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DOE OSTI2025

Shock propagation in aerogel and TPP foams for inertial fusion energy target design

Achieving practical inertial fusion energy (IFE) requires the development of target designs with well-characterized microstructure and compression response. We measured shock dynamics in low-density (17.5–500 mg/cm 3 ) aerogel and two-photon polymerization (TPP) foams using x-ray phase contrast imaging (XPCI) methods and the Velocity Interferometer System for Any Reflector. By analyzing shock front evolution, we examined how target type and density influence shock propagation and energy dissipation. Talbot-XPCI shows that aerogels support a smooth, bowed shock front due to their homogeneous nanometer-scale pore network. In contrast, TPP foams exhibit irregular, stepwise propagation driven by interactions with their periodic micrometer-scale lattice. Shock velocity follows a power-law relation: aerogels deviate from classical ρ −1/2 scaling due to pore-collapse dissipation, while TPP foams follow the trend with larger uncertainties from density variations. Comparisons with xRAGE simulations reveal systematic underestimation of shock speeds. These results provide the first experimental constraints on shock propagation in TPP foams over a wide density range and highlight the influence of internal structure on anisotropic shock behavior. Our findings support improved benchmarking of EOS and hydrodynamic models and inform the design of foam architectures that promote implosion symmetry in IFE capsules.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1986

Investigation of long-lived eddies on Jupiter

Quasi-geostrophic, two layer models of the Jovian atmosphere are under development; these may be used to simulate eddy phemonena in the atmosphere and include tracer dynamics explicitly. The models permit the investigation of the dynamics of quasi-geostrophic eddies under more controlled conditions than are possible in the laboratory. They can also be used to predict the distribution and behavior of tracer species, and hence to discriminate between different models of the mechanisms forcing the eddies, provided suitable observations can be obtained. At the same time, observational strategies are being developed for the Near Infrared Mapping Spectrometer on the Galileo Orbiter, with the objective of obtaining composition measurements for comparison with the models. Maps of features at thermal infrared wavelengths near 5 micron and reflected sunlight maps as a function of wavelength and phase angle will be obtained. These should provide further useful information on the morphology, composition and microstructure of clouds within eddy features. Equilibrium chemistry models which incorporate advection may then be used to relate these results of the dynamical models and provide addtional means of classifying different types of eddies.

Lewis, S. R.↗

NASA NTRS1994

Strength characteristics and crack growth behavior of a composite with well aligned fibers

Continuous fiber composites have shown tremendous promise in industrial applications. Their microstructures, however, are very complex and in many instances difficult to characterize. In this project, the fracture characteristics of a specially made fiber reinforced composite with different fiber spacing are investigated. The experimental results so far have shown that after an initial transient phase the crack speed reaches a steady phase, i.e., independent of the crack length. Within the steady crack growth phase debonding along the fibers in the bridging zone grows in a self-similar manner. During the steady phase the energy dissipation per cycle is constant. Afterwards, an increase of the energy dissipation is observed that is accompanied by a decrease in crack speed. This latter trend is presumed to be the result of relatively large amounts of energy dissipated in the bulk of the specimen. Using appropriate Green's function and computer simulations, the stress intensity factor at the crack tip is evaluated for various cases of bridging stresses. In this way the effects of specimen size and fiber spacing on the overall fracture behavior of the composite system are analyzed. The steady crack speed and the steady rate of debonding have a similar power dependence on stress level. Dimensional analysis demonstrates that the particular fracture process is not governed by dimensional invariance but on the detailed micromechanisms in the bridging zone.

Botsis, John↗

NASA NTRS2019

Coordinated Analysis of an Ion Irradiated Carbonaceous Chondrite Suggests Complex Space Weathering Effects

Surfaces of airless planetary bodies are exposed to micrometeorite bombardment and solar wind irradiation which alter the microstructural, compositional, and optical properties of regoliths over time. These processes are collectively known as space weathering, and they complicate the interpretation of remote sensing data and the subsequent characterization of airless surfaces. Within the next 5 years, NASA’s OSIRIS-REx (Origins, Spectral Interpretation, Resource Identification, Security, Regolith Explorer) and JAXA (Japan Aerospace Exploration Agency)’s Hayabusa2 missions will return samples from C-type asteroids Bennu and Ryugu, respectively. Compared to the Moon and S-type asteroids, our understanding of the space weathering of C-complex asteroids is limited. In order to maximize scientific return from remote sensing data and to prepare for the analysis of returned samples from these missions, we must better understand the effects of space weathering on hydrated, organic-rich materials. We can do so by simulating these processes in the laboratory. In this study, we simulate solar wind exposure through ion irradiation of the CM2 carbonaceous chondrite Murchison - a suitable analog for C-complex asteroids. Here, we present coordinated analyses of a sample before and after ion irradiation.

Laczniak, D. L.↗

DOE OSTI2022

The effect of elastic anisotropy on the symmetry selection of irradiation-induced void superlattices in cubic metals

We report self-organized microstructures and patterns have been widely observed in non-equilibrium physical systems. In particular, irradiation in metals creates far-from-equilibrium environments, in which the competing dynamics of defect production and annihilation can lead to unique self-organized superlattice structures, e.g., void and gas bubble superlattices. From a physical point of view, the superlattice structures are dictated by the intrinsic symmetry breaking in the metals, i.e., anisotropy caused by the breaking of continuous rotational symmetry. In the literature, two distinctive anisotropies, elastic anisotropy and diffusion anisotropy of interstitials, have been proposed to be the origins of superlattice formation. However, it is still unclear which anisotropy dominates the symmetry selection of superlattice structures. In this paper, we study elastic anisotropy and its effect on the symmetry of void superlattices. By using theoretical analyses and phase field simulations, we show that elastic anisotropy in cubic metals can lead to either face-centered cubic or simple cubic superlattices depending on the Zener anisotropy ratio. The superlattices formed under this elastic anisotropy mechanism must form under the influence of spinodal decomposition, as the mechanism requires perturbations in the vacancy concentration field to develop into spatially-static concentration waves. We compare to existing work on symmetry selection in superlattices via diffusion anisotropy and to experimental observations, and we suggest that concentration wave development under the influence of elastic anisotropy is not the mechanism for symmetry selection during the formation of irradiation-induced void superlattices, but that diffusion anisotropy could be the dominant mechanism.

36 MATERIALS SCIENCE↗

DOE OSTI2023

A data-driven method for modelling dissipation rates in stratified turbulence

We present a deep probabilistic convolutional neural network (PCNN) model for predicting local values of small-scale mixing properties in stratified turbulent flows, namely the dissipation rates of turbulent kinetic energy and density variance, $\varepsilon$ and $\chi$ . Inputs to the PCNN are vertical columns of velocity and density gradients, motivated by data typically available from microstructure profilers in the ocean. The architecture is designed to enable the model to capture several characteristic features of stratified turbulence, in particular the dependence of small-scale isotropy on the buoyancy Reynolds number $Re_b:=\varepsilon /(\nu N^2)$ , where $\nu$ is the kinematic viscosity and $N$ is the background buoyancy frequency, the correlation between suitably locally averaged density gradients and turbulence intensity and the importance of capturing the tails of the probability distribution functions of values of dissipation. Empirically modified versions of commonly used isotropic models for $\varepsilon$ and $\chi$ that depend only on vertical derivatives of density and velocity are proposed based on the asymptotic regimes $Re_b\ll 1$ and $Re_b\gg 1$ , and serve as an instructive benchmark for comparison with the data-driven approach. When trained and tested on a simulation of stratified decaying turbulence which accesses a range of turbulent regimes (associated with differing values of $Re_b$ ), the PCNN outperforms assumptions of isotropy significantly as $Re_b$ decreases, and additionally demonstrates improvements over the fitted empirical models. A differential sensitivity analysis of the PCNN facilitates a comparison with the theoretical models and provides a physical interpretation of the features enabling it to make improved predictions.

42 ENGINEERING↗

DOE OSTI2020

Ion acceleration from microstructured targets irradiated by high-intensity picosecond laser pulses

Structures on the front surface of thin foil targets for laser-driven ion acceleration have been proposed to increase the ion source maximum energy and conversion efficiency. While structures have been shown to significantly boost the proton acceleration from pulses of moderate-energy fluence, their performance on tightly focused and high-energy lasers remains unclear. Here, we report the results of laser-driven three-dimensional (3D)-printed microtube targets, focusing on their efficacy for ion acceleration. Using the high-contrast (~10 12) PHELIX laser (150 J, 10 21 W / cm 2 ), we studied the acceleration of ions from 1-μm-thick foils covered with micropillars or microtubes, which we compared with flat foils. The front-surface structures significantly increased the conversion efficiency from laser to light ions, with up to a factor of 5 higher proton number with respect to a flat target, albeit without an increase of the cutoff energy. An optimum diameter was found for the microtube targets. Our findings in this work are supported by a systematic particle-in-cell modeling investigation of ion acceleration using 2D simulations with various structure dimensions. Simulations reproduce the experimental data with good agreement, including the observation of the optimum tube diameter, and reveal that the laser is shuttered by the plasma filling the tubes, explaining why the ion cutoff energy was not increased in this regime.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

On the effect of elemental partitioning to secondary phases after solution and aging heat treatments in a Co-Ni-based superalloy

Here, this paper presents the phase stability and elemental partitioning in a Co-40Ni-10Al-7.5W-10Cr-3Nb-0.06B-0.6C (at.%) superalloy (referred to as 3Nb) after a two-step heat treatment. The resulting microstructure consisted of γ, γ', MC carbides and µ-Co 7 W 6 phase decorating the regions near and at the grain boundaries. Nb preferentially partitioned to the γ'-phase and other elements such as Ni, Cr and W were responsible for the μ-phase formation.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Corrosion of Al-Fe self-pierce riveting joints with multiphysics-based modeling and experiments

Self-piercing riveting (SPR) is an extensively used joining technique to assemble dissimilar materials. However, this joining of the dissimilar materials can generate galvanic/crevice corrosion, which can drastically impact the mechanical properties and the service life of the joint. In this study, a multiphysics-based hybrid modeling approach is developed for the galvanic corrosion of the Al-Fe SPR joints, which can consider the corrosion initiation and corrosion evaluation jointly. Experimental studies are first performed to extract information regarding the corrosion initiation sites, corrosion evolution and overall corrosion induced material loss in SPR joints. The initiation information is then passed onto the multiphysics FE model thus making it a hybrid model. This model can help understand the influences of metal microstructure on the corrosion propagation while the morphology changes can also be analyzed. Using the developed hybrid modeling approach, thorough parametric studies can be performed to explore the coupled impacts of multiple corrosion factors on the corrosion behavior of the joints. The developed hybrid model is validated on the prediction of galvanic corrosion for the SPR joints by comparing with experimental observations.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Low-Tortuosity Thick Electrodes with Active Materials Gradient Design for Enhanced Energy Storage

The ever-growing energy demand of modern society calls for the development of high-loading and high-energy-density batteries, and substantial research efforts are required to optimize electrode microstructures for improved energy storage. Low-tortuosity architecture proves effective in promoting charge transport kinetics in thick electrodes; however, heterogeneous electrochemical mass transport along the depth direction is inevitable, especially at high C-rates. In this work, we create an active material gradient in low-tortuosity electrodes along ion-transport direction to compensate for uneven reaction kinetics and the nonuniform lithiation/delithiation process in thick electrodes. The gradual decrease of active material concentration from the separator to the current collector reduces the integrated ion diffusion distance and accelerates the electrochemical reaction kinetics, leading to improved rate capabilities. Further, the structure advantages combining low-tortuosity pores and active material gradient offer high mass loading (60 mg cm –2 ) and enhanced performance. Comprehensive understanding of the effect of active material gradient architecture on electrode kinetics has been elucidated by electrochemical characterization and simulations, which can be useful for development of batteries with high-energy/power densities.

25 ENERGY STORAGE↗

DOE OSTI2022

In Situ Nano-Indentation of a Gold Sub-Micrometric Particle Imaged by Multi-Wavelength Bragg Coherent X-ray Diffraction

The microstructure of a sub-micrometric gold crystal during nanoindentation is visualized by in situ multi-wavelength Bragg coherent X-ray diffraction imaging. The gold crystal is indented using a custom-built atomic force microscope. A band of deformation attributed to a shear band oriented along the (221) lattice plane is nucleated at the lower left corner of the crystal and propagates towards the crystal center with increasing applied mechanical load. After complete unloading, an almost strain-free and defect-free crystal is left behind, demonstrating a pseudo-elastic behavior that can only be studied by in situ imaging while it is invisible to ex situ examinations. The recovery is probably associated with reversible dislocations nucleation/annihilation at the side surface of the particle and at the particle-substrate interface, a behavior that has been predicted by atomistic simulations. The full recovery of the particle upon unloading sheds new light on extraordinary mechanical properties of metal nanoparticles obtained by solid-state dewetting.

36 MATERIALS SCIENCE↗

NASA NTRS2024

Finite Element Simulation of the Direct Energy Deposition using Comsol Multiphysics

Direct Energy Deposition (DED) is an emerging technology extensively employed in metal Additive Manufacturing (AM). Despite its widespread industrial application, mathematical modeling in this domain remains challenging. This complexity arises from the intricate nature of the modeling approach and the nonlinear behavior of material parameters across a broad temperature range. Consequently, experimentalists often resort to a trial-and-error method to achieve structures with desired properties. However, this approach can be time-consuming and may not always yield parts with the requisite characteristics, highlighting the necessity for mathematical modeling to enhance manufacturing success. This study focuses on thin-walled manufacturing with a single bead thickness, adjusting laser parameters to produce such structures. The laser cladding speed, typical for DED manufacturing, is considered to be on the order of centimeters per second. The various wall thicknesses and heights are explored to discern the general characteristics of walls manufactured via this DED approach. Our modeling approach diverges from the conventional DED modeling based on activation-deactivation of predefined mesh domains, commonly implemented in many finite element codes. Instead, a method is proposed that effectively models layer cladding and melt pool dynamics, enabling predictions of the microstructure in the resulting structures. The formation mechanisms of cellular, dendritic columnar, and stray (equiaxed) grains, which arise from the interplay between nucleation and growth from the surface is analyzed. The study also examines the feasibility of microstructure formation to demonstrate the various thermal characteristics inherent in wall manufacturing. Our results illustrate how different process parameters influence the temperature gradient and cooling rate of the molten pool, subsequently affecting the primary dendrite arm spacing (PDAS). This modeling technique allows for the investigation of diverse thermal conditions, facilitating the prediction of microstructure and residual stresses in the manufactured parts.

modeling↗

DOE OSTI2021

Capture efficiency and bias from the defect dynamics near grain boundaries in BCC Fe using mesoscale simulations

The capture efficiency describes the capability of a sink, such as a grain boundary (GB), dislocation, and void, to absorb point defects (PDs). The bias defines the difference in capture efficiency between the absorption of a vacancy and dumbbell at a sink. Complete kinetic information on PDs, including diffusion barriers and diffusion orientations, as well as accurate saddle points, are needed to determine the capture efficiency and bias at a sink accurately, which is computationally demanding. Here, in the present study, the Self-Evolving Atomistic Kinetic Monte Carlo (SEAKMC) method was used to investigate the defect dynamics of PDs near different types of grain boundaries (GBs) (with both $\langle$100$\rangle$ and $\langle$110$\rangle$ families) accurately in body-centered cubic (BCC) iron (Fe). The capture efficiency, sink strength, and bias factor of different types of GBs were determined in Fe, which, different from traditional rate theory estimation, showed a distinct capture efficiency, sink strength, and bias in different GBs. The results demonstrate a strong positive correlation between the capture efficiency and the GB strain width, instead of the GB misorientation, GB energy, or GB-PD binding energy, which have been investigated previously. This work provides valuable insight into the radiation-induced microstructural evolution of GBs.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Modeling Single-Crystal Battery Materials: From Fundamental Understanding to Performance Evaluation

The performance of rechargeable batteries is fundamentally influenced by the physicochemical properties and microstructural features of their key material components. Recent experimental advancements have highlighted the potential of single-crystal (SC) morphologies to address inherent limitations of polycrystalline (PC) electrodes and solid-state electrolytes, offering tunable charge transport kinetics and improved cell cycling performance. Here, this review examines how state-of-the-art computational modeling, from atomistic and mesoscale to continuum-level approaches, including machine learning methodologies, has been utilized to investigate the critical factors governing the electrochemical behavior of SC battery materials. We explore how predictive modeling can elucidate the processing–structure–property–performance relationships of SC cathodes, anodes, and solid-state electrolytes, with a focus on unique SC characteristics such as crystallographic anisotropy, size effects, and facet-dependent properties. Additionally, we identify limitations in commonly used modeling techniques and discuss strategies to address these challenges. By integrating high-fidelity simulations with experimental insights, this review aims to outline a clear path for the rational design and optimization of SC battery components, paving the way for accelerated advancements in energy storage technologies.

Materials science↗

DOE OSTI2022

In-situ Characterizations of Microstructural Degradation of Perovskite Solar Cells

Rapid progress has been achieved in perovskite solar cells (PSCs), and their efficiencies have improved from 3.8 % to 24.2 % in less than a decade. With low-cost processing, PSCs have shown exciting photovoltaic (PV) properties, such as effective optical absorption, a long carrier lifetime, and unique defect tolerance. While recent studies demonstrated improved stability up to 100 days, PSC technology is still challenged to meet the stringent industry requirements for commercialization. Despite considerable efforts, the underlying physical mechanisms for the inferior stability of PSCs are not well understood. One reason for this divergence is that many established measurement techniques (e.g., quantum efficiency, photoluminescence) probe the properties on length scales far greater than that of electronic and/or structural inhomogeneity (i.e., < 1 μm near grain boundaries) and therefore characterize convoluted and/or averaged properties. Ion/electron beam-based techniques have been extensively used to access the microstructures of PSCs, enabling atomic/nanoscale structural, chemical, optical, and electrical characterizations. For example, focused ion beam (FIB) milling produces an atomically smooth surface that minimizes the artifacts attributed to the surface roughness. FIB techniques can also create a well-defined cross-section of PSCs without mechanical damage in a physical cleaving sample preparation. While powerful, there are some concerns about possible beam damage of inorganic-organic perovskites via chemical-bond breakage and local heating. This project aims to comprehensively understand how the microstructural/interfacial properties of PSCs (e.g., Methylammonium Lead Iodide [MAPbI 3 ]) are modified under the irradiating ion beams. Specifically, we investigate the sub-surface properties of PSCs before and after Ar-ion beam injections. Kelvin probe force microscopy (KPFM) measures the contact potential differences (CPDs). Photoluminescence (PL) microscopy in conjunction with Finite-Difference Time-Domain (FDTD) simulations infers the formation of a “dead layer” (< 15 nm) on the subsurface of MAPbI 3 during Ar+ milling processes while preserving the initial bulk properties. The x-ray photoemission spectroscopy (XPS) confirms this modified surface is a lead-rich and iodine-deficient surface. We initiate customizing in-situ measurement setup while measuring the local optical and electrical properties of PSC under thermal (cooling, heating) and light stressors. Our results provide in-depth knowledge of the ion-beam impact on metal-halide perovskites and how this modified sub-surface impacts their properties under accelerated stressors of light and heat. Intensive Monte Carlo simulations of an electron beam interacting with PSCs provide the beam energy distribution in PSCs, proposing possible measurement conditions of using e-beam with minimizing beam damage. Our in-situ measurement platform can accommodate the diverse architecture of PSC devices for studying deterioration mechanisms under mixed environmental stressors.

14 SOLAR ENERGY↗

NASA NTRSDate not supplied

Aqueous alteration of Cb-type asteroid Ryugu

The samples from the asteroid Ryugu, which returned to Earth in the winter of 2020 [1], were stored under pure Nitrogen conditions at the Extraterrestrial Materials Curation Center of ISAS. After basic description [2-3], they were distributed to six initial analysis teams in Japan in June 2021. The initial analysis "Stone" team, which was responsible for the analysis of coarse particles (>1 mm in size), consisted of about 150 scientists from Japan and abroad, and conducted a series of analyses We analyzed sixteen coarse Ryugu particles 1 ~ 8 mm in size: six from the 1st touch-down site and ten from the 2nd touch-down site. Individual coarse samples were cut by Xe-FIB or wire-saw to expose particular objects or textures to be exposed on the surface based on 3D structure and element distribution obtained by synchrotron X-ray CT analysis and XRF analysis, respectively. FE-SEM/EDS and FE-EPMA/WDS analysis were made on all polished sections. TEM observation of many FIB sections was made to see microstructures and to compare with carbonaceous chondrites. Many other analyses were carried out to characterize mineralogical and compositional properties and summary of the analysis procedures is described in [4]. X-ray CT analysis showed that all sixteen Ryugu particles are composed of fine-grained material, with no chondrules and CAIs larger than 100 μm in size. FE-EPMA observation showed that Ryugu samples are breccias, consisting of many small rock fragments of different compositions, lithologies, and histories. The most common lithology includes Mg-rich saponite and serpentine, dolomite, magnesite, hydroxyapatite, pyrrhotite, and magnetite as main constituents. The mineralogy of this major lithology supports the classification of Ryugu samples as CI chondrites, which experienced extensive aqueous alteration in Ryugu’s parent asteroid. Based on the obtained mineralogical properties, we performed chemical modeling of aqueous alteration of Ryugu’s parent asteroid [5]. Numerical simulations [6-8] to reproduce thermal history and impact-induced destruction of the Ryugu’s parent asteroid were also carried out using mineralogical and physical properties of the Ryugu samples. In the talk, I would like to explain the conditions of aqueous alteration occurred in the parent asteroid of Ryugu in order to show how the water in the asteroid changed the mineralogy and chemistry of the nebular dust.

T. Nakamura↗

DOE OSTI2020

Chemical short-range order in derivative Cr–Ta–Ti–V–W high entropy alloys from the first-principles thermodynamic study

The development of high-entropy alloys (HEAs) focuses on exploring compositional regions in multi-component systems with all alloy elements in equal or near-equal atomic concentrations. Initially it was based on the main idea that high mixing configurational entropy contributions to the alloy free energy could promote the formation of a single solid solution phase. By using the ab-initio based Cluster Expansion (CE) Hamiltonian model constructed for the quinary bcc Cr–Ta–Ti–V–W system in combination with Monte Carlo (MC) simulations, we show that the phase stability and chemical short-range order (SRO) of the equiatomic quinary and five sub-quaternary systems, as well as their derivative alloys, can dramatically change the order–disorder transition temperatures (ODTT) as a function of alloy compositions. In particular, it has been found, that the equiatomic quaternary Ta–Ti–V–W and Cr–Ta–Ti–W alloys had the lowest order–disorder transition temperature (500 K) among all the analysed equiatomic compositions. In all investigated alloy systems, the strongest chemical ordering has been observed between Cr and V, which led to the conclusion that decreasing the concentration of either Cr or V might be beneficial in terms of decreasing the ODTT. It also predicts that increasing concentration of Ti significantly decreases the ODTT. Our analysis of chemical SRO as a function of alloy composition allows to understand the microstructure evolution of HEAs as a function of temperature in excellent agreement with available experimental observations. Importantly, our free energy of mixing and SRO calculations predict that the origin of precipitates formed by Cr- and V-rich in the sub-quaternary Cr–Ta–V–W system is driven by the thermodynamics. The modelling results are in an excellent agreement with experimental observation of Cr and V segregation in the W 0.38 Ta 0.36 Cr 0.15 V 0.11 alloy which in turns shows an exceptional radiation resistance.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2019

A Three-Dimensional Thermodynamically Based Function for the Progressive Failure of Unidirectional Composites

A thermodynamically-based work potential theory for modeling progressive damage for laminated, unidirectional composites assuming plane stress (2D Schaperystheory) is extended to three dimensioanl (3D). An internal state variable, S, is defined to account for the dissipated energy due to damage evolution in the form of microstructure changes in the matrix. With the stationary of the total work potential with respect to the internal state variable, a thermodynamically-consistent set of evolution equationsis derived. The internal state variable is related to the transverse and shear modulithrough microdamage functions. In the first part of this work, coupon specimensare prepared to conduct experiments to characterize the relations between the internalstate variable and the transverse modulus as well as shear modulus. The informationis subsequent used for the prediction of three point bending test. In the second partof this work, objectivity is studied. Three separate methods utilizing different definitions of a reduced internal state variable or of the order of the polynomials are used to represent the matrix micro-damage functions are employed. The three methods are implemented in a user defined subroutine within a commercial finite element method software package. Results from numerical simulations of a center-notched composites panel are compared. The agreement in the maximum stress predictions among the three methods indicates that objectivity, with respect to the functional form of themicrodamage functions, is satisfied.

carbon fiber reinforced polymer composites↗