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At least 289 records · Page 16

Large Engine Technology (LET) Short Haul Civil Tiltrotor Contingency Power Materials Knowledge and Lifing Methodologies

This report documents the results of an experimental program conducted on two advanced metallic alloy systems (Rene' 142 directionally solidified alloy (DS) and Rene' N6 single crystal alloy) and the characterization of two distinct internal state variable inelastic constitutive models. The long term objective of the study was to develop a computational life prediction methodology that can integrate the obtained material data. A specialized test matrix for characterizing advanced unified viscoplastic models was specified and conducted. This matrix included strain controlled tensile tests with intermittent relaxtion test with 2 hr hold times, constant stress creep tests, stepped creep tests, mixed creep and plasticity tests, cyclic temperature creep tests and tests in which temperature overloads were present to simulate actual operation conditions for validation of the models. The selected internal state variable models where shown to be capable of representing the material behavior exhibited by the experimental results; however the program ended prior to final validation of the models.

Spring, Samuel D.↗

Optimizing Earthquake Nowcasting With Machine Learning: The Role of Strain Hardening in the Earthquake Cycle

Abstract Nowcasting is a term originating from economics, finance, and meteorology. It refers to the process of determining the uncertain state of the economy, markets or the weather at the current time by indirect means. In this paper, we describe a simple two‐parameter data analysis that reveals hidden order in otherwise seemingly chaotic earthquake seismicity. One of these parameters relates to a mechanism of seismic quiescence arising from the physics of strain‐hardening of the crust prior to major events. We observe an earthquake cycle associated with major earthquakes in California, similar to what has long been postulated. An estimate of the earthquake hazard revealed by this state variable time series can be optimized by the use of machine learning in the form of the Receiver Operating Characteristic skill score. The ROC skill is used here as a loss function in a supervised learning mode. Our analysis is conducted in the region of 5° × 5° in latitude‐longitude centered on Los Angeles, a region which we used in previous papers to build similar time series using more involved methods (Rundle & Donnellan, 2020, https://doi.org/10.1029/2020EA001097 ; Rundle, Donnellan et al., 2021, https://doi.org/10.1029/2021EA001757 ; Rundle, Stein et al., 2021, https://doi.org/10.1088/1361-6633/abf893 ). Here we show that not only does the state variable time series have forecast skill, the associated spatial probability densities have skill as well. In addition, use of the standard ROC and Precision (PPV) metrics allow probabilities of current earthquake hazard to be defined in a simple, straightforward, and rigorous way.

58 GEOSCIENCES↗

On the Recoverability of Reactor Dynamics from Point Kinetics Data using SINDYc

Data driven models for reactor dynamics tend to face a few notable challenges. First, the broad range of timescales present across the various feedback mechanisms. Next, high standards for safety and importance of model performance in all operational domains. Finally, the correlations between state variables observed in most transients leads to difficulties when methods attempt to attribute certain dynamic phenomena to a particular cause. The current paper seeks to support efforts towards incorporating physics knowledge into one particular data-driven method for finding reactor dynamics called ``Sparse Identification of Nonlinear Dynamics with Control (SINDYc). The incorporation of physical knowledge into SINDYc will help address the challenges listed above by giving the model an initial understanding of the system being modeled. The demonstration of an exact representation of a set of point reactor dynamics equations in SINDYc is provided. Then, this allows for further discussion with mathematical justification as to why SINDYc, and other data-driven methods, may be difficult to apply to nuclear reactor dynamics due to correlations in the state variables. A particularly useful result of this work is the set of candidate functions required in SINDYc to exactly represent the reactor dynamics under a point approximation. In the future, SINDYc can be integrated with point models for reactor dynamics before being applied to the physical system to yield higher accuracy.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗

Anderson acceleration stability in NDA-accelerated k-eigenvalue problems

Anderson acceleration (AA) has been used to improve the stability and convergence rate of multiphysics iterative methods for reactor analysis. Most applications studied assume a tightly converged solution for the different physics problems, and AA is usually applied to state variables like temperature, density, and heat generation rate. In this paper, we study the theoretical performance of AA in NDA-accelerated k-eigenvalue problems. The problems and algorithms studied are simplified from the coupled iteration scheme adopted by MPACT and many other high-fidelity whole-core reactor codes. Compared to previous analyses of AA for these iteration schemes, we study the case with a partially converged neutronics solution and possibly partially converged nonlinear diffusion acceleration (NDA)/coarse mesh finite difference (CMFD) solutions. We observe that the performance of the iteration scheme with AA is very sensitive to the initial guess and is affected by the partially converged CMFD solutions. When the NDA solution is fully converged, using AA cannot achieve the optimal convergence rate in large-sized problems. Conversely, if the NDA solution is partially converged, the iteration scheme with AA can diverge or converge extremely slowly. It is found that the loss of robustness for AA is due to the fact that it is applied to the iterative subspace of state variables rather than the fundamental unknowns of the governing equations. To improve the robustness, the scalar flux should also be considered in the implementation of AA. After considering the residuals of flux, we observe that the stability is regardless of the partial convergence of NDA solutions. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

TRAILS Output Files

Overview This data repository contains ZIP files that store compressed versions of the output of running the WaterPaths utility planning and management tool in the DU Re-Evaluation mode (to download the tool, please see this GitHub repository). The tool was used to simulate the six-utility North Carolina Research Triangle problem. Details on the contents of each ZIP file can be seen below. Data details Temporal range: Weekly data for 2,344 weeks from 2015 to 2060 (45 years). Spatial range: Six water utilities in the North Carolina Research Triangle region (0: Chapel Hil/OWASA, 1: Durham, 2: Cary, 3: Raleigh, 4: Pittsboro, and 5: Chatham) File types: CSV and OUT Different solutions available The solution numbers correspond to the different pathway strategies (henceforth referred to as "solutions") discussed in paper's main and supporting text (abstract and link to the paper here). They are as follows: Sol92: The Durham-focused pathway strategy Sol132: The Raleigh-focused pathway strategy Sol140: The regionally-robust pathway strategy Objectives files These files can be accessed by unzipping solXX_objectives_pathways.zip that contains 1,000 Objectives_RDMXX_solsXX_to_XX.csv files. Each CSV file will consist of a row representing all the objective values for that specific solution, while every six columns represents the reliability, restriction frequency, infrastructure net present value ($ mil), peak financial cost, worst-case cost, and unit cost ($ per MG; in that order) for each of the six utilities. There will be 1,000 such files, denoting the performance of the six utilities across the 1,000 deeply uncertain states of the world (DU SOWs). Pathway files These files can be accessed by unzipping solXX_objectives_pathways.zip that contains 1,000 Pathways_sXX_RDMXX.out file. Each OUT corresponds to the set of infrastructure being triggered in a specific DU SOW, and each file will have the name file will consist of four tab-delimited columns that are described as follows: Realization: The realization in which an infrastructure options being triggered utility: The utility currently triggering infrastructure week: The week in which a specific infrastructure option is being triggered infra.: The infrastructure option being triggered If the OUT file contains only the header line, no infrastructure was triggered for that specific DU SOW. Policies files These files can be obtained by unzipping Policies.zip. Each of the 1,000 CSV files within the unzipped folder will contain weekly water use restriction policies for all 1,000 hydroclimatic realizations within a specific DU SOW. The column structure is as follows: 0rest_m: restriction multiplier for utility 0 (values between 0 and 1) 1rest_m: restriction multiplier for utility 1 (values between 0 and 1) 2rest_m: restriction multiplier for utility 2 (values between 0 and 1) 3rest_m: restriction multiplier for utility 3 (values between 0 and 1) 4rest_m: restriction multiplier for utility 4 (values between 0 and 1) 5rest_m: restriction multiplier for utility 5 (values between 0 and 1) 0transf: transfer volume for utility 0 (in MGD) 1transf: transfer volume for utility 1 (in MGD) 2transf: transfer volume for utility 2 (in MGD) 3transf: transfer volume for utility 3 (in MGD) 4transf: transfer volume for utility 4 (in MGD) 5transf: transfer volume for utility 5 (in MGD) Water Sources files These files can be obtained by unzipping WaterSources_subset.zip. Each of the 100 CSV files within the unzipped folder will contain weekly state variables at each water source for all 1,000 hydroclimatic realizations within a specific DU SOW. The column structure is as follows: Xvolume: available water volume from source X (in MGD) Xs_area: surface area of source X (in ACF) Xdemand: demand drawn from a water source from source X (in MGD) Xup_spill: upstream spillage from source X (in MGD) Xww_inflow: wastewater inflow from source X (in MGD) Xcatch_inflow: upstream catchment inflow to source X (in MGD) Xevap: evaporation multiplier for source X (values between 0 and 1) Xds_spill: downstream spillage from source X (in MGD) X_Y_alloc_cap: the allocated capacity from source X to utility Y (values between 0 and 1) X_Y_alloc_dem: the allocated demand from source X to utility Y (values between 0 and 1) Xtrmt_alloc_Y: the allocated treatment capacity from source X to utility Y (values between 0 and 1) Utilities files These files can be obtained by unzipping Utilities_subset.zip. Each of the 100 CSV files within the unzipped folder will contain weekly state variables at each utility for all 1,000 hydroclimatic realizations within a specific DU SOW. The column structure is as follows: Xst_vol: total available storage volume of utility X (in MG) Xcapacity: total storage capacity of utility X (in MG) Xnet_inf: : net inflow for all storage infrastructure for utility X (in MGD) Xst_rof: short term ROF for utility X (values between 0 and 1) Xst_stor_rof: short-term storage ROF for utility X (values between 0 and 1) Xst_trmt_rof: short-term treatment ROF for utility X (values between 0 and 1) Xlt_rof: long-term ROF for utility X (values between 0 and 1) Xlt_stor_rof: long-term storage ROF for utility X (values between 0 and 1) Xlt_trmt_rof: long-term treatment ROF for utility X (values between 0 and 1) Xrest_demand: restricted demand for utility X (in MGD) Xunrest_demand: unrestricted demand for utility X (in MGD) Xunfulf_demand: unfulfilled demand for utility X (in MGD) Xwastewater: wastewater return for utility X (in MGD) Xtreat_capacity: total treatment capacity for utility X (in MG) Xcont_fund: reserve (contingency) fund balance for utility X Xins_pout: insurance payout for utility X (% annual volumetric revenue) Xins_price: insurance price for utility X (% annual volumetric revenue) Xinfra_npv: infrastructure net present value for utility ($mil) Xst_vol: total available storage volume of utility X (in MG) Xdebt_serv: debt service for utility X (usually once per year if the infrastructure is triggered; % annual volumetric revenue) Xstor_vol: total stored volume (in MGD) Xobs_ann_dem: observed annual demand for utility X (in MGD) Xproj_dem: projected annual demand for utility X (in MGD) Xpv_debt_serv: present value of debt service payments for utility X (% annual volumetric revenue) Xgross_rev: gross revenue for utility X ($mil) Acknowledgment IM3 is a multi-institutional effort led by Pacific Northwest National Laboratory and supported by the U.S. Department of Energy's Office of Science as part of research in MultiSector Dynamics, Earth and Environmental Systems Modeling Program.

Artificial Intelligence↗

A Small Temperate Lake in the 21st Century: Dynamics of Water Temperature, Ice Phenology, Dissolved Oxygen, and Chlorophyll a

It is unclear how small temperate lakes will evolve physically and biologically in the whole water column under future climate because previous modeling studies usually focused on only one or two physical or biological state variables in the surface waters. To fill this gap, we used a well-validated lake biogeochemistry model driven with different climate scenarios to predict the dynamics of ice phenology, water temperature, dissolved oxygen (DO) and chlorophyll in a small Canadian temperate lake during the 21st century, considering the influence of catchment hydrology. We find that the ice season and ice thickness of the lake would shrink substantially, resulting in a positive energy feedback between climate and the lake. Due to the reduced heat diffusion and water mixing, the dynamics of water temperature in surface waters and deep waters are considerably different, with surface waters warmed dramatically but deep waters muted to warming. The lake DO concentrations would be depleted by warming in the whole column but the controlling processes are depth dependent. The chlorophyll concentration in the lake is inertia to climate change, mainly due to the mismatch of the timings of peak solar radiation and thermal and nutrient optima. Our analysis indicates that the influence of catchment hydrology is large on the dynamics of DO, but not on other state variables we have examined. Finally, this study suggests that small temperate lakes could be sensitive to climate change but their physical and biological responses could be diverse.

54 ENVIRONMENTAL SCIENCES↗

Production of cold beams of ND{sub 3} with variable rotational state distributions by electrostatic extraction of He and Ne buffer-gas-cooled beams

The measurement of the rotational state distribution of a velocity-selected, buffer-gas-cooled beam of ND{sub 3} is described. In an apparatus recently constructed to study cold ion-molecule collisions, the ND{sub 3} beam is extracted from a cryogenically cooled buffer-gas cell using a 2.15 m long electrostatic quadrupole guide with three 90° bends. (2+1) resonance enhanced multiphoton ionization spectra of molecules exiting the guide show that beams of ND{sub 3} can be produced with rotational state populations corresponding to approximately T{sub rot} = 9–18 K, achieved through manipulation of the temperature of the buffer-gas cell (operated at 6 K or 17 K), the identity of the buffer gas (He or Ne), or the relative densities of the buffer gas and ND{sub 3}. The translational temperature of the guided ND{sub 3} is found to be similar in a 6 K helium and 17 K neon buffer-gas cell (peak kinetic energies of 6.92(0.13) K and 5.90(0.01) K, respectively). The characterization of this cold-molecule source provides an opportunity for the first experimental investigations into the rotational dependence of reaction cross sections in low temperature collisions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Data-Driven Closures and Assimilation for Stiff Multiscale Random Dynamics

Here, we introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white noise, a deterministic equation for the joint probability density function (PDF) of RODE state variables does not exist in closed form. Moreover, such an equation would require as many phase-space variables as there are states in the RODE system. To alleviate this curse of dimensionality, we instead derive exact, albeit unclosed, reduced-order PDF (RoPDF) equations for low-dimensional observables/quantities of interest. The unclosed terms take the form of state-dependent conditional expectations, which are directly estimated from data at sparse observation times. However, for systems exhibiting stiff, multiscale dynamics, data sparsity introduces regression discrepancies that compound during RoPDF evolution. This is overcome by introducing a kinetic-like defect term to the RoPDF equation, which is learned by assimilating in sparse, low-fidelity RoPDF estimates. Two assimilation methods are considered, namely nudging and deep neural networks, which are successfully tested against Monte Carlo simulations.

97 MATHEMATICS AND COMPUTING↗

Low-thrust perturbation guidance

Two perturbation guidance schemes, time-to-go guidance and minimum-distance guidance, are reexamined, in the context of a low-thrust orbit transfer problem. The two schemes, which use different techniques for indexing feedback gains, are shown to be comparable in performance. Both schemes are found to produce terminal state errors which are orders of magnitude smaller than those obtained in several previous studies. Various small modifications or enhancements of the algorithms are thought to account for a portion of the dramatic improvement in results. The problem investigated is a hypothetical earth to Mars orbit transfer, with six state variables, two control variables, and six terminal state constraints.

Bauer, T. P.↗

White dwarfs in cataclysmic variables - Low state IUE observations of V794 Aquilae, MR Serpentis, and AN Ursae Majoris

IUE low-dispersion observations of one novalike system (V794 Aql) and two AM Her systems (MR Ser and AN UMa) during low or intermediate-low accretion-rate states are reported. The decreased UV emission during these times was used to place limits on the white dwarf temperatures. When these results are added to the existing data on white dwarf temperatures, it appears that the white dwarfs in systems with normal high accretion rates and only occasional low-accretion-rate states remain hotter than the white dwarfs in systems with low average accretion rates.

Szkody, Paula↗

Strike-slip faulting, wrinkle ridges, and time variable stress states in the Coprates Region of Mars

The existence of strike-slip faults was recently documented in two locations on Mars. Two clear examples are reviewed located southeast of Valles Marineris and preliminary evidence is presented for more widespread strike-slip deformation elsewhere in Coprates. The first two examples show that strike-slip faulting occurred in a broad zone east of the Coprates Rise spanning approximately 400 km east-west by perhaps 1000 km north-south. The last example suggests that the growth of major wrinkle ridges throughout Coprates may have been influenced by horizontally directed shear stresses and that more than one generation of ridges was produced. Thus, 'compressional' deformation of ridged plains south of Valles Marineris was spatially heterogeneous and a temporal change in stress may have been involved.

Schultz, Richard A.↗

An integrated airloads-inflow model for use in rotor aeroelasticity and control analysis

The airloads-inflow model presented is ideally suited for rotor aeroelasticity and control analysis, especially where eigenvalues are sought. The model, which is derived from thin-airfoil theory with an extension that allows for other airfoil effects, is of hierarchical-lift type and may be simplified to any degree desired; the inflow is also expanded in shape functions which may be truncated to any desired texture. Both models are written in closed-form, state-variable equations without hidden states and without integrals over the wake.

Peters, David A.↗

Enabling in-time Prognostics with Surrogate Modeling through Physics-enhanced Dynamic Mode Decomposition Method

Computational models provide essential quantitative tools for assessing and predicting the health and performance of physical systems. However, high-fidelity models are rarely used in real-time operations or large optimization loops, due to their time-intensive nature. A common approach to improving computational efficiency of prognosis is to employ surrogate models. Such models can significantly decrease computation time for some accuracy loss. In this context, use of Dynamic Mode Decomposition (DMD) is proposed to generate surrogate models for lithium-ion (Li-ion) battery discharge. DMD has been suggested and used successfully in the area of fluid dynamics for over a decade, but it has not been applied to the PHM domain, where far-ahead prediction of nonlinear behavior is crucial to propagate faults or predict Remaining Useful Life (RUL). For Li-ion battery health management, the standard application of DMD using only the observable quantities of interest was unable to capture the nonlinear discharge of batteries exhibited in lab testing. The Koopman theory, however, provides a mechanism to tradeoff low dimensional nonlinear models with high-dimensional linear ones in a DMD framework, by augmenting nonlinear state variables into the system representation. In this way, DMD allows for configurable simulation accuracy dependent on the dimensionality of the Koopman operator. For battery health management, we augmented the observable variables with the hidden states of a higher-fidelity physics model to build the DMD surrogate. In comparison to a high-fidelity model, the surrogate improved computational efficiency with only a minimal loss of accuracy, and enabled long-term prognostics horizons. A generalized method for this was implemented in the prog models python package.

prognostics and health management↗

Irrigation Water Demand Sensitivity to Climate Variability across the Contiguous United States

Climate variability is an important driver of irrigation water use in many regions. Efforts to anticipate climate change impacts on future water availability can benefit from understanding how irrigation water demand has responded to these drivers to date. Here we apply satellite derived data, meteorological reanalysis, an advanced land surface model, and available state level reports to quantify irrigation demand sensitivities to temperature and precipitation across the Contiguous United States, for the period of 2002-2017. As expected, strong negative correlations are found between precipitation and irrigation withdrawals, both simulated and reported. Temperature sensitivities, however, vary by region and season, as do the interactive effects of temperature and precipitation on irrigation. Climate-induced irrigation variability is largest in transitional climate zones. These transitional zones are generally separate from the regions where rates of irrigation withdrawals are greatest, such that climate-induced variability in irrigation demand represents a water resource consideration that is distinct from chronic over pumping.

Wanshu Nie↗

Converging towards atomic and nuclear pressures (Final Report)

his report details the development of transformational tools and techniques, allowing the accurate characterization of matter at the most extreme conditions yet studied in the high energy density (HED) domain. Before this work, most experiments quantitatively mapping the nature of matter in the HED realm were performed using planar geometry, which allows for the isolation and measurement of variables in a single thermodynamic state. Such measurements include equation of state variables, optical conductivity, heat transport and more. However, due to a variety of plasma processes, such experiments are limited to below ~10 TPa (100 Mbar) pressures. To achieve higher pressures, convergent experiments are needed. Historically, convergent experiments have not been used for benchmark data because they are integral measurements. That is each part of a convergent target undergoes a time dependent wide range of states, making it difficult to accurately isolate any particular quantity for a given thermodynamic state. This effort developed innovative convergent HED platforms and techniques enabling the exploration of matter from atomic to nuclear scale pressures. This effort also performed pioneering experiments that yielded the first rigorous benchmark data at these extreme conditions. This funding award began with the overarching goal to understand the behavior of matter at extreme (atomic-to-nuclear scale) pressures. The motivation for these goals lie in the fact that every time scientists explore matter beyond the threshold of an atomic unit, there is a fundamental shift in science. The atomic unit for energy, mass, charge, length, and time have each been explored, and each time such a threshold was crossed, a new sequence of discoveries was made resulting in significant awards such as the Nobel Prize. The only unexplored atomic unit is pressure, and this effort set the course for exploring matter at and beyond such pressures. That most of the recently discovered extrasolar planets and stars, as well as matter in the late implosion stages of inertial fusion targets, have deep internal pressures at and beyond atomic pressures amplifies the importance of this effort. Much of the initial work in developing techniques to create these atomic-to-nuclear pressures already existed within the HED community, predominantly at large scale laser facilities such as the National Ignition Facility (NIF) and the Omega60 laser the University of Rochester and although these experiments were routinely performed the ability to extract information about the underlying physical states and processes remained elusive due to the complexity of the experiments, extreme scales in both time and space, and the integrated nature of all the measurements. This work built a rigorous framework so such measurements can routinely be made. This was done in part through the introduction of Bayesian inference techniques into the field of HED science. These techniques allow for the self-consistent extraction of the relevant variables and their explicit and implicit correlations, so as to make use of integrated experimental data to constrain physical models and provide accurate uncertainty bounds for the data. The techniques developed here are fully transparent and proved immediately useful providing quantitative rigorous benchmarks for physical states and processes at some of the most extreme conditions yet explored on Earth. This funding is directly or partly responsible for 7 publications in major peer-reviewed scientific journals, a doctoral thesis, 3 invited talks at major conferences, and the training of a post-doc, 2 graduate students, and 1 undergraduate student. Beyond the effort supported by this award launched the introduction of Bayesian inference into the HED physics community and helped push the usage if modern data-science techniques within the physics community at large.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Materials with periodic internal structure: Computation based on homogenization and comparison with experiment

The combination of thermal and mechanical loading expected in practice means that constitutive equations of metal matrix composites must be developed which deal with time-independent and time-dependent irreversible deformation. Also, the internal state of composites is extremely complicated which underlines the need to formulate macroscopic constitutive equations with a limited number of state variables which represent the internal state at the micro level. One available method for calculating the macro properties of composites in terms of the distribution and properties of the constituent materials is the method of homogenization whose formulation is based on the periodicity of the substructure of the composite. A homogenization procedure was developed which lends itself to the use of the finite element procedure. The efficiency of these procedures, to determine the macroscopic properties of a composite system from its constituent properties, was demonstrated utilizing an aluminum plate perforated by directionally oriented slits. The selection of this problem is based on the fact that, extensive experimental results exist, the macroscopic response is highly anisotropic, and that the slits provide very high stress gradients which severely test the effectiveness of the computational procedures. Furthermore, both elastic and plastic properties were investigated so that the application to practical systems with inelastic deformation should be able to proceed without difficulty. The effectiveness of the procedures was rigorously checked against experimental results and with the predictions of approximate calculations. Using the computational results it is illustrated how macroscopic constitutive equations can be expressed in forms of the elastic and limit load behavior.

Jansson, S.↗