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DOE OSTI2022

System Modeling Frameworks for Wind Turbines and Plants: Review and Requirements Specifications

System modeling frameworks for wind turbines and plants are used by research groups and industry to design wind energy systems that take into account key trade-offs across performance, cost, and reliability at both the turbine and plant level. The frameworks are exercised using a variety of multi-disciplinary design, analysis and optimization (MDAO) methods. To improve inter-operability and foster collaboration, this report proposes a classification system for the frameworks along dimensions of model fidelity and scope. The classification system is first motivated with reviews the state-of-the-art in the development of software frameworks for integrated wind turbine and plant simulation. Within each major wind turbine and power plant subsystem, a matrix is developed for the disciplines used and the fidelity levels with which each discipline can be modeled. The existing frameworks are then classified according to the matrix. Next, an ontology is proposed that will allow for standardizing how data is transferred between the most common discipline-fidelity combinations used in the frameworks. A common representation of data creates the ability to 1) share system descriptions and analysis results, supporting more transparent benchmarks and comparison, and 2) integrate models together into workflows within and across organizations for improving the efficiency and performance of wind turbine and power plant design processes. Ultimately, this integration leads to better overall wind energy system designs with high performance and low costs.

17 WIND ENERGY↗

NASA NTRS2011

Mars Science Laboratory Flight Software Boot Robustness Testing Project Report

On the surface of Mars, the Mars Science Laboratory will boot up its flight computers every morning, having charged the batteries through the night. This boot process is complicated, critical, and affected by numerous hardware states that can be difficult to test. The hardware test beds do not facilitate testing a long duration of back-to-back unmanned automated tests, and although the software simulation has provided the necessary functionality and fidelity for this boot testing, there has not been support for the full flexibility necessary for this task. Therefore to perform this testing a framework has been build around the software simulation that supports running automated tests loading a variety of starting configurations for software and hardware states. This implementation has been tested against the nominal cases to validate the methodology, and support for configuring off-nominal cases is ongoing. The implication of this testing is that the introduction of input configurations that have yet proved difficult to test may reveal boot scenarios worth higher fidelity investigation, and in other cases increase confidence in the robustness of the flight software boot process.

Mars Science Laboratory (MSL)↗

DOE OSTI2025

Improvements to MOOSE user workflow through polyhedral elements, automation, and concise physics syntax

The MOOSE framework is a foundational capability used by the NEAMS program to create over 15 different simulation tools for advanced nuclear reactors. Due to MOOSE's broad use, improvements to the framework in support of modeling and simulation goals are critical to the program. Such improvements can take many forms, including optimization, improved user experience, streamlined application programming interfaces (APIs), parallelism, and new capabilities. The work described in this report was conducted in direct support of NEAMS tools and includes: addition of support for polyhedral elements, incorporation of mesh smoothers for mesh repair, integration of the Physics and ActionComponents systems, expansion of the Convergence system, and exploration of automated input file generation. These five areas of development are fundamental capabilities that will be leveraged by many NEAMS applications.

97 - MATHEMATICS AND COMPUTING↗

NASA NTRS2000

Implications of Simulation Conceptual Model Development for Simulation Management and Uncertainty Assessment

A simulation conceptual model is a simulation developers way of translating modeling requirements (i. e., what is to be represented by the simulation or its modification) into a detailed design framework (i. e., how it is to be done), from which the software, hardware, networks (in the case of distributed simulation), and systems/equipment that will make up the simulation can be built or modified. A conceptual model is the collection of information which describes a simulation developers concept about the simulation and its pieces. That information consists of assumptions, algorithms, characteristics, relationships, and data. Taken together, these describe how the simulation developer understands what is to be represented by the simulation (entities, actions, tasks, processes, interactions, etc.) and how that representation will satisfy the requirements to which the simulation responds. Thus the conceptual model is the basis for judgment about simulation fidelity and validity for any condition that is not specifically tested. The more perspicuous and precise the conceptual model, the more likely it is that the simulation development will both fully satisfy requirements and allow demonstration that the requirements are satisfied (i. e., validation). Methods used in simulation conceptual model development have significant implications for simulation management and for assessment of simulation uncertainty. This paper suggests how to develop and document a simulation conceptual model so that the simulation fidelity and validity can be most effectively determined. These ideas for conceptual model development apply to all simulation varieties. The paper relates these ideas to uncertainty assessments as they relate to simulation fidelity and validity. The paper also explores implications for simulation management from conceptual model development methods, especially relative to reuse of simulation components.

Pace, Dale K.↗

NASA NTRS2020

Description and Evaluation of the Specified-Dynamics Experiment in the Chemistry-Climate Model Initiative

We provide an overview of the REF-C1SD specified-dynamics experiment that was conducted as part of phase 1 of the Chemistry-Climate Model Initiative (CCMI). The REF-C1SD experiment, which consisted of mainly nudged general circulation models (GCMs) constrained with (re)analysis fields, was designed to examine the influence of the large-scale circulation on past trends in atmospheric composition. The REF-C1SD simulations were produced across various model frameworks and are evaluated in terms of how well they represent different measures of the dynamical and transport circulations. In the troposphere there are large (~40 %) differences in the climatological mean distributions, seasonal cycle amplitude, and trends of the meridional and vertical winds. In the stratosphere there are similarly large (~50 %) differences in the magnitude, trends and seasonal cycle amplitude of the transformed Eulerian mean circulation and among various chemical and idealized tracers. At the same time, interannual variations in nearly all quantities are very well represented, compared to the underlying reanalyses. We show that the differences in magnitude, trends and seasonal cycle are not related to the use of different reanalysis products; rather, we show they are associated with how the simulations were implemented, by which we refer both to how the large-scale flow was prescribed and to biases in the underlying free-running models. In most cases these differences are shown to be as large or even larger than the differences exhibited by free-running simulations produced using the exact same models, which are also shown to be more dynamically consistent. Overall, our results suggest that care must be taken when using specified-dynamics simulations to examine the influence of large-scale dynamics on composition.

Clara Orbe↗

DOE OSTI2022

Coalescence dynamics of prismatic dislocation loops due to vacancy supersaturation

Recovery processes in metals with a high defect concentration are at the heart of a structural alloy's usability in engineering applications. However, such processes take place via nonconservative mechanisms mediated by point defect diffusion and are governed by their interactions with the underlying microstructure. Indeed, one of the main challenges in studying recovery processes is their intrinsic multiscale complexity, which often negates the direct use of experimental techniques. Here, in this Research Letter, we study the mechanism of dislocation loop coalescence in metals by simulating the interaction dynamics between vacancies and prismatic loops using a stochastic framework that seamlessly bridges point defect kinetics with dislocation mechanics. Our simulations reveal two fundamental discoveries: first, that climb processes are governed by local fluctuations that are not captured by continuum elastodiffusion models, and, second, that prismatic loops create internal traps for vacancies, leading to the formation of rings around the perimeter of the loops that affect how coalescence takes place. Our results show an excellent agreement with in situ experimental observations of loop coalescence in Fe under irradiation.

36 MATERIALS SCIENCE↗

DOE OSTI2025

ITreeForeCast: An integrated modeling software to simulate tree level growth and forest carbon storage

Healthy trees in forest act as a natural carbon sink, capturing carbon. As they grow, they store carbon in their trunks, leaves and roots. Not all trees store carbon at the same rate, or in the same quantities, as it depends on a variety of biophysical and climatic factors. Furthermore, although carbon estimation in trees can be complex, the precision of estimates is tightly linked to trees growth, both in diameter and height. However, the simulation of carbon uptake by forest and forest growth has each been modeled separately, and independently at differing levels of detail and spatial resolution. In this paper, we introduce ITreeForeCast, a simulation model combining the two types of modeling on a unified platform, enabling the investigation of impacts of management strategies on carbon sequestration and wood products. ITreeForeCast is a user-extendable framework that offers new opportunities to model, simulate, and visualize the dynamics of individual trees in a forest, simulate management strategies over time, and carbon uptake.

09 - BIOMASS FUELS↗

DOE OSTI2021

Laponite-Incorporated UiO-66-NH2-Polyethylene Oxide Composite Membranes for Protection against Chemical Warfare Agent Simulants

A strategy is developed to enhance the barrier protection of polyethylene oxide (PEO)-metal–organic framework (MOF) composite films against chemical warfare agent simulants. To achieve enhanced protection, an impermeable high-aspect-ratio filler in the form of Laponite RD (LRD) clay platelets was incorporated into a composite PEO film containing MOF UiO-66-NH 2 . The inclusion of the platelets aids in mitigating permeation of inert hydrocarbons (octane) and toxic chemicals (2-chloroethyl ethyl sulfide, 2-CEES) of dimensions/chemistry similar to prominent vesicant threats while still maintaining high water vapor transport rates (WVTR). By utilizing small-angle neutron scattering, small-angle X-ray scattering, and wide-angle X-ray scattering, the LRD platelet alignment of the films was determined, and the structure of the films was correlated with performance as a barrier material. Performance of the membranes against toxic chemical threats was assessed using permeation testing of octane and 2-CEES, a common simulant for the vesicant mustard gas, and breathability of the membranes was assessed using WVTR measurements. To assess their robustness, chemical exposure (in situ diffuse reflectance infrared Fourier transform spectroscopy) and mechanical (tensile strength) measurements were also performed. It was demonstrated that the barrier performance of the film upon inclusion of the LRD platelets exceeds that of other MOF-polymer composites found in the literature and that this approach establishes a new path for improving permselective materials for chemical protection applications.

36 MATERIALS SCIENCE↗

NASA NTRS1999

Crack Growth Prediction Methodology for Multi-Site Damage: Layered Analysis and Growth During Plasticity

A finite element program has been developed to perform quasi-static, elastic-plastic crack growth simulations. The model provides a general framework for mixed-mode I/II elastic-plastic fracture analysis using small strain assumptions and plane stress, plane strain, and axisymmetric finite elements. Cracks are modeled explicitly in the mesh. As the cracks propagate, automatic remeshing algorithms delete the mesh local to the crack tip, extend the crack, and build a new mesh around the new tip. State variable mapping algorithms transfer stresses and displacements from the old mesh to the new mesh. The von Mises material model is implemented in the context of a non-linear Newton solution scheme. The fracture criterion is the critical crack tip opening displacement, and crack direction is predicted by the maximum tensile stress criterion at the crack tip. The implementation can accommodate multiple curving and interacting cracks. An additional fracture algorithm based on nodal release can be used to simulate fracture along a horizontal plane of symmetry. A core of plane strain elements can be used with the nodal release algorithm to simulate the triaxial state of stress near the crack tip. Verification and validation studies compare analysis results with experimental data and published three-dimensional analysis results. Fracture predictions using nodal release for compact tension, middle-crack tension, and multi-site damage test specimens produced accurate results for residual strength and link-up loads. Curving crack predictions using remeshing/mapping were compared with experimental data for an Arcan mixed-mode specimen. Loading angles from 0 degrees to 90 degrees were analyzed. The maximum tensile stress criterion was able to predict the crack direction and path for all loading angles in which the material failed in tension. Residual strength was also accurately predicted for these cases.

James, Mark Anthony↗

NASA NTRS2000

Filtering in Hybrid Dynamic Bayesian Networks

We implement a 2-time slice dynamic Bayesian network (2T-DBN) framework and make a 1-D state estimation simulation, an extension of the experiment in (v.d. Merwe et al., 2000) and compare different filtering techniques. Furthermore, we demonstrate experimentally that inference in a complex hybrid DBN is possible by simulating fault detection in a watertank system, an extension of the experiment in (Koller & Lerner, 2000) using a hybrid 2T-DBN. In both experiments, we perform approximate inference using standard filtering techniques, Monte Carlo methods and combinations of these. In the watertank simulation, we also demonstrate the use of 'non-strict' Rao-Blackwellisation. We show that the unscented Kalman filter (UKF) and UKF in a particle filtering framework outperform the generic particle filter, the extended Kalman filter (EKF) and EKF in a particle filtering framework with respect to accuracy in terms of estimation RMSE and sensitivity with respect to choice of network structure. Especially we demonstrate the superiority of UKF in a PF framework when our beliefs of how data was generated are wrong. Furthermore, we investigate the influence of data noise in the watertank simulation using UKF and PFUKD and show that the algorithms are more sensitive to changes in the measurement noise level that the process noise level. Theory and implementation is based on (v.d. Merwe et al., 2000).

Andersen, Morten Nonboe↗

DOE OSTI2026

A bioinspired approach for adaptive solid-solid phase change material coatings with optimized surface features for passive thermal regulation

The necessity to reduce global energy consumption calls for innovative strategies in building thermal management. Passive thermal regulation, particularly through bio-inspired designs, offers a promising avenue by mimicking nature's efficient control of optical properties. This research introduces a novel, climate-responsive coating that integrates optimized bio-inspired surface features with a solid-solid phase change material (SS-PCM) to dynamically manage solar absorptivity without adding additional thickness, enabling both heating and cooling as needed. Drawing on the photonic architectures of the Saharan silver ant and Morpho Didius butterfly, we employed a modeling and multi-objective optimization framework to tailor these surface features. Simulations reveal that surface texture, rather than the intrinsic phase transition of the SS PCM, dominates optical control. Relative to a flat SS PCM coating, optimized isotropic random roughness and broader range features yielded the highest passive heating power increase of about 144 % and 319 % respectively suitable for cold climates. Saharan ant-inspired features enhanced passive cooling for hot climates, achieving a 21.8 % improvement. For moderate climates, Butterfly-wing-inspired surface features provided a balanced enhancement of 19 % for heating and 7 % for cooling. Across all cases, the optimized surface features reduced combined heating and cooling energy demand more effectively than the baseline coating, while preserving material thickness. These findings demonstrate that climate-adaptive, optimized bio-inspired surface features can unlock the full potential of SS PCM coatings, providing a versatile pathway to significant energy savings in buildings and other applications. The methodology establishes a framework for designing next-generation adaptive envelopes that leverage natural photonic principles for high-impact, low-cost thermal regulation.

36 MATERIALS SCIENCE↗

NASA NTRS2026

Development and Experimental Validation of a Path-Dependent Spin Forming Finite Element Model

Spin forming is an advanced manufacturing process widely used in the aerospace and defense sectors to produce lightweight, high-strength cylindrical components with tight dimensional tolerances. This study explores the applicability of the path-dependent Mechanical Threshold Stress (MTS) constitutive model by simulating the evolution of geometry, machining forces, and plastic deformation during the spin forming of a 10-mm thick 6061-O aluminum cylinder. While numerical modeling of spin forming has advanced substantially over the past decade, systematic verification and experimental validation of material models remain limited, particularly in predicting through-thickness process evolution. The MTS model, incorporating a Voce hardening rule, is employed for its ability to represent cyclic loading, rapidly varying temperature fields, and strain rates characteristic of spin forming. Numerical convergence analysis indicates discretization uncertainties between 0.3% and 9.2% for key quantities of interest. Experimental validation demonstrates that the MTS model, when implemented with a verified mesh, accurately reproduces both elastic and plastic behavior of 6061-O aluminum, predicting peak roller loads within 11–18% of measurements, geometric tolerances within 3%, and plastic strain distributions within 10% of experimental values. Collectively, these results establish a validated computational framework for predictive spin-forming simulations with quantified confidence, providing a foundation for extension to other alloys, geometries, and forming conditions.

Spin forming↗

DOE OSTI2026

Microstructure, Transport, and Mechanics of Compacted Clay Simulated at the 0.1 μm Scale (1400 Smectite Clay Particles) Using a Coarse-Grained Model with Explicit Counterions

Clay-rich geomaterials play a critical role in many subsurface systems. The macroscale properties of these materials (low permeability, high ionic conductivity, high swelling pressure, etc.) are sensitive to molecular-level adsorption and hydration interactions at clay−water interfaces. Efforts to develop multiscale simulation approaches to predict these properties reveal a scale gap between atomistic simulations (typically limited to systems smaller than 10 nm) and continuum-scale models (which use computational grid elements with dimensions ≳ 10 μm). In this study, we present a coarse-grained (CG) framework that partly bridges this gap by simulating compacted smectite clay assemblages with dimensions of 0.1 μm containing 1,400 clay particles across a range of dry densities (1,050 to 1,850 kg·m −3 ) and Na/Ca counterion compositions (Na fraction ranging from 0.2 to 1). The simulated systems, along with their reconstructed binary three-dimensional pore networks, are used to evaluate the microstructure, pore size distribution, tortuosity, ion diffusivity, and swelling pressure of compacted smectite clay. Results show that our approach captures important features of the mesoscale heterogeneity of compacted clays, including tactoid formation, hierarchical porosity, and anisotropic pore networks. Results also reveal how compaction and counterion composition govern emergent behaviors, including dominant pore sizes, directional transport, and electrochemical response. This work highlights the potential of CG simulations to bridge molecular and continuum scales and to advance geotechnical and environmental applications involving clay-rich materials as well as related nanoporous media such as geopolymers and calcium-silicate-hydrate. However, the results also suggest that accurate prediction of certain microstructural and mechanical properties (e.g., swelling pressure) may require even larger-scale systems on the order of 1 μm.

02 PETROLEUM↗

DOE OSTI2020

Constraining the Milky Way Mass Profile with Phase-space Distribution of Satellite Galaxies

We estimate the Milky Way (MW) halo properties using satellite kinematic data including the latest measurements from Gaia DR2. With a simulation-based 6D phase-space distribution function (DF) of satellite kinematics, we can infer halo properties efficiently and without bias, and handle the selection function and measurement errors rigorously in the Bayesian framework. Applying our DF from the EAGLE simulation to 28 satellites, we obtain an MW halo mass of $M={1.23}_{-0.18}^{+0.21}\times {10}^{12}{M}_{\odot }$ and a concentration of $c={9.4}_{-2.1}^{+2.8}$ with the prior based on the M–c relation. The inferred mass profile is consistent with previous measurements but with better precision and reliability due to the improved methodology and data. Potential improvement is illustrated by combining satellite data and stellar rotation curves. Using our EAGLE DF and best-fit MW potential, we provide much more precise estimates of the kinematics for those satellites with uncertain measurements. Compared to the EAGLE DF, which matches the observed satellite kinematics very well, the DF from the semi-analytical model based on the dark-matter-only simulation Millennium II (SAM-MII) over-represents satellites with small radii and velocities. We attribute this difference to less disruption of satellites with small pericenter distances in the SAM-MII simulation. Finally, by varying the disruption rate of such satellites in this simulation, we estimate a ~5% scatter in the inferred MW halo mass among hydrodynamics-based simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2015

Tetrahedral-Mesh Simulation of Turbulent Flows with the Space-Time Conservative Schemes

Direct numerical simulations of turbulent flows are predominantly carried out using structured, hexahedral meshes despite decades of development in unstructured mesh methods. Tetrahedral meshes offer ease of mesh generation around complex geometries and the potential of an orientation free grid that would provide un-biased small-scale dissipation and more accurate intermediate scale solutions. However, due to the lack of consistent multi-dimensional numerical formulations in conventional schemes for triangular and tetrahedral meshes at the cell interfaces, numerical issues exist when flow discontinuities or stagnation regions are present. The space-time conservative conservation element solution element (CESE) method - due to its Riemann-solver-free shock capturing capabilities, non-dissipative baseline schemes, and flux conservation in time as well as space - has the potential to more accurately simulate turbulent flows using unstructured tetrahedral meshes. To pave the way towards accurate simulation of shock/turbulent boundary-layer interaction, a series of wave and shock interaction benchmark problems that increase in complexity, are computed in this paper with triangular/tetrahedral meshes. Preliminary computations for the normal shock/turbulence interactions are carried out with a relatively coarse mesh, by direct numerical simulations standards, in order to assess other effects such as boundary conditions and the necessity of a buffer domain. The results indicate that qualitative agreement with previous studies can be obtained for flows where, strong shocks co-exist along with unsteady waves that display a broad range of scales, with a relatively compact computational domain and less stringent requirements for grid clustering near the shock. With the space-time conservation properties, stable solutions without any spurious wave reflections can be obtained without a need for buffer domains near the outflow/farfield boundaries. Computational results for the isotropic turbulent flow decay, at a relatively high turbulent Mach number, show a nicely behaved spectral decay rate for medium to high wave numbers. The high-order CESE schemes offer very robust solutions even with the presence of strong shocks or widespread shocklets. The explicit formulation in conjunction with a close to unity theoretical upper Courant number bound has the potential to offer an efficient numerical framework for general compressible turbulent flow simulations with unstructured meshes.

Chang, Chau-Lyan↗

DOE OSTI2026

An Integrated Modeling Framework for Sediment Dynamics During Urban Flooding: Application to Hurricane Harvey in Houston

Floodwater can mobilize and redistribute large volumes of sediment from upland to downstream urban areas, threatening infrastructure, water quality, and ecosystem health. However, existing modeling approaches often fail to capture sediment dynamics in urban floodplains due to the lack of integration between upland hydrological processes and riverine sediment transport. This study presents the first integrated modeling framework that couples the Energy Exascale Earth System Model (E3SM) land component, which simulates runoff and hillslope erosion, with TELEMAC-GAIA, a two-dimensional hydrodynamic and sediment transport model. This framework enables the fully distributed, process-based simulation of high-resolution (as fine as 30 m) sediment dynamics from hillslopes to floodplains. Applied to a highly urbanized watershed in Houston during Hurricane Harvey, this framework reproduced observed water levels at 16 USGS gauges (median R 2 = 0.83 and KGE = 0.78), key sediment dynamics such as sediment transport and deposition processes, and reproduced spatial deposition patterns consistent with LiDAR-derived data. Based on the simulation, we estimate 8.0 million m 3 of event-scale sediment deposition, including 5.7 million m 3 trapped in the flood-control reservoirs and 2.3 million m 3 deposited along major channels and floodplains. Using a representative unit removal cost, this corresponds to an estimated dredging cost of $581 million for total deposition. These results provide a first-order, physically based quantification of Harvey-scale sediment impacts. This study provides a valuable tool for the holistic analysis of sediment dynamics triggered by extreme urban flooding, supporting flood-resilience planning. More broadly, it highlights the importance of integrating physically based hydrological processes for urban flooding and sediment research.

Hurricane Harvey↗

DOE OSTI2023

A projection-based analytical Jacobian framework for chemical kinetics applications

A major challenge in simulating complex combustion systems with detailed chemical kinetic models is the cost of integrating the chemical source terms, often done using stiff ODE solvers that require frequent Jacobian evaluations. Using analytically derived Jacobian matrices instead of divided-difference-based numerical Jacobian approximations can significantly reduce the associated computational cost. However, ambiguities arise in the formulation of analytical Jacobians because the chemical state of the system, or state vector, can be expressed in multiple ways, involving variables that are typically not independent from one another. Here, in this work, the consequences of those ambiguities on practical calculations are characterized in detail, and a generalized, projection-based framework is proposed as a mitigation strategy. Performances are assessed in a series of test cases involving a variety of configurations and numerical solution approaches. Results show that with proper treatment, commonly used analytical Jacobian formulations can be considered as equivalent for practical purposes, thereby alleviating concerns that the state vector chosen to express the governing equations and corresponding analytical Jacobian may significantly impact the accuracy of the simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

A Micromorphic Length-Scale Coupling Framework for the Determination of Higher-Order Constitutive Models and the Multi-Scale Simulation of Heterogeneous Materials [Thesis]

Heterogeneous materials and materials with complex microstructures pose a unique challenge in the development of accurate models of their response to external stimuli. These difficulties principally arise due to the difficulty in characterizing and modeling the constituents and their interactions. It is usually possible, though non-trivial, to construct an explicit representation of the microstructure (a direct numeric simulation or DNS) but the method by which the complex modes of deformation and other processes can be homogenized to a reduced-order approximation is frequently unclear. Many homogenization approaches are ad-hoc and lack a strong justification beyond ease of computation. Furthermore, the homogenization approach can, in some cases, not utilize the full breadth of information available in the computation of the macro-scale stresses and deformation measures. It is also noteworthy that homogenization, by its very nature, will tend to obfuscate details of processes occurring at the lower length-scale. It is therefore of interest to include as much information as possible in the construction of the reduced-order model so as to be predictive in a variety of loading environments. We here present a length-scale bridging technique based upon the micromorphic continuum mechanics of Eringen which incorporates volume and surface area averages as a part of its construction. This approach enforces the balance equations at the micro-scale and then studies the effect of the spatially varying nature on the macro-scale. This leads, naturally, to further balance equations which are solved at the macro-scale. This work details a homogenization framework which arises naturally from the micromorphic construction of Eringen attempting to introduce no definitions beyond which are justifiable from micro-structural considerations. One of the results of this effort is the so-called “micromorphic filter” which has been developed and applied to several DNS to demonstrate its effectively. In order to determine the macroscopic degrees of freedom we utilize the special case of an overlap coupling technique where the macro-scale is fully constrained to the micro-scale. This enables us to study the resulting material properties as expected but also allows us to further study the boundary conditions on the additional degrees of freedom at the macro-scale.

42 ENGINEERING↗