to produce a desired shape by this inverse method.

Motivated by the need for an efficient fatigue crack growth prediction infrastructure for both legacy and novel materials, we have initiated the development of an automated computational framework capable of determining crack growth model parameters for an equationally defined model. As a first step in addressing this need, the present paper focuses on the Hartman-Schijve crack growth variant of the NASGRO equation by exploring and comparing various global optimization methods for parameter determination and evaluating their performance by using both synthetic and actual data. It also introduces the concept of the total least-squares minimization criterion within the context of crack growth modeling. The development of an open-source software library and an application implementing the approach are also described and are available for distribution to the technical community.

Mesoscale simulations of discrete defects in metals provide an ideal framework to investigate the micro-scale mechanisms governing the plastic deformation under high thermal and mechanical loading conditions. To bridge size and time-scale while limiting computational effort, typically the concept of representative volume elements (RVEs) is employed. This approach considers the microstructure evolution in a volume that is representative of the overall material behavior. However, in settings with complex thermal and mechanical loading histories careful consideration of the impact of modeling constraints in terms of time scale and simulation domain on predicted results is required. We address the representation of heterogeneous dislocation structure formation in simulation volumes using the example of residual stress formation during cool-down of laser powder-bed fusion (LPBF) of AISI 316L stainless steel. This is achieved by a series of large-scale three-dimensional discrete dislocation dynamics (DDD) simulations assisted by thermo-mechanical finite element modeling of the LPBF process. Our results show that insufficient size of periodic simulation domains can result in dislocation patterns that reflect the boundaries of the primary cell. More pronounced dislocation interaction observed for larger domains highlight the significance of simulation domain constraints for predicting mechanical properties. We formulate criteria that characterize representative volume elements by capturing the conformity of the dislocation structure to the bulk material. This work provides a basis for future investigations of heterogeneous microstructure formation in mesoscale simulations of bulk material behavior.

Stochastic mesoscale inhomogeneity of material properties and material symmetries are investigated in a 3D-printed material. The analysis involves a spatially-dependent characterization of the microstructure in 316 L stainless steel, obtained through electron backscatter diffraction imaging. These data are subsequently fed into a Voigt–Reuss–Hill homogenization approximation to produce maps of elasticity tensor coefficients along the path of experimental probing. Information-theoretic stochastic models corresponding to this stiffness random field are then introduced. The case of orthotropic fields is first defined as a high-fidelity model, the realizations of which are consistent with the elasticity maps. To investigate the role of material symmetries, an isotropic approximation is next introduced through ad-hoc projections (using various metrics). Both stochastic representations are identified using the dataset. In particular, the correlation length along the characterization path is identified using a maximum likelihood estimator. Uncertainty propagation is finally performed on a complex geometry, using a Monte Carlo analysis. It is shown that mechanical predictions in the linear elastic regime are mostly sensitive to material symmetry but weakly depend on the spatial correlation length in the considered propagation scenario.

The advent of additive manufacturing (AM) has enabled the prototyping of periodic and non-periodic metamaterials (a.k.a. lattice or cellular structures) that could be deployed in a variety of engineering applications where certain combinations of performance features are desirable. For example, these structures could be used in a variety of naval engineering applications where light-weight, large surface area, energy absorption, heat dissipation, and acoustic bandgaps are critical. Furthermore, combining the multifunctional design optimization of these structures with progressive degradation due to cyclic fatigue would create attritable systems with tailorable performances not yet in reach by current conventional systems. Nevertheless, in order to deploy these complex geometry structures their multiphysics response has to be well understood and characterized. The objective of the current effort is to describe an initial approach for designing a uniaxial fatigue specimen as the first step toward the design of a multiaxial fatigue test coupon. In order to compare bending- and stretching-dominated structures, two strut-based lattices made of Ti-6Al-4V alloy consisting of the octet and tetrakaidecahedron (or Kelvin) cells are examined. The specimens are designed to fail in the central gauge area where edge effects are minimized. Finite element results of the relevant structural mechanics are used to compare the performance of the four geometries and to evaluate the effect of relative density on fatigue life.

A three-stage, comprehensive yet lean methodology for optimizing CNC machining is presented by example of rough cutting a complex pocket in a steel part to minimize machining time. First, CAM software is used for toolpath planning according to experience. Second, Taguchi method determines the best values of toolpath parameters (depth of cut, overlap, cutting pattern and cutter diameter) and their relative importance on the pertinent criterion, in this case machining time. In the third stage, machining parameters, i.e. cutting speed, feed per tooth and depth of cut were optimized by a genetic algorithm. The objective function included machining time, while taking into consideration technological and quality constraints, i.e. power, surface roughness and dynamic stability. The approach is demonstrated through CAM-based simulation.

The presence of damage in the adhesive material as well as combined environmental excitation in multi-material adhesive step-lap joints (ASLJs) often encountered in aircraft industries are frequently neglected. Historically, the ASLJ design is based only within the scope of elastoplastic failure. The present work describes the implementation and application of a computational framework enabling the quasistatic performance evaluation of such joints under the simultaneous presence of plasticity, damage, and hygrothermal environmental stimuli. In particular, ASLJ linking Ti-6Al-4V alloy adherents with an FM-300K adhesive are modeled under the proposed framework for various material responses and environmental excitations. It is shown that the assumption of using only elastoplastic failure for the adhesive may not be an adequate assumption for designing and qualifying ASLJs. Specifically, consideration of the presence of plasticity, damage, and environmental effects indicates that there are reasons to re-examine the design practices of such joints and to determine the relevant material constants associated with the multiphysics cross-coupling effects.

The presence of gaps and spurious non-physical artifacts in datasets is a nearly ubiquitous problem in many scientific and engineering domains. In the context of multiphysics numerical models, data gaps may arise from lack of coordination between modeling elements and limitations of the discretization and solver schemes employed. In the case of data derived from physical experiments, the limitations of sensing and data acquisition technologies, as well as myriad sources of experimental noise, may result in the generation of data gaps and artifacts. In the present work we develop and demonstrate a machine learning (ML) meta-framework for repairing such gaps in multiphysics datasets. A unique “cross-training” methodology is used to ensure that the ML models capture the underlying multiphysics of the input datasets, without requiring training on datasets free of gaps/artifacts. The general utility of this approach is demonstrated by the repair of gaps in a multiphysics dataset taken from hypervelocity impact simulations. Subsequently, we examine the problem of removing scan artifacts from X-ray computed micro-tomographic (XCMT) datasets. A unique experimental methodology for acquiring XCMT data, wherein articles are scanned multiple times under different conditions, enables the ready identification of artifacts, their removal from the datasets, and the filling of the resulting gaps using the ML framework. This work concludes with observations regarding the unique features of the developed methodology, and a discussion of potential future developments and applications for this technology.