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At least 523 records · Page 29

Seeing in with X-rays: 4D Strain and Thermometry Measurements for Thermal-Mechanical Testing

Understanding temperature-dependent material decomposition and structural deformation induced by combined thermal-mechanical environments is critical for safety qualification of hardware under accident scenarios. Seeing in with X-rays elucidated the physics necessary to develop X-ray strain and thermometry diagnostics for use in optically opaque environments. Two parallel thermometry schemes were explored: X-ray fluorescence and X-ray diffraction of inorganic doped ceramics– colloquially known as thermographic phosphors. Two parallel surface strain techniques–Path-Integrated Digital Image Correlation and Frequency Multiplexed Digital Image Correlation–were demonstrated. Finally, preliminary demonstration of time-resolved digital volume correlation was performed by taking advantage of limited view reconstruction techniques. Additionally, research into blended ceramic-metal coatings was critical to generating intrinsic thermographic patterns for the future combination of X-ray strain and thermometry measurements.

36 MATERIALS SCIENCE↗

A new coupled multiphase flow–finite strain deformation–fault slip framework for induced seismicity

Production of hydrocarbons and water from subsurface reservoirs are known to cause permanent deformation of the reservoir and seismicity along faults both of which are detrimental to sustainable development of natural resources. Most of the prior studies on understanding fluid flow-induced plasticity and seismicity have focused on one or the other phenomenon due to the numerical difficulty associated with simultaneous modeling of the two failure phenomena because stress and deformation evolve non-linearly in both plasticity and seismicity. However, in reservoirs undergoing long-term production, plastic failure can alter the stress paths of points on a fault such that the onset, location, and magnitude of actual seismic events can no longer be predicted by a poroelastic simulation due to inaccurate stress and deformation history. We present a computational framework for coupled multiphase flow, finite strain poroplastic deformation, and dynamic fault slip and use it to understand the impact of plastic deformation on the onset, location, and magnitude of induced fault slip events. We evaluate the impact of plasticity on reservoir pressure, deformation, induced stress, and fault slip by comparing infinitesimal strain elastic and finite strain poro-elastoplastic models. For real-world applications, we consider different scenarios where the reservoir is either mechanically weaker or stronger than the caprock. We analyze the stress evolution as a function of the change in reservoir pressure to understand the role of contrast in reservoir and caprock elastic moduli on geomechanical stability. The results show that the poroplastic reservoir exhibits larger vertical deformation and delayed slip than the poroelastic reservoir after the same amount of oil production. For the same amount of pressure drop, a reservoir with a smaller modulus than the caprock displays a larger vertical displacement and an earlier onset of both plastic failure and fault slip. For a reservoir with a larger modulus than the caprock, vertical displacement is larger on the reservoir top boundary and smaller on the ground surface, and a higher pressure drop is needed to induce plastic failure and fault slip.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mitigation of spall fracture by evolving porosity

Ductile materials subject to impact loading conditions can undergo spall fracture when an incoming compressive stress wave reflects off interfaces and free surfaces as a tensile stress wave. Experimental observations suggest that in ductile materials, spall fracture is driven by the evolution of porosity. However, the presence of initial porosity in ductile materials also introduces plastic compressibility, which can attenuate the incoming compressive stress wave and, as a result, reduce the amplitude of the reflected tensile stress wave. This, in turn, can mitigate or delay spall fracture. In this work, we report on finite deformation finite element calculations that analyze the response of porous ductile materials subjected to impact loading conditions. Two sets of calculations are carried out, in the first set the material contains initial porosity values ranging from 0% to 5% while in the second set the material also undergoes stress-controlled porosity nucleation. Both sets of calculations are carried out for a wide range of imposed impact velocities. Here, our results show that porosity in ductile materials can, under certain circumstances, mitigate spall fracture by attenuating stress waves. Results correlating the effects of impact velocity, initial porosity, and porosity nucleation on spall fracture are presented and the underlying mechanisms are discussed.

36 MATERIALS SCIENCE↗

Melting and Ejecta Produced by High Velocity Microparticle Impacts of Steel on Tin

At sufficiently high velocities, a microparticle impacting a metal substrate can cause ejection of material from the substrate and impact-induced melting, both of which can result in erosion. Here, we directly image the impact of individual hard steel microparticles on soft tin substrates, at controlled impact velocities in the range of ~100 to 1000 m/s. By using scanning electron and laser scanning confocal microscopy, we characterize the surface morphology, depth, and volume of each impact crater. We observe a gradual onset of impact-induced melting in the craters, as well as the production of increasing amounts of ejecta from the target metal. By comparing measurements of impact and rebound velocity to an elastic-plastic model, we observe that at a high enough impact velocity, melting and ejection begin to consume additional kinetic energy beyond that expected by plastic deformation of the target material alone. By calculating the excess energy dissipation using this elastic-plastic model, we show that although this divergent behavior is associated with the onset of melting, the majority of the ejected volume must be solid rather than liquid.

Mechanics↗

Structure and Mechanical Adaptability of a Modern Elasmoid Fish Scale from the Common Carp

The carp (Cyprinus carpio) has typical elasmoid scales commonly found on teleosts. They provide protection while retaining flexibility and maneuverability of the fish. The exterior surface of the scale consists of an ultrathin discontinuous mineral layer on top of mineralized woven collagen fibrils. The underlying foundation is composed of two collagenous components. The major one consists of a single-twisted ‘‘Bouligand’’ structure with a twisting angle of 36°. A secondary ‘‘sheet-like’’ structure, formed by thinner collagen fibrils oriented along the thickness direction, acts to increase the integrity of the scale. In this work, we identify the deformation and failure mechanisms of the carp scale, revealing slight tensile anisotropy. Using in situ small-angle X-ray scattering during tensile testing, the toughening mechanisms of the scale, including the adaptive structural reorientation of lamellae as well as fibrillar sliding and elastic deformation, are quantified and compared with those of other fish scales.

59 BASIC BIOLOGICAL SCIENCES↗

Properties of the neutron star crust: Quantifying and correlating uncertainties with improved nuclear physics

A compressible liquid-drop model (CLDM) is used to correlate uncertainties associated with the properties of the neutron star (NS) crust with theoretical estimates of the uncertainties associated with the equation of state (EOS) of homogeneous neutron and nuclear matter. For the latter, we employ recent calculations based on Hamiltonians constructed using chiral effective-field theory (χEFT). Fits to experimental nuclear masses are employed to constrain the CLDM further, and we find that they disfavor some of the χEFT Hamiltonians. The CLDM allows us to study the complex interplay between bulk, surface, curvature, and Coulomb contributions, and their impact on the NS crust. It also reveals how the curvature energy alters the correlation between the surface energy and the bulk symmetry energy. Here our analysis quantifies how the uncertainties associated with the EOS of homogeneous matter implies significant uncertainties for the composition of the crust, its proton fraction, and the volume fraction occupied by nuclei. We find that the finite-size effects impact the crust composition but have a negligible effect on the net isospin asymmetry of matter. The isospin asymmetry is largely determined by the bulk properties and the isospin dependence of the surface energy. The most significant uncertainties associated with matter properties in the densest regions of the crust, the precise location of the crust-core transition, are found to be strongly correlated with uncertainties associated with the Hamiltonians. By adopting a unified model to describe the crust and the core of NSs, we tighten the correlation between their global properties such as their mass-radius relationship, moment of inertia, crust thickness, and tidal deformability with uncertainties associated with the nuclear Hamiltonians.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A comparison of surrogate constitutive models for viscoplastic creep simulation of HT-9 steel

Mechanistic microstructure-informed constitutive models for the mechanical response of polycrystals are a cornerstone of computational materials science. However, as these models become increasingly more complex – often involving coupled differential equations describing the effect of specific deformation modes – their associated computational costs can become prohibitive, particularly in optimization or uncertainty quantification tasks that require numerous model evaluations. To address this challenge, surrogate constitutive models that balance accuracy and computational efficiency are highly desirable. Data-driven surrogate models, that learn the constitutive relation directly from data, have emerged as a promising solution. In this work, we develop two local surrogate models for the viscoplastic response of a steel: a piecewise response surface method and a mixture of experts model. These surrogates are designed to adapt to complex material behavior, which may vary with material parameters or operating conditions. The surrogate constitutive models are applied to creep simulations of HT-9 steel, an alloy of considerable interest to the nuclear energy sector due to its high tolerance to radiation damage, using training data generated from viscoplastic self-consistent (VPSC) simulations. In conclusion, we define a set of test metrics to numerically assess the accuracy of our surrogate models for predicting viscoplastic material behavior, and show that the mixture of experts model outperforms the piecewise response surface method in terms of accuracy.

36 MATERIALS SCIENCE↗

Modeling low cycle fatigue (LCF) of additively manufactured Hastelloy X using An accelerated crystal plasticity fatigue damage model

This paper presents a microstructure-based model for low cycle fatigue (LCF) behavior and life of Nickel-based alloy Hastelloy X manufactured using laser-powder bed fusion (L-PBF) additive manufacturing (AM). AM Hastelloy X, a solution-strengthened alloy, is tested at elevated temperature under fully reversed LCF conditions at different strain levels. A generalized plane strain finite element model is generated from electron backscatter diffraction (EBSD) characterization. The constitutive behavior of the material under fatigue is modeled using crystal plasticity and calibrated with both monotonic tensile and cyclic stress–strain data. The fatigue micro-crack initiation and propagation in the microstructure is modeled using a modified Chaboche fatigue damage model. An embedded boundary condition with a homogenous medium is used to apply the cyclic deformation and prevent numerically introduced over-constraints during fatigue simulation. A ‘cycle-jump’ method is used to accelerate the fatigue simulation and reduce the computational cost. The simulation results are compared to LCF experiments, showing satisfactory matches in cyclic stress behavior and number of cycles to macro-crack initiation for all applied strain ranges. In addition, the model illustrates the potential for quantifying microscale fatigue life impacting factors such as microstructure and surface roughness, which is needed to accurately quantify the reliability of AM components in service.

36 MATERIALS SCIENCE↗

Critical length scales for chemical heterogeneity at Cu/Nb 3D interfaces by atom probe tomography

Cu/Nb nanocomposites containing sharp, two-dimensional (2D) interfaces have outstanding strength but limited deformability. In contrast, Cu/Nb with three dimensional (3D) biphase interfaces exhibiting crystallographic, topological, and chemical variations in all spatial dimensions overcomes this limitation by simultaneously enhancing material strength and deformability. Here, while structural characterization of 3D interfaces has been performed to understand their mechanical behavior, three dimensional chemical characterization of such interfaces is lacking. In this work we quantify the local chemistry of 3D interfaces in Cu/Nb nanocomposites using atom probe tomography (APT). Our analysis demonstrates chemical heterogeneities along all spatial dimensions in 3D interfaces, establishes the length scale of such features, and quantifies the morphology of 3D interfaces. 3D interface heterogeneities form by surface diffusion during physical vapor deposition (PVD), suggesting that deposition parameters can be used to control interface structure and provide unique ways to explore processing-structure-property relationships in interface-dominated nanocomposites.

36 MATERIALS SCIENCE↗

Molecular Dynamics Simulations of Calcite Fracture in Water

Calcite (CaCO 3 ) is one of the most common minerals in geologic and engineered systems. It is often in contact with aqueous solutions, causing chemically assisted fracture that is critical to understanding the stability of subsurface systems and manmade structures. Calcite fracture was evaluated with reactive molecular dynamics simulations, including the impacts of crack tip geometry (notch), the presence of water, and surface hydroxyl groups. Chemo-mechanical weakening was assessed by comparing the loads where fracture began to propagate. Our analyses show that in the presence of a notch, the load at which crack growth begins is lower, compared to the effect of water or surface hydroxyls. Additionally, the breaking of two adjacent Ca–O bonds is the kinetic limitation for crack initiation, since transiently broken bonds can reform, not resulting in crack growth. In aqueous environments, fresh (not hydroxylated) calcite surfaces exhibited water strengthening. Manual addition of H + and/or OH – species on the (104) calcite surface resulted in chemo-mechanical weakening of calcite by 9%. Achieving full hydroxylation of the calcite surface was thermodynamically and kinetically limited, with only 0.17–0.01 OH/nm 2 surface hydroxylation observed on the (104) surface at the end of the simulations. In conclusion, the limited reactivity of pure water with the calcite surface restricts the chemo-mechanical effects and suggests that reactions between physiosorbed water and localized structural defects may be dominating the chemo-mechanical process in the studies where water weakening has been reported.

Calcite↗

DECOVALEX-2023: Task F1 Final Report

DECOVALEX-2023 Task F is a comparison of models and methods for post-closure performance assessment (PA) of a deep geologic repository for radioactive waste. The general aims of Task F are to build confidence in the models, methods, and software used for PA and to stimulate additional research and development in PA methodologies. The task objectives are to motivate development of PA modelling skills and capabilities, to examine the influence of model choices on calculated repository performance, and to compare the uncertainties introduced by model choices to other sources of uncertainty. Task F involves no actual experiment or site. It is a PA modelling exercise that requires the conceptual development of hypothetical repository designs and geologic settings. Because three of the teams were interested in salt and the rest of the teams were interested in crystalline rock, Task F was split into two branches: Task F1 for crystalline rock and Task F2 for salt. This report is for Task F1, crystalline rock. Teams from seven countries (Canada, Czech Republic, Germany, Korea, Sweden, Taiwan, and United States) participated in Task F1. The teams worked together to define the features, events, and processes of the reference case repository and established a set of performance measures. In addition, they defined a set of benchmark problems designed to test and compare modelling capabilities for fracture flow and transport at different scales. The repository design and benchmark problems are documented in a Task Specification that evolved over time as the group honed the specifications. The benchmark problems verified that each team can aptly model flow and transport in fractured media in 1-, 2-, and 3-dimensions. Two general approaches were used for the 3-dimensional benchmarks: discrete fracture network (DFN) and equivalent continuous porous medium (ECPM). DFN modelling involves explicit meshing of each fracture while ECPM modelling aims to capture the effective porosity and directional permeability of each cell in a space-filling mesh as affected by intersecting fractures. In some models, a combination of the two is used, i.e., DFN for large known fractures and ECPM for the rest of the domain. Transport is solved by using either the advection-dispersion equation or particle tracking. Although some variation is observed among model breakthrough curves in the benchmark problems, there is strong agreement in breakthrough behaviour up to at least the 75 th percentile for all benchmarks. At the 90 th percentile, breakthrough results show larger differences, suggesting several models retain substantially higher fractions of tracer in regions of slower moving water. In addition to the flow and transport benchmarks, several teams completed the source term benchmark, verifying capabilities for modelling radionuclide decay and ingrowth, waste package breach, instant release fractions, fuel matrix degradation rates, and radionuclide solubility limitations. The reference case is conceptualized as a generic spent fuel repository at a depth of 450 m in fractured crystalline rock. The repository has 50 parallel backfilled drifts, each with 50 deposition holes 6 m apart. Each deposition hole contains a 4-PWR waste package and bentonite buffer. The rock domain is 5 km in length, 2 km in width, and 1 km in depth. It has 6 deterministic fractured deformation zones and a multitude of stochastic fractures. Teams generally used the ECPM approach for the entire rock or a hybrid approach in which the deterministic fracture zones are modelled with a DFN and the rest of the rock is modelled by ECPM. Of the reference case problems specified, only the results of the initial reference case problem are compared in this report. The initial problem focuses on transport from the deposition holes to the surface, i.e., it neglects waste package performance. Tracers are released at all waste package locations at time zero and tracked for their releases to the near field and ground surface. The water fluxes calculated at the ground surface entry and exit regions of the domain are similar for all models except for two that have considerably lower fluxes. For tracer transport, large differences are observed among models in the magnitude of tracer transported. Much of the difference appears to be due to how the repository is implemented and hence the different degrees of repository simplification. Models that exclude the drifts, buffer, and backfill from the domain tend to show greater release of tracers and radionuclides from the repository. The initial study presented here indicates that major differences in modelling important processes within the repository (e.g., diffusion through buffer and backfill) can produce broadly different release and transport results, especially when those processes are excluded. Even for the models that included all specified features, events, and processes, the results show significant differences and demonstrate the importance of examining multiple modelling approaches in performance assessment. The differences in results observed in this study are expected to motivate teams to either increase complexity in future versions of the reference case models or to improve methods to account for the effects of simplified features and processes. Either way, future improvements in these models are expected to produce results that more closely agree.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Thermal and electric field driven rf breakdown precursor formation on metal surfaces

The phenomenon of electric breakdown poses serious challenges to the design of devices that operate in high electric field environments. Experimental evidence points toward breakdown events that are accompanied by elevated temperatures and dark current spikes, which is attributed to high-asperity nanostructure formation that enhances the local electric field and triggers a runaway process. However, the exact mechanistic origin of such nanostructures under typical macroscopic operational conditions of electric field and magnetic-field-mediated heating remains poorly understood. In this work, we simulate the evolution of a copper surface under the combined action of the electric fields and elevated temperatures. Using a mesoscale curvature-driven surface evolution model, we show how a copper surface can undergo a type of dynamical instability that naturally leads to the formation of sharp asperities in realistic experimental conditions. Exploring the combined effect of fields and temperature rise, we identify the critical regimes that allow for the formation of breakdown precursors. The results show that thermoelastic stresses, while not essential, can significantly lower the critical electric field required for runaway surface instability, which is consistent with experimental observations that thermal effects can increase breakdown rates. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

Friction surface layer deposition of triple-phase Al 10 Cr 12 Fe 35 Mn 23 Ni 20 high entropy alloy: Process optimization and microstructural evolution

A high-strength Co-free triple-phase Al 10 Cr 12 Fe 35 Mn 23 Ni 20 high-entropy alloy (HEA) was successfully fabricated using Friction Surface Layer Deposition (FSLD), a bulk manufacturing method. Multiple single-layer deposits were produced by varying forging force (F) and traverse speeds (T r ) to optimize the process parameters. The optimized conditions (F = 40 kN & T r = 200 mm/min) were then applied to manufacture a scaled-up multi-layer specimen. The initial microstructure of the HEA consisted of coarse grains of the soft FCC-phase, long columnar dendrites of the hard BCC-phase, and small precipitates of the harder B2-phase within the BCC-dendrites. During FSLD, the FCC-matrix underwent continuous dynamic recrystallization due to high-temperature severe plastic deformation, forming finer equiaxed grains. Simultaneously, the BCC-dendrites fractured into smaller fragments, some of which experienced partial growth and coarsening under applied stress, resulting in an hourglass morphology. In contrast, the small B2-precipitates within the BCC-fragments dissolved during the elevated temperatures of FSLD and reprecipitated as substantially finer precipitates during continuous cooling post-FSLD. Additionally, the orientation relationships between the FCC and BCC/B2 phases were completely destroyed by the severe thermoplastic deformation inherent to FSLD. The microstructural refinements led to a substantial improvement in hardness from 177 HV to 283 HV, driven by Hall-Petch strengthening. The increased number of interfaces, including coherent BCC-B2 interfaces, potentially enhances the sink strength and radiation tolerance of the HEA, making it a promising candidate for nuclear applications. In conclusion, this study also highlights FSLD as a versatile technique for achieving tunable properties in HEAs, with detailed schematics illustrating the complex mechanisms of phase transformations during processing.

Additive Manufacturing↗

Evaluating the state-of-the-art in remote volcanic eruption characterization Part I: Raikoke volcano, Kuril Islands

Raikoke, a small, unmonitored volcano in the Kuril Islands, erupted in June 2019. We integrate data from satellites (including Sentinel-2, TROPOMI, MODIS, Himawari-8), the International Monitoring System (IMS) infrasound network, and global lightning detection network (GLD360) with information from local authorities and social media to retrospectively characterize the eruptive sequence and improve understanding of the pre-, syn- and post- eruptive behavior. In this work, we observe six infrasound pulses beginning on 21 June at 17:49:55 UTC as well as the main Plinian phase on 21 June at 22:29 UTC. Each pulse is tracked in space and time using lightning and satellite imagery as the plumes drift eastward. Post-eruption visible satellite imagery shows expansion of the island's surface area, an increase in crater size, and a possibly-linked algal bloom south of the island. We use thermal satellite imagery and plume modeling to estimate plume height at 10–12 km asl and 1.5–2 × 10 6 kg/s mass eruption rate. Remote infrasound data provide insight into syn-eruptive changes in eruption intensity. Our analysis illustrates the value of interdisciplinary analyses of remote data to illuminate eruptive processes. However, our inability to identify deformation, pre-eruptive outgassing, and thermal signals, which may reflect the relatively short duration (~12 h) of the eruption and minimal land area around the volcano and/or the character of closed-system eruptions, highlights current limitations in the application of remote sensing for eruption detection and characterization.

58 GEOSCIENCES↗

Evolution of microstructure and strength of a high entropy alloy undergoing the strain-induced martensitic transformation

In a recent work, we have reported outstanding strength and work hardening exhibited by a metastable high entropy alloy (HEA), Fe 42 Mn 28 Co 10 Cr 15 Si 5 (in at. %), undergoing the strain-induced martensitic transformation from metastable gamma austenite (γ) to stable epsilon martensite (ε). However, the alloy exhibited poor ductility, which was attributed to the presence of the brittle sigma (σ) phase in its microstructure. The present work reports the evolution of microstructure, strength, and ductility of a similar HEA, Fe 38.5 Mn 20 Co 20 Cr 15 Si 5 Cu 1.5 (in at. %), designed to suppress the formation of σ phase. A cast and then rolled plate of the alloy was processed into four conditions by annealing for 10 and 30 min at 1100 °C and by friction stir processing (FSP) at tool rotation rates of 150 and 400 revolutions per minute (RPM) to facilitate detailed examinations of variable initial grain structures. Neutron diffraction and electron microscopy were employed to characterize the microstructure and texture evolution. The initial materials had variable grain size but nearly 100% γ structure. Diffusionless strain induced γ→ε phase transformation took place under compression with higher rate initially and slower rate at the later stages of deformation, independent on the initial grain size. The transformation facilitated part of plastic strain accommodation and rapid strain hardening owing to a transformation-induced dynamic Hall-Petch-type barrier effect, increase in dislocation density, and texture. Here, the peak strength of nearly 2 GPa was achieved under compression using the structure created by double pass FSP (150 RPM followed by 150 RPM). Remarkably, the tensile elongation exhibited by the alloy was nearly 20% with fracture surfaces featuring a combination of ductile dimples and cleavage.

36 MATERIALS SCIENCE↗

Strain Gradient Elasticity in SrTiO 3 Membranes: Bending versus Stretching

Young’s modulus determines the mechanical loads required to elastically stretch a material and also the loads required to bend it, given that bending stretches one surface while compressing the opposite one. Flexoelectric materials have the additional property of becoming electrically polarized when bent. The associated energy cost can additionally contribute to elasticity via strain gradients, particularly at small length scales where they are geometrically enhanced. Here, we present nanomechanical measurements of freely suspended SrTiO 3 crystalline membrane drumheads. In this work, we observe an unexpected nonmonotonic thickness dependence of Young’s modulus upon small deflections. Furthermore, the modulus inferred from a predominantly bending deformation is three times larger than that of a predominantly stretching deformation for membranes thinner than 20 nm. In this regime we extract a strain gradient elastic coupling of ~2.2 μN, which could be used in new operational regimes of nanoelectro-mechanics.

36 MATERIALS SCIENCE↗

Digital and Gradient Refractive Index Planar Optics by Nanoimprinting Mesoporous Silicon

We report the realization of digital and gradient index flat-optics and planar waveguides using the ‘nanoimprinting refractive index’ (NIRI) technique applied to mesoporous silicon. This technique combines the distinct optical and mechanical metamaterial qualities of mesoporous silicon, including its widely tunable effective refractive index and ability to undergo plastic deformation with a near zero Poisson ratio. Nanoimprinting with premastered and reusable stamps containing analog or digital features enables the continuous or discontinuous patterning of refractive index with high contrast Δn ≥ 0.8 and subwavelength resolution. Using NIRI we experimentally demonstrate a wavefront shaping flat microlens array operating in the visible (405–635 nm) and mesoporous silicon and silica waveguides operating near 1310 nm. This study demonstrates the viability of patterning arbitrary refractive index distributions, n(x,y), on the surface of a chip while circumventing the challenges and limitations of top-down lithographic techniques – thus opening a low-cost and scalable approach for the realization of advanced planar optical technologies.

36 MATERIALS SCIENCE↗

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↗