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Variational Asymptotic Homogenization of Finitely Deformed Viscoelastic-Viscoplastic Composites

The objective of this paper is to develop a constitutive model for finitely deformed viscoelastic-viscoplastic materials and a micromechanics approach to homogenizing composites consisting of such materials. The development of the constitutive model involves establishing a thermodynamic framework based on finite strain theory, developing a viscoelasticity and a viscoplasticity model based on the thermodynamic framework, developing a radial return algorithm based on a classic framework, and deriving a closed-from incremental constitutive relation in the spatial configuration. The development of the micromechanics approach involves pulling-back the above constitutive relation to the material configuration, formulating a variational statement with the resulting constitutive relation, discretizing variational statement in a finite-dimensional space, and solving the discretized variational statement using an Euler–Newton predictor–corrector method. The constitutive model is calibrated via monotonic uniaxial compression tests on a polymer, and the calibrated model is validated by comparing its predictions with the cyclic test data. It is shown capable of characterizing viscoelasticity, viscoplasticity, and complex loading paths. The micromechanics approach’s capabilities are demonstrated through homogenizing a unidirectional fiber-reinforced composite, subjected to uniaxial, biaxial, and shear loading, at different strain rates. It is demonstrated to be capable of handling rate dependence and complex loading paths. The present framework can be further improved by implementing more sophisticated viscoelasticity and viscoplasticity models in future work.

Finite element analysis↗

NASA NTRS1994

Correlation of finite element free vibration predictions using random vibration test data

Finite element analysis is regularly used during the engineering cycle of mechanical systems to predict the response to static, thermal, and dynamic loads. The finite element model (FEM) used to represent the system is often correlated with physical test results to determine the validity of analytical results provided. Results from dynamic testing provide one means for performing this correlation. One of the most common methods of measuring accuracy is by classical modal testing, whereby vibratory mode shapes are compared to mode shapes provided by finite element analysis. The degree of correlation between the test and analytical mode shapes can be shown mathematically using the cross orthogonality check. A great deal of time and effort can be exhausted in generating the set of test acquired mode shapes needed for the cross orthogonality check. In most situations response data from vibration tests are digitally processed to generate the mode shapes from a combination of modal parameters, forcing functions, and recorded response data. An alternate method is proposed in which the same correlation of analytical and test acquired mode shapes can be achieved without conducting the modal survey. Instead a procedure is detailed in which a minimum of test information, specifically the acceleration response data from a random vibration test, is used to generate a set of equivalent local accelerations to be applied to the reduced analytical model at discrete points corresponding to the test measurement locations. The static solution of the analytical model then produces a set of deformations that once normalized can be used to represent the test acquired mode shapes in the cross orthogonality relation. The method proposed has been shown to provide accurate results for both a simple analytical model as well as a complex space flight structure.

Chambers, Jeffrey A.↗

NASA NTRS2010

Modeling Optical Properties of Mineral Aerosol Particles by Using Nonsymmetric Hexahedra

We explore the use of nonsymmetric geometries to simulate the single-scattering properties of airborne dust particles with complicated morphologies. Specifically, the shapes of irregular dust particles are assumed to be nonsymmetric hexahedra defined by using the Monte Carlo method. A combination of the discrete dipole approximation method and an improved geometric optics method is employed to compute the single-scattering properties of dust particles for size parameters ranging from 0.5 to 3000. The primary optical effect of eliminating the geometric symmetry of regular hexahedra is to smooth the scattering features in the phase function and to decrease the backscatter. The optical properties of the nonsymmetric hexahedra are used to mimic the laboratory measurements. It is demonstrated that a relatively close agreement can be achieved by using only one shape of nonsymmetric hexahedra. The agreement between the theoretical results and their measurement counterparts can be further improved by using a mixture of nonsymmetric hexahedra. It is also shown that the hexahedron model is much more appropriate than the "equivalent sphere" model for simulating the optical properties of dust particles, particularly, in the case of the elements of the phase matrix that associated with the polarization state of scattered light.

Bi, Lei↗

NASA NTRS1995

MODTRAN3: An update and recent validations against airborne high resolution interferometer measurements

MODTRAN, the Moderate Resolution Atmospheric Radiance and Transmittance Model, encompasses all the capabilities of LOWTRAN 7, the widely used 20 cm(exp -1) resolution radiance code, but incorporates a much more sensitive molecular band model with 2 cm(exp -1) resolution. MODTRAN contains many important elements that other band model based radiative transfer codes do not incorporate. It shares with FASCODE: spherical geometry, single and multiple scattering default atmospheric profile descriptors (gases, aerosols, clouds, fogs, and rain), and molecular continua (H2O, CO2, O3, O2, N2). In addition, it can calculate the solar/lunar direct and scattered radiation. MODTRAN3 was released to the general public in November 1994. It has several important features that the previous version, MODTRAN2, does not have. Chloro-fluorocarbon (CFC) and related heavy molecules (whose spectroscopic properties first appear on the HITRAN92 data base as temperature-dependent cross sections) have been incorporated into pseudo-band models, with provision for using both default and user supplied profiles. The addition of SO2 and O2 in the UV, along with upgraded ozone Chappuis bands in the visible is also part of MODTRAN3. An improved multiple scattering algorithm, the DIScrete Ordinate Radiative Transfer (DISORT) has also been incorporated into MODTRAN3. MODTRAN is very fast: simple timing runs of MODTRAN3 vs. FASCOD3 show an improvement of more than a factor of 100 for a typical 500 cm(exp -1) spectral interval and comparable vertical layering. Speed is an important consideration in heating/cooling rates calculations, where a large number of radiative transfer calculations are needed. The MODTRAN3 used in this study is based on HITRAN92, but as mentioned, above, it will be upgraded to HITRAN94 upon its release at the end of 1994. MODTRAN has been adopted by: some researchers in the AVIRIS program as one radiative transfer code to derive surface reflectance from AVIRIS measurements. The accuracy of the code is very important because any errors in the radiative transfer calculation will directly translate into errors in the derived surface reflectance. In this paper, the new solar irradiance calculated by Kurucz, which is adopted in MODTRAN3, will be presented. Recent validations of MODTRAN3 with airborne high resolution interferometer measurements over ocean will be discussed. Good agreeement between model calculations and measurements was achieved.

Anderson, Gail P.↗

NASA NTRS2000

Fast Particle Methods for Multiscale Phenomena Simulations

We are developing particle methods oriented at improving computational modeling capabilities of multiscale physical phenomena in : (i) high Reynolds number unsteady vortical flows, (ii) particle laden and interfacial flows, (iii)molecular dynamics studies of nanoscale droplets and studies of the structure, functions, and evolution of the earliest living cell. The unifying computational approach involves particle methods implemented in parallel computer architectures. The inherent adaptivity, robustness and efficiency of particle methods makes them a multidisciplinary computational tool capable of bridging the gap of micro-scale and continuum flow simulations. Using efficient tree data structures, multipole expansion algorithms, and improved particle-grid interpolation, particle methods allow for simulations using millions of computational elements, making possible the resolution of a wide range of length and time scales of these important physical phenomena.The current challenges in these simulations are in : [i] the proper formulation of particle methods in the molecular and continuous level for the discretization of the governing equations [ii] the resolution of the wide range of time and length scales governing the phenomena under investigation. [iii] the minimization of numerical artifacts that may interfere with the physics of the systems under consideration. [iv] the parallelization of processes such as tree traversal and grid-particle interpolations We are conducting simulations using vortex methods, molecular dynamics and smooth particle hydrodynamics, exploiting their unifying concepts such as : the solution of the N-body problem in parallel computers, highly accurate particle-particle and grid-particle interpolations, parallel FFT's and the formulation of processes such as diffusion in the context of particle methods. This approach enables us to transcend among seemingly unrelated areas of research.

Koumoutsakos, P.↗

DOE OSTI2023

On Practical Aspects of Variational Consistency in Contact Dynamics

Usage of contact mechanics methodologies is a pervasive modeling requirement in dynamic simulations. While for some trivial problems, solutions taken from analytical geometry are available, use of a finite element framework is common to achieve formulation generality. This work explores two dynamic contact formulations: one based on the traditional node-to-segment (NTS) approach, and a variationally consistent segment-to-segment (STS) mortar formulation. The NTS formulation employed here enforces the constraints kinematically (i.e., the interpenetration is enforced to the solver tolerance), whereas the mortar approach uses Lagrange multipliers to enforce the contact constraints. Both approaches are implemented in the open-source finite element framework Multiphysics Object-Oriented Simulation Environment (MOOSE). The results highlight two relevant contact-interface-related dynamic phenomena in finite element simulations. First, stabilization of contact constraints is discussed, taking into account the evolution of the total energy in a benchmark problem. Second, the influence of finite element discretization on both of the aforementioned contact formulations is analyzed by exercising a large-deformation example with continuous relative sliding. Variationally consistent contact approaches such as the mortar formulation lead to improved energy preservation and avoid spurious excitation of the system's frequencies. This is especially relevant in settings where inertia and vibrations are of importance.

42 ENGINEERING↗

DOE OSTI2024

Exploring the Regimes of Particle Behavior upon Impact via the Discrete Element Method

Discrete element method simulations are conducted to probe the various regimes of post-impact behavior of particles with solid surfaces. The impacting particles are described as spherical agglomerates consisting of smaller constituent (or primary) particles held together via surface adhesion. Under the influence of a wide range of impact velocities and particle surface energies, five distinct behavioral regimes—rebounding, vibration, fragmentation, pancaking, and shattering—are identified, and force transmission patterns are linked to post-impact behavior. In the rebounding regime, the coefficient of restitution decreases linearly as impact velocity increases and the particle agglomerate experiences compaction. In the fragmentation regime, rebound velocity generally decreases with increasing fragment size. The rebound velocity of fragments decreases with time except for the smallest fragments, which can increase in velocity due to collisions with other fragments of high velocity. Particle breakage in the pancaking regime does not follow common mechanistic models of breakage.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Improving Time Step Convergence in an Atmosphere Model With Simplified Physics: The Impacts of Closure Assumption and Process Coupling

Convergence testing is a common practice in the development of dynamical cores of atmospheric models but is not as often exercised for the parameterization of sub-grid physics. An earlier study revealed that the stratiform cloud parameterizations in several predecessors of the Energy Exascale Earth System Model (E3SM) showed strong time-step sensitivity and slower-than-expected convergence when the model's time step was systematically refined. In this work, a simplified atmosphere model is configured that consists of the spectral-element dynamical core of the E3SM atmosphere model coupled with a large-scale condensation parameterization based on commonly used assumptions. This simplified model also resembles E3SM and its predecessors in the numerical implementation of process coupling and shows poor time-step convergence in short ensemble tests. We present a formal error analysis to reveal the expected time-step convergence rate and the conditions for obtaining such convergence. Numerical experiments are conducted to investigate the root causes of convergence problems. We show that revisions in the process coupling and closure assumption help to improve convergence in short simulations using the simplified model; the same revisions applied to a full atmosphere model lead to significant changes in the simulated long-term climate. This work demonstrates that causes of convergence issues in atmospheric simulations can be understood by combining analyses from physical and mathematical perspectives. Addressing convergence issues can help to obtain a discrete model that is more consistent with the intended representation of the physical phenomena.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Multiscale simulations for multi-continuum Richards equations

In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pressure head), and these equations are coupled to one another by transfer terms. On its own, Richards equation is already a nonlinear partial differential equation, and it is exceedingly difficult to solve numerically due to the extra nonlinear dependencies involving the soil water. To deal with multiple scales, our strategy is that starting from a microscopic scale, we upscale the coupled system of dual-continuum Richards equations via homogenization by the two-scale asymptotic expansion, to obtain a homogenized system, at an intermediate scale (level). Based on a hierarchical approach, the homogenization’s effective coefficients are computed through solving the arising cell problems. Furthermore, to tackle the nonlinearity, after time discretization, we use Picard iteration procedure for linearization of the homogenized Richards equations. At each Picard iteration, some degree of multiscale still remains from the intermediate level, so we utilize the generalized multiscale finite element method (GMsFEM) combining with a multi-continuum approach, to upscale the homogenized system to a macroscopic (coarse-grid) level. This scheme involves building uncoupled and coupled multiscale basis functions, which are used not only to construct coarse-grid solution approximation with high accuracy but also (with the coupled multiscale basis) to capture the interactions among continua. These prospects and convergence are demonstrated by several numerical results for the proposed method.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2016

Simulation of Satellite, Airborne and Terrestrial LiDAR with DART (I):Waveform Simulation with Quasi-Monte Carlo Ray Tracing

Light Detection And Ranging (LiDAR) provides unique data on the 3-D structure of atmosphere constituents and the Earth's surface. Simulating LiDAR returns for different laser technologies and Earth scenes is fundamental for evaluating and interpreting signal and noise in LiDAR data. Different types of models are capable of simulating LiDAR waveforms of Earth surfaces. Semi-empirical and geometric models can be imprecise because they rely on simplified simulations of Earth surfaces and light interaction mechanisms. On the other hand, Monte Carlo ray tracing (MCRT) models are potentially accurate but require long computational time. Here, we present a new LiDAR waveform simulation tool that is based on the introduction of a quasi-Monte Carlo ray tracing approach in the Discrete Anisotropic Radiative Transfer (DART) model. Two new approaches, the so-called "box method" and "Ray Carlo method", are implemented to provide robust and accurate simulations of LiDAR waveforms for any landscape, atmosphere and LiDAR sensor configuration (view direction, footprint size, pulse characteristics, etc.). The box method accelerates the selection of the scattering direction of a photon in the presence of scatterers with non-invertible phase function. The Ray Carlo method brings traditional ray-tracking into MCRT simulation, which makes computational time independent of LiDAR field of view (FOV) and reception solid angle. Both methods are fast enough for simulating multi-pulse acquisition. Sensitivity studies with various landscapes and atmosphere constituents are presented, and the simulated LiDAR signals compare favorably with their associated reflectance images and Laser Vegetation Imaging Sensor (LVIS) waveforms. The LiDAR module is fully integrated into DART, enabling more detailed simulations of LiDAR sensitivity to specific scene elements (e.g., atmospheric aerosols, leaf area, branches, or topography) and sensor configuration for airborne or satellite LiDAR sensors.

Gastellu-Etchegorry, Jean-Philippe↗

DOE OSTI2021

The interpenetration polymer network in a cement paste–waterborne epoxy system

The formation of the interpenetrating polymer network (IPN) structure within the cement-polymer system has been revealed by experiments from 2 dimensional to 3-dimensional scales. However, the microstructure design and performance prediction of IPN as a function of specific C-S-H/polymer components or ingredients' parameters e.g. water to cement ratios (w/c), polymer to cement ratios (p/c), monomer components, degree of polymerization (DP), etc. is by far not available. Here we developed a mesoscale model for IPN visualization based on the Flory-Huggins interaction theory which was applied to cement science for the first time. All the ingredients in the micro-structure were considered as soluble beads with rational sizes based on their properties obtained by molecular dynamic methods. The interaction parameters of each bead were then determined based on their element ratios and chemical backbones. The model was validated with the waterborne epoxy-cement material (WECM) in which a novel waterborne epoxy resin (WEP) was prepared and impregnated. The verification results on the 2D-3D scale show that the developed model predicts the WECM's IPN structures by rule and line concerning DP, w/c, and p/c in the mixture. The C-S-H beads were progressively scaled in size which alters the C-S-H texture to have completely different dissolution characteristics. Beads of diameter ~6 Å are more unstable and soluble which enable them to form a continuous phase in water or a composite structure with WEP. In contrast, beads with diameters larger than 10 Å have different properties with stronger nucleation effects. The results also suggest the impregnation content of WEP in cement-based material should be limited to 10% vol. to prevent the polymer IPN from decomposing into discrete clusters. The application of Flory-Huggins theory in cement-based composites demonstrates great potential in performance prediction and microstructure design.

36 MATERIALS SCIENCE↗

NASA NTRS1988

Autocorrelation and regularization in digital images. I - Basic theory

Spatial structure occurs in remotely sensed images when the imaged scenes contain discrete objects that are identifiable in that their spectral properties are more homogeneous within than between them and other scene elements. The spatial structure introduced is manifest in statistical measures such as the autocovariance function and variogram associated with the scene, and it is possible to formulate these measures explicitly for scenes composed of simple objects of regular shapes. Digital images result from sensing scenes by an instrument with an associated point spread function (PSF). Since there is averaging over the PSF, the effect, termed regularization, induced in the image data by the instrument will influence the observable autocovariance and variogram functions of the image data. It is shown how the autocovariance or variogram of an image is a composition of the underlying scene covariance convolved with an overlap function, which is itself a convolution of the PSF. The functional form of this relationship provides an analytic basis for scene inference and eventual inversion of scene model parameters from image data.

Jupp, David L. B.↗

NASA NTRS1992

Boundary formulations for shape sensitivity of temperature dependent conductivity problems

Used in concert with the Kirchhoff transformation, implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities. For problems with specified temperature and heat flux boundary conditions, a linear problem results for both the analysis and sensitivity analysis. In problems with either convection or radiation boundary conditions, a nonlinear problem is generated. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems is presented that have closed form solutions. Exact analytical expressions for the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation.

Kane, James H.↗

NASA NTRS2005

Business Intelligence Modeling in Launch Operations

This technology project is to advance an integrated Planning and Management Simulation Model for evaluation of risks, costs, and reliability of launch systems from Earth to Orbit for Space Exploration. The approach builds on research done in the NASA ARC/KSC developed Virtual Test Bed (VTB) to integrate architectural, operations process, and mission simulations for the purpose of evaluating enterprise level strategies to reduce cost, improve systems operability, and reduce mission risks. The objectives are to understand the interdependency of architecture and process on recurring launch cost of operations, provide management a tool for assessing systems safety and dependability versus cost, and leverage lessons learned and empirical models from Shuttle and International Space Station to validate models applied to Exploration. The systems-of-systems concept is built to balance the conflicting objectives of safety, reliability, and process strategy in order to achieve long term sustainability. A planning and analysis test bed is needed for evaluation of enterprise level options and strategies for transit and launch systems as well as surface and orbital systems. This environment can also support agency simulation .based acquisition process objectives. The technology development approach is based on the collaborative effort set forth in the VTB's integrating operations. process models, systems and environment models, and cost models as a comprehensive disciplined enterprise analysis environment. Significant emphasis is being placed on adapting root cause from existing Shuttle operations to exploration. Technical challenges include cost model validation, integration of parametric models with discrete event process and systems simulations. and large-scale simulation integration. The enterprise architecture is required for coherent integration of systems models. It will also require a plan for evolution over the life of the program. The proposed technology will produce long-term benefits in support of the NASA objectives for simulation based acquisition, will improve the ability to assess architectural options verses safety/risk for future exploration systems, and will facilitate incorporation of operability as a systems design consideration, reducing overall life cycle cost for future systems. The future of business intelligence of space exploration will focus on the intelligent system-of-systems real-time enterprise. In present business intelligence, a number of technologies that are most relevant to space exploration are experiencing the greatest change. Emerging patterns of set of processes rather than organizational units leading to end-to-end automation is becoming a major objective of enterprise information technology. The cost element is a leading factor of future exploration systems.

Bardina, Jorge E.↗

DOE OSTI2022

A multi-resolution approach to hydraulic fracture simulation

Abstract We present a multi-resolution approach for constructing model-based simulations of hydraulic fracturing, wherein flow through porous media is coupled with fluid-driven fracture. The approach consists of a hybrid scheme that couples a discrete crack representation in a global domain to a phase-field representation in a local subdomain near the crack tip. The multi-resolution approach addresses issues such as the computational expense of accurate hydraulic fracture simulations and the difficulties associated with reconstructing crack apertures from diffuse fracture representations. In the global domain, a coupled system of equations for displacements and pressures is considered. The crack geometry is assumed to be fixed and the displacement field is enriched with discontinuous functions. Around the crack tips in the local subdomains, phase-field sub-problems are instantiated on the fly to propagate fractures in arbitrary, mesh independent directions. The governing equations and fields in the global and local domains are approximated using a combination of finite-volume and finite element discretizations. The efficacy of the method is illustrated through various benchmark problems in hydraulic fracturing, as well as a new study of fluid-driven crack growth around a stiff inclusion.

58 GEOSCIENCES↗

NASA NTRS2006

Simulations of Sea-Ice Dynamics Using the Material-Point Method

In recent years, the availability of large volumes of recorded ice motion derived from high-resolution SAR data has provided an amazingly detailed look at the deformation of the ice cover. The deformation is dominated by the appearance of linear kinematic features that have been associated with the presence of leads. These remarkable data put us in a position to begin detailed evaluation of current coupled mechanical and thermodynamic models of sea ice. This presentation will describe the material point method (MPM) for solving these model equations. MPM is a numerical method for continuum mechanics that combines the best aspects of Lagrangian and Eulerian discretizations. The material points provide a Lagrangian description of the ice that models convection naturally. Thus, properties such as ice thickness and compactness are computed in a Lagrangian frame and do not suffer from errors associated with Eulerian advection schemes, such as artificial diffusion, dispersion, or oscillations near discontinuities. This desirable property is illustrated by solving transport of ice in uniform, rotational and convergent velocity fields. Moreover, the ice geometry is represented by unconnected material points rather than a grid. This representation facilitates modeling the large deformations observed in the Arctic, as well as localized deformation along leads, and admits a sharp representation of the ice edge. MPM also easily allows the use of any ice constitutive model. The versatility of MPM is demonstrated by using two constitutive models for simulations of wind-driven ice. The first model is a standard viscous-plastic model with two thickness categories. The MPM solution to the viscous-plastic model agrees with previously published results using finite elements. The second model is a new elastic-decohesive model that explicitly represents leads. The model includes a mechanism to initiate leads, and to predict their orientation and width. The elastic-decohesion model can provide similar overall deformation as the viscous-plastic model; however, explicit regions of opening and shear are predicted. Furthermore, the efficiency of MPM with the elastic-decohesive model is competitive with the current best methods for sea ice dynamics. Simulations will also be presented for an area of the Beaufort Sea, where predictions can be validated against satellite observations of the Arctic.

Sulsky, D.↗

DOE OSTI2020

Advanced Newton methods for geodynamical models of Stokes flow with viscoplastic rheologies

Strain localization and resulting plasticity and failure play an important role in the evolution of the lithosphere. These phenomena are commonly modeled by Stokes flows with viscoplastic rheologies. The nonlinearities of these rheologies make the numerical solution of the resulting systems challenging, and iterative methods often converge slowly or not at all. Yet accurate solutions are critical for representing the physics. Moreover, for some rheology laws, aspects of solvability are still unknown. We study a basic but representative viscoplastic rheology law. The law involves a yield stress that is independent of the dynamic pressure, referred to as von Mises yield criterion. Two commonly used variants, perfect/ideal and composite viscoplasticity, are compared. We derive both variants from energy minimization principles, and we use this perspective to argue when solutions are unique. We propose a new stress-velocity Newton solution algorithm that treats the stress as an independent variable during the Newton linearization but requires solution only of Stokes systems that are of the usual velocity-pressure form. To study different solution algorithms, we implement 2-D and 3-D finite element discretizations, and we generate Stokes problems with up to 7 orders of magnitude viscosity contrasts, in which compression or tension results in significant nonlinear localization effects. Comparing the performance of the proposed Newton method with the standard Newton method and the Picard fixed-point method, we observe a significant reduction in the number of iterations and improved stability with respect to problem nonlinearity, mesh refinement, and the polynomial order of the discretization.

Rudi, Johann↗

DOE OSTI2020

Estimation of elastic properties of an additively manufactured lattice using resonant ultrasound spectroscopy

Development of improved approaches in the characterization of additively manufactured structures continues to be a topic of interest for the advanced manufacturing community. This article will investigate an approach using resonant ultrasound spectroscopy (RUS) to determine the effective elastic constants of an orthotropic lattice structure. The evaluation is performed on a cube shaped 316 L stainless steel test specimen, constructed using selective laser melting techniques. The approach uses RUS techniques in conjunction with the assumption that in the frequency regime of interest, the wavelength of the diagnostic ultrasound is greater than the discrete structural features of the unit cell of the lattice; thus, the AM structure can be treated as an anisotropic continuum with effective material properties and symmetry inherited from the unit cell. The RUS analysis estimates the nine elastic coefficients associated with orthotropic sample symmetry, which, in turn, are used to determine the elastic moduli and Poisson ratios. Current results show good agreement between experiments and modeled data. Comparisons to published results are also in good agreement, indicating the potential applicability of this characterization technique for estimating the linear elastic properties of innovative additive manufactured metal lattice structures.

36 MATERIALS SCIENCE↗