Trade-offs in the latent representation of microstructure evolution
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Composite materials with different microstructural material symmetries are common in engineering applications where grain structure, alloying and particle/fiber packing are optimized via controlled manufacturing. In fact these microstructural tunings can be done throughout a part to achieve functional gradation and optimization at a structural level. To predict the performance of particular microstructural configuration and thereby overall performance, constitutive models of materials with microstructure are needed. In this work we provide neural network architectures that provide effective homogenization models of materials with anisotropic components. These models satisfy equivariance and material symmetry principles inherently through a combination of equivariant and tensor basis operations. We demonstrate them on datasets of stochastic volume elements with different textures and phases where the material undergoes elastic and plastic deformation, and show that the these network architectures provide significant performance improvements.
Due to the growing popularity of laser powder bed fusion (LPBF) as a metal additive manufacturing technique, there is a strong need to be able to accurately predict build outcomes. Full fidelity simulations of this process are not feasible due to the vast range of length and time scales inherent to it. While part-scale codes for simulating residual stress and distortion have shown reasonable predictive capability, they often neglect many aspects of the process occurring over smaller length/time scales, and thus are unable to capture effects of process parameter adjustments or the behavior of fine features. One way of capturing aspects at more refined length scales is through the use of adaptive mesh refinement (AMR). AMR allows for the process to be simulated at scales approaching the physical spatial dimensions without drastically increasing the total degrees of freedom in the simulation. This manuscript describes the implementation of an AMR algorithm within a multiphysics, parallelized finite element code, and its application to the LPBF problem. In this work, part-scale examples are provided where the use of AMR has allowed for higher fidelity thermal and thermomechanical simulations, as compared to experimental measurements. Results from these higher resolution simulations show that while AMR is a necessary component for increased accuracy in a computationally efficient manner, other improvements are also necessary, including handling of the multiple time scales inherent to the problem and the need for improved AM-specific material models.
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Erosion and flooding impacts to Arctic coastal environments are intensifying with nearshore oceanographic conditions acting as a key environmental driver. Robust and comprehensive assessment of the nearshore oceanographic conditions require knowledge of the following boundary conditions: incident wave energy, water level, incident wind energy, ocean temperature and salinity, bathymetry, and shoreline orientation. The number of offshore oceanographic boundary conditions can be large, requiring a significant computational investment to reproduce nearshore conditions. This present study develops location-independent typologies to reduce the number of boundary conditions needed to assess nearshore oceanographic environments in both a Historical (2007–2019) and Future (2020–2040) timespan along the Alaskan North Slope. We used WAVEWATCH III® and Delft3D Flexible Mesh model output from six oceanographic sites located along a constant ~50 m bathymetric line spanning the Chukchi to Beaufort Seas. K-means clustering was applied to the energy-weighted joint-probability distribution of significant wave height (H s ) and peak period (T p ). Distributions of wave and wind direction, wind speed, and water level associated with location-independent centroids were assigned single values to describe a reduced order, typological rendition of offshore oceanographic conditions. Reanalysis data (e.g., ASRv2, ERA5, and GOFS) grounded the historical simulations while projected conditions were obtained from downscaled GFDL-CM3 forced under RCP8.5 conditions. Location-dependence for each site is established through the occurrence joint-probability distribution in the form of unique scaling factors representing the fraction of time that the typology would occupy over a representative year. As anticipated, these typologies show increasingly energetic ocean conditions in the future. They also enable computationally efficient simulation of the nearshore oceanographic environment along the North Slope of Alaska for better characterization of coastal processes (e.g., erosion, flooding, or sediment transport).
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In the face of climate change and population growth in coastal regions, land-use analysis efforts are more challenging than ever. Land-use decision-makers in coastal communities are burdened with the difficult choices of where to place new homes versus other assets. While there has been an increased focus on hazard mitigation and disaster resilience in the field of planning, evidence points towards continued development in risk-prone areas including flood zones. Residential development within flood zones specifically continues to be a major issue. To help counter this trend, this study introduces a novel land-use analysis method, coupling topographic flood inundation mapping techniques with digital elevation model (DEM) adaptations. This Topographic Model Scenario Generation workflow can be used by planners early in the land-use decision making process and provides an alternative to high-computational hydraulic models. The analysis also includes the identification of strengths and weaknesses of topographic models' recognition of built infrastructure assets, adding to a limited body of knowledge addressing recommended uses of such models. Levees and canals prove particularly functional in this context while detention ponds less so, likely due to a lack of total water mass accountability. Lastly, we provide a functional demonstration in Southeast Texas to illustrate the workflow's ability to create multiple infrastructure scenarios and visualize their effects across different flood events.
When deformation gradients act on the scale of the microstructure of a part due to geometry and loading, spatial correlations and finite-size effects in simulation cells cannot be neglected. We propose a multiscale method that accounts for these effects using a variational autoencoder to encode the structure–property map of the stochastic volume elements making up the statistical description of the part. In this paradigm the autoencoder can be used to directly encode the microstructure or, alternatively, its latent space can be sampled to provide likely realizations. Furthermore, we demonstrate the method on three examples using the common additively manufactured material AlSi10Mg in: (a) a comparison with direct numerical simulation of the part microstructure, (b) a push forward of microstructural uncertainty to performance quantities of interest, and (c) a simulation of functional gradation of a part with stochastic microstructure.
Wind plant power has seen tremendous growth in the US and worldwide, representing the most significant renewable energy installed capacity besides hydropower. While wind power enables decarbonizing the electricity grid, the rising amount of end-of-life (EOL) wind blades - which are arduous to recycle - present a challenge for landfills if disposed of whole and a missed opportunity to recover valuable composite materials. The circular economy (CE) concept proposes strategies to rethink, reuse and recover products, components, and materials. However, transitioning to a CE implies changing how business models, supply chains, and behaviors deal with products and waste; changes arduously captured with traditional methods used to assess circularity such as life cycle assessment or material flow analysis (MFA). Here we present an agent-based model (ABM) that captures behavioral aspects impacting wind blade circularity in the US. The ABM also accounts for wind plant projects and landfills heterogeneity - a characteristic not easily included in top-down approaches such as MFA, input-output analysis, or system dynamics. Results show that recycling is divided as most recycling facilities are on the eastern side of the country, a challenge that could be alleviated by shredding blades before transportation. Recycling programs from the wind industry could also seed recycling behaviors within wind plant owners. Better yet, new blade designs could increase circularity if original equipment manufacturers accept the risks involved with the investments needed to adapt the production lines.
The aggregation of clay minerals in liquid water exemplifies colloidal self-assembly in nature. These negatively charged aluminosilicate platelets interact through multiple mechanisms with different sensitivities to particle shape, surface charge, aqueous chemistry, and interparticle distance and exhibit complex aggregation structures. Experiments have difficulty resolving the associated colloidal assemblages at the scale of individual particles. Conversely, all-atom molecular dynamics (MD) simulations provide detailed insight on clay colloidal interaction mechanisms, but they are limited to systems containing a few particles. We develop a new coarse-grained (CG) model capable of representing assemblages of hundreds of clay particles with accuracy approaching that of MD simulations, at a fraction of the computational cost. Our CG model is parameterized based on MD simulations of a pair of smectite clay particles in liquid water. A distinctive feature of our model is that it explicitly represents the electrical double layer (EDL), i.e., the cloud of charge-compensating cations that surrounds the clay particles. Our model captures the simultaneous importance of long-range colloidal interactions (i.e., interactions consistent with simplified analytical models, already included in extant clay CG models) and short-range interactions such as ion correlation and surface and ion hydration effects. The resulting simulations correctly predict, at low solid-water ratios, the existence of ordered arrangements of parallel particles separated by water films with a thickness up to ~10 nm and, at high solid-water ratios, the coexistence of crystalline and osmotic swelling states, in agreement with experimental observations.
Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.
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