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Systematic Approaches To Tailor the Morphologies and Transport Properties of Solution-Cast Sulfonated Pentablock Copolymers

Sulfonated block polymers are widely studied for applications in water management and electrochemical devices because they combine the properties of ionomers and thermoplastic elastomers in a single materials platform. Sulfonated block polymers are often processed into thin film membranes by casting from solution, and the resulting film morphology is strongly influenced by polymer–solvent interactions. In this work, we used mixtures of polar and nonpolar solvents to control solution-state interactions. We examined the self-assembled structures of solutions and corresponding films with small angle scattering and high-resolution microscopies. When the solvent mixture is selective to one block, the polymer self-assembles into lamellar phases in solution, and films cast from these solutions are also lamellar. On the other hand, a more neutral solvent mixture will produce a disordered structure in solution, leading to films with a disordered, network-like arrangement of lamellar domains. These distinct film morphologies are confirmed with measurements of transport properties; the transition from ordered lamellae to a disordered network produces a 2-fold increase in water uptake and 5-fold increase in proton conductivity at 52% relative humidity. Furthermore these studies demonstrate that measurements of solution-state structure can inform process development, providing a simple route to achieve targeted film morphologies and transport properties.

36 MATERIALS SCIENCE↗

Thermodynamic constraints on the textural evolution of eucrite, EET 90020

Basaltic eucrites, which are possibly parts of the Vestan crust, formed as either lava flows or intrusions, and can offer insights into early crust formation. However most eucrites have experienced thermal metamorphism, which exacerbates the challenges of understanding these samples. A variety of petrogenetic models such as, partial melting of a primitive source, fractional crystallization of magmas emplaced in a primitive crust, and/or partial melting of a eucritic source coupled with melt mixing and assimilation have been proposed in order to explain observed petrologic and chemical characteristics of eucrites. EET 90020 is an unbrecciated eucrite that has experienced significant thermal metamorphism, with temperatures of metamorphic equilibration calculated to be ~840-1040°C. Its petrologic history remains contentious, in part due to differences in trace element analyses [10,17, this work], which has led to multiple metamorphic interpretations [8,10-11]. Here, we combined petrologic observations, chemical analyses, and thermodynamic modeling, to interpret micro-domain textures identified in EET 90020 and better constrain its petrologic history. Ultimately, the development of such textures is a direct result of the geologic processes operating on a young Vesta or similar asteroid. Sample description: We identified three textural domains in EET 90020 (Figure 1); (I) A coarse grain domain with granoblastic plagioclase and pyroxene, (II) a medium grain domain with curved grain boundaries between plagioclase and pyroxene, and (III) a fine grain domain dominated by tridymite that fills in interstitial space between spherical plagioclase. Major element chemistry in phases is consistent across domains. Pyroxene have distinctive high Ca lamellae (Wo40.92En28.1Fs31.0) forming from the low-Ca pigeonite host (Wo3.5En33.7Fs62.8). There are small amounts of fayalitic olivine along pyroxene/oxide grain boundaries, where pyroxenes have reacted with ilmenite/chromite clasts. Plagioclase is anorthitic (Avg ~An88), with little variation (An86-92.5). Trace element bulk rock analyses were collected via ICP-MS and individual mineral analyses with LA-ICP-MS (Figure 2). The bulk sample has an observable enrichment in light rare earth elements, with a notable depletion in Eu. Plagioclase is enriched in LREEs, depleted in HREEs, and has a positive Eu anomaly while pyroxene is enriched in HREEs with a negative Eu anomaly. Variations in trace element analyses is likely influenced by the presence of phosphates because are highly enriched in REEs and have a dramatic effect on the bulk domain compositions. Thermodynamic modeling: The software package, Perple_X, was used to calculate mineral phase equilibria over a range of conditions using a Gibbs free energy minimization approach [12]. Models used all major/minor elements except P2O5. Thermodynamic properties from [13] were used to constrain endmember phase stabilities. Activity models were used to describe mixing in phases with solid solution. Isochemical P-T phase diagrams were constructed for the bulk thin section, and the coarse, medium and fine grain domain compositions. Domain compositions were determined using microprobe analyses of phases identified in each domain and observed modal mineral abundancies. Thermodynamically stable pyroxene compositions were extracted from model results and compared to pyroxene compositions collected via EMPA, allowing us to calculate temperatures for metamorphic equilibrium. Results: Results that use the coarse domain composition (Fig. 3a) demonstrate overlap at T ~ 1020°C indicating high T equilibration. There was no overlap for the medium and fine grain domains, or the bulk composition (e.g., Fig. 3b) indicating that these are not equilibrium assemblages. These results were replicated using data from [8,20]. Discussion: The disequilibrium results from the bulk rock, fine grain and medium grain models imply that EET 90020 was modified during and/or after peak metamorphism (open system behavior). However, this is in contrast to the coarse domain where it appears as if equilibrium was maintained. We suggest that this conflict is explained by highly localized equilibrium occurring at millimeter length-scales, which has been observed in terrestrial metamorphism where aqueous fluid infiltrate [14] or melt loss occurs [15]. It is unlikely that aqueous alteration was significant in modifying the bulk composition of EET 90020, because it lacks hydrated minerals. However, the presence of melt is supported by the presence of an abundance of curved grain boundaries and spherical grains in the medium and fine grain domains This contrasts the coarse domain, where grain boundaries are angular. Given the evidence for disequilibrium in the medium and fine grain domains, it would be inappropriate to draw additional conclusions about textural evolution using thermodynamic models of those domains. However, modeling results of the coarse grain domain, where equilibrium was maintained, can provide useful insights into the geologic evolution of EET 90020. We approximate maximum metamorphic temperatures, using the Ca component in pyroxene, at ~1020°C (Fig. 4), which is consistent with previous two-pyroxene thermometry [11]. At this temperature, up to 10 vol % melt can be produced in the coarse grain domain, which is at the boundary of minimum melt needed in order to segregate and form a melt network [16]. Tridymite and plagioclase would be the first minerals to melt out during heating starting ~990°C. This is consistent with the observed melt textures formed by tridymite and plagioclase in the fine grain domain. We suggest that a partial melting model best explains the textural development of EET 90020. Upon heating, melt generated was either trapped, resulting in no net change in the localized rock composition, or migrated, resulting in disequilibrium between pyroxene and the surrounding matrix. A positive Eu anomaly in plagioclase indicates that all of the plagioclase was melted previously. This is consistent with previous studies that have suggested that EET 90020 represents a residual eucrite that experienced partial melting and subsequent melt loss [8]. We speculate that partial melting could have occurred when EET 90020 was heated in the asteroid’s lower crust or adjacent to an intrusion [7]. Future work will study other, texturally heterogeneous samples to see if EET 90020 presents a unique circumstance or whether crustal partial melting was ubiquitous on the eucrite asteroid.

Eucrites↗

Reactive flash sintering and characterization of bulk high entropy nitrides

Over the past decade, numerous high-entropy ceramics have been synthesized, often displaying attractive properties. However, the study on facile preparation of bulk high entropy nitrides (HEN) are limited, despite its broad potential applications. This research demonstrates for the first time rapid fabrication (within ∼6 min) of bulk high-entropy nitrides, especially (Al 0.17 Nb 0.17 Ta 0.17 Ti 0.32 Zr 0.17 )N, from binary nitride powder mixtures using a highly efficient reactive flash sintering (RFS) technique. X-ray diffraction (XRD) shows the HENs from RFS are near single-phase solid solutions with a rock salt crystal structure, while in situ synchrotron study carried out during RFS captured in real time the formation of HEN, which was preserved upon cooling, suggesting thermodynamic stability of the HEN phase, even up to extreme pressure (∼35.6 GPa). Microscopic analyses using SEM, STEM, and EDS reveal decent uniformity for HEN with no obvious segregation of elements, even to submicron scale. Some properties of the obtained bulk HENs are consistent with expectations. For example, their hardness and bulk modulus are close to estimates based on rule-of-mixture (ROM) values from the constituent binary nitrides. Meanwhile, some other measured properties seem to show surprises. For example, the fracture toughness for the HENs (e.g., 7.81 ± 1.40 MPa•m 1/2 or higher) turns out to be more than double of the expected ROM estimates. The significantly improved fracture toughness is attributed to the observed nano-layered structure of the HENs, despite the HEN’s cubic crystal structure and high hardness. In addition, the oxidation resistance shows improvement up till ∼800°C, possibly due to Ta doping that suppress oxygen vacancy formation in the oxide shell, while the 5-metal HEN of (Al 0.17 Nb 0.17 Ta 0.17 Ti 0.32 Zr 0.17 )N displays superconductivity (T c of ∼5–7 K from magnetism and resistivity measurements, slightly lower than ROM estimate), despite insulating property of starting AlN. Furthermore, future study combining experimental investigation using larger samples to confirm the observed increase in fracture toughness and oxidation resistance, theoretical modeling at different length scale, and more detailed structural/chemical characterization, especially at the atomic scale, are all needed to fully understand the inter-relationships between composition, processing, structure, and novel properties for these HENs and the development of related new materials for different applications.

Flash sintering↗

Structure and magnetism of AlCoCrCuFeNi high-entropy alloy

We report on the investigation of magnetic and structural properties of AlCoCrCuFeNi, which is known to crystallize in a dual phase solid solution: the face-centred cubic (FCC) or the body-centred cubic (BCC). The results of neutron (NPD) and synchrotron powder diffraction (SXRD) allow to partially resolve magnetic information coming from BCC and FCC phases, which is impossible in the bulk magnetic measurements. Electron diffraction (PED) revealed that AlCoCrCuFeNi forms dendritic microstructure with the Cu-rich FCC phase and the Ni-rich BCC phase. Lattice parameters obtained from PED method are in good agreement with parameters obtained after refinement on the basis of powder X-ray diffraction measurements. The local crystal and electronic structure around Co was studied using Co K X-ray Absorption Spectroscopy (XAS). The magnetic measurements show that AlCoCrCuFeNi reveal a ferromagnetic transition at about 330K and displays magnetic hysteresis loop at the room temperature. Results from NPD suggest that the magnetic moment is mostly located in the BCC subsystem. The alloy shows soft magnetic properties. Saturated magnetizations (M s ), remanence ratio (M r /M s ) and coercivity (H c ) of the cast are estimated to be 45.10emu/g, 5.1% and 56 Oe at 300K, respectively. Finally, the BCC-FCC phase transformation up to 673K (400°C) was investigated using temperature dependent NPD, where a possible second BCC phase was identified.

36 MATERIALS SCIENCE↗

A six year timing solution for PSR B1951 + 32

Six years of pulse time-of-arrival measurements have been collected from observations of the young, fast pulsar PSR B1951 + 32 in the CTB 80 supernova remnant using the Jodrell Bank and Arecibo radio telescopes. The combined data allow for the determination of a phase connected solution between 1987 August 21 and 1993 September 21. This solution provides an accurate rotational ephemeris for high energy x-ray and gamma-ray observations of this source made during the six years of radio timing observations to an accuracy of better than one tenth of a pulse period (4 ms). The pulsar has an activity parameter comparable with the value seen in the Crab pulsar.

Foster, R. S.↗

Modeling magnetic evolution and exchange hardening in disordered magnets: The example of Mn 1 - x Fe x Ru 2 Sn Heusler alloys

We demonstrate how exchange hardening can arise in a chemically disordered solid solution from a first-principles statistical mechanics approach. A general mixed-basis chemical and magnetic cluster expansion has been developed, and applied to the Mn 1-x Fe x Ru 2 Sn Heusler alloy system; single-phase solid solutions between antiferromagnetic MnRu 2 Sn and ferromagnetic FeRu 2 Sn with disorder on the Mn/Fe sublattice that exhibit unexpected exchange hardening. Monte Carlo simulations applied to the cluster expansion are able to reproduce the experimentally measured magnetic transition temperatures and the bulk magnetization as a function of composition. The magnetic ordering around a site is shown to be dependent not only on bulk composition, but also on the identity of the site and the local composition around that site. The simulations predict that local antiferromagnetic orderings form inside a bulk ferromagnetic region at intermediate compositions that drives the exchange hardening. Furthermore, the antiferromagnetic regions disorder at a lower temperature than the ferromagnetic regions, providing an atomistic explanation for the experimentally observed decrease in exchange hardening with increasing temperature. These effects occur on a length scale too small to be resolved with previously used characterization techniques.

36 MATERIALS SCIENCE↗

Advanced Semi-Supervised Learning with Uncertainty Estimation for Phase Identification in Distribution Systems

The integration of advanced metering infrastructure (AMI) into power distribution networks generates valuable data for tasks such as phase identification; however, the limited and unreliable availability of labeled data in the form of customer phase connectivity presents challenges. To address this issue, we propose a semi-supervised learning (SSL) framework that effectively leverages labeled and unlabeled data. Our approach incorporates self-training, label spreading, and Bayesian neural networks (BNNs) to enhance phase identification with AMI data. Our method uses an ensemble of multilayer perceptron classifiers in a self-training setup, iteratively adding high-confidence pseudo-labels to improve robustness. We also apply label spread to propagate labels based on data similarity, which enhances generalization across diverse distributions. In addition, we employ a BNNs with uncertainty estimation, boosting confidence in predictions and reducing phase identification errors. In our case study, we achieved approximately 98% +/- 0.08 accuracy with uncertainty using minimal and unreliable labeled data from a real U.S. utility, Duquesne Light Company. Our SSL approach, combined with uncertainty estimation, provides an efficient solution for phase identification in AMI data, ultimately improving the reliability of smart grid applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Advanced Semi-Supervised Learning With Uncertainty Estimation for Phase Identification in Distribution Systems

The integration of advanced metering infrastructure (AMI) into power distribution networks generates valuable data for tasks such as phase identification; however, the limited and unreliable availability of labeled data in the form of customer phase connectivity presents challenges. To address this issue, we propose a semi-supervised learning (SSL) framework that effectively leverages labeled and unlabeled data. Our approach incorporates self-training, label spreading, and Bayesian neural networks (BNNs) to enhance phase identification with AMI data. Our method uses an ensemble of multilayer perceptron classifiers in a self-training setup, iteratively adding high-confidence pseudo-labels to improve robustness. We also apply label spread to propagate labels based on data similarity, which enhances generalization across diverse distributions. In addition, we employ a BNNs with uncertainty estimation, boosting confidence in predictions and reducing phase identification errors. In our case study, we achieved approximately 98% +/- 0.08 accuracy with uncertainty using minimal and unreliable labeled data from a real U.S. utility, Duquesne Light Company. Our SSL approach, combined with uncertainty estimation, provides an efficient solution for phase identification in AMI data, ultimately improving the reliability of smart grid applications.

24 POWER TRANSMISSION AND DISTRIBUTION↗

An improved technique for determining reflection from semi-infinite atmospheres with linearly anisotropic phase functions

A solution to the problem of reflection from a semi-infinite atmosphere is presented, based upon Chandrasekhar's H-function method for linearly anisotropic phase functions. A modification to the Gauss quadrature formula which gives about the same accuracy with 10 points as the conventional Gauss quadrature does with 100 points was developed. A computer program achieving this solution is described and results are presented for several illustrative cases.

Fricke, C. L.↗

The Evolution of the Deformation Substructure in a Ni-Co-Cr Equiatomic Solid Solution Alloy

The equiatomic NiCoCr alloy exhibits an excellent combination of strength and ductility, even greater than the FeNiCrCoMn high entropy alloy, and also displays a simultaneous increase in strength and ductility with decreasing the testing temperature. To systemically investigate the origin of the exceptional properties of NiCoCr alloy, which are related to the evolution of the deformation substructure with strain, interrupted tensile testing was conducted on the equiatomic NiCoCr single-phase solid solution alloy at both cryogenic and room temperatures at five different plastic strain levels of 1.5%, 6.5%, 29%, 50% and 70%. The evolution of deformation substructure was examined using electron backscatter diffraction (EBSD), transmission Kikuchi diffraction (TKD), conventional transmission electron microscopy (CTEM), diffraction contrast imaging using STEM (DCI-STEM) and atomic resolution scanning transmission electron microscopy. While the deformation substructure mainly consisted of planar dislocation slip and the dissociation of dislocations into stacking faults at small strain levels (≤6.5%), at larger strain levels, additional substructures including nanotwins and a new phase with hexagonal close packed (HCP) lamellae also appeared. The volume fraction of the HCP lamellae increases with increasing deformation, especially at cryogenic temperature. First principles calculations at 0 K indicate that the HCP phase is indeed energetically favorable relative to FCC for this composition. The effects of the nanotwin and HCP lamellar structures on hardening rate and ductility at both cryogenic and room temperature are qualitatively discussed.

Twinning↗

Effect of Different Zirconium Contents on the Corrosion Resistance of ZrO{sub 2}-TiO{sub 2} Film-Coated Stainless Steel

This work discusses the corrosion resistance of x%zirconia (ZrO{sub 2})–x%titania (TiO{sub 2}) nanocomposite films with different percentages of ZrO{sub 2} prepared on stainless steel by dipping the substrates in sol–gel solutions. The phase compositions and microstructures of the films were investigated by x-ray diffraction (XRD) and scanning electron microscopy (SEM). Tafel polarization curves and electrochemical impedance spectroscopy (EIS) were employed to investigate the corrosion resistance of the coated steel substrates during immersion in a 5% NaCl solution at room temperature. The results showed that when the percentage of ZrO{sub 2} in the sol–gel was relatively low, the film contained cracks, leading to a poor corrosion resistance. When the percentage of ZrO{sub 2} was higher, the corrosion resistance of the film was also affected by the sintering temperature; a sintering temperature of 650 °C gave the best protection of the metal surface, and the protection efficiency was 95%.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Microsegregation Measurement: Methods and Applications

Microsegregation is chemical variation at the microstructural level in a solidified ingot, which can cause undesirable effects on material properties. Its formation is driven by different levels of solute elemental solubility between solid and liquid phases, resulting in solute buildup or depletion in the liquid phase during solidification. Characterization of microsegregation can be essential for understanding its formation and removing it through heat treatment. Measurement is frequently carried out via scanning electron microscope (SEM), though metallographic analysis, mechanical testing and optical radiography have been used. SEM analysis can consist of point measurements on single dendrites, line scans across or along dendrites, elemental maps, and extended line-based or grid-based analyses extending over many dendrites, which can generate large amounts of data. Line-based or grid-based data can be analyzed using scatterplots of element concentrations to visualize segregation behavior and sorting/ranking of data by a single element or a combination of elements, to give compositional profiles as a function of extent of solidification. For both qualitative and quantitative analyses, effects of phase transformations and secondary phases need to be considered as well as sorting of measurement errors when generating compositional profiles. Applications of analysis include determination of partition ratios, examination of solute–element interactions, determination of effects of cooling rate and back diffusion, applications to freckling studies, validations of modeling, and development of heat-treatment profiles.

36 MATERIALS SCIENCE↗

In situ reductive dissolution to remove Iodine-129 from aquifer sediments

The use of an aqueous reductant (Na-dithionite) with pH buffer (K-carbonate, pH 12) was evaluated in this laboratory study as a potential remedial approach for removing Fe oxide associated iodine and enhancing pump-and-treat extraction from iodine-contaminated sediments in the unconfined aquifer in the 200 West Area of the Hanford site. X-ray fluorescence data of untreated sediment indicated that iodine was largely associated with Fe (i.e., incorporated into Fe oxides), however, XANES data was inconclusive as to valence state. During groundwater leaching, aqueous and adsorbed iodine was quickly released, then additional iodine was slowly released potentially from dissolution of one or more surface phases. The Na-dithionite treatment removed greater iodine mass (2.9x) at a faster rate (1 to 4 orders of magnitude) compared to leaching with groundwater alone. Iron extractions for untreated and treated sediments showed a decrease in Fe(III)-oxides, which likely released iodine to aqueous solution. Solid phase inorganic carbon and aqueous Ca and Mg analysis further confirmed that significant calcite dissolution did not occur in these experiments meaning these phases did not release significant iodine. Although it was expected that, after treatment, 127 I concentrations would eventually be lower than untreated sediments, leaching experiments showed continued, elevated iodine concentrations for treated samples over 750 hours. Stop flow events during 1-D column leaching suggested that some iodide precipitated within the first few pore volumes. In the survey of metals during leaching, some silver was detected which could have been solubilized by the elevated pH of initial Na-dithionite injection. Then, silver (or other metals) could have subsequently precipitated with iodide during the initial stop flow event forming a slowly dissolving source. Although significantly greater iodine is removed with treatment, the long-term leaching needs to be investigated further as it may limit dithionite treatment at the field scale.

54 ENVIRONMENTAL SCIENCES↗

Seeding picoscale solutions for social macro goals: complex thinking in projects for vulnerable communities

This chapter presents lessons learned from two experiences of implementing sociopoliticalsustainability strategies to achieve environmental and economic sustainability.The projects were carried out in rural communities in Guinea-Bissau andJamaica, which are both vulnerable to climate change. Each experience, developedfrom a systemic perspective and under two frameworks (the water–food–energynexus and ‘Appropriate Technology’), is described in four phases (problemcharacterization, solution design, solution pre-evaluation, and implementation),with the significant findings made by the team in terms of challenges, rewards, andessential conditions for development. Both deal with environment-friendly solutionsthat solve the problems of water and energy provision. Based on complex thinking,the experiences are analyzed from the social inclusion, participation, empowerment,and learning theory viewpoints. Finally, the insights gained by the team arehighlighted: communication requirements, the level of dependency of industrializedsolutions, budget constraints, training, testing, and planning recommendations, thediversity of interaction with the communities, and partners’ skills. As a result, futureactions can exploit these experiences and contribute to the success of subsequentprojects.

Pereira Pinto, Joao↗

Extreme shear-deformation-induced modification of defect structures and hierarchical microstructure in an Al–Si alloy

Abstract Extreme shear deformation is used for several material processing methods and is unavoidable in many engineering applications in which two surfaces are in relative motion against each other while in physical contact. The mechanistic understanding of the microstructural evolution of multi-phase metallic alloys under extreme shear deformation is still in its infancy. Here, we highlight the influence of shear deformation on the microstructural hierarchy and mechanical properties of a binary as-cast Al-4 at.% Si alloy. Shear-deformation-induced grain refinement, multiscale fragmentation of the eutectic Si-lamellae, and metastable solute saturated phases with distinctive defect structures led to a two-fold increase in the flow stresses determined by micropillar compression testing. These results highlight that shear deformation can achieve non-equilibrium microstructures with enhanced mechanical properties in Al–Si alloys. The experimental and computational insights obtained here are especially crucial for developing predictive models for microstructural evolution of metals under extreme shear deformation.

36 MATERIALS SCIENCE↗

In-Situ Study of Microstructure Evolution of Spinodal Decomposition in an Al-Rich High-Entropy Alloy

High-entropy alloys (HEAs) are materials which leverage the entropy of mixing to motivate the formation of single-phase solid solutions, even of immiscible elements. While these materials are well-recognized for their application to structural engineering, there is increasing interest in the use of HEAs for functional applications such as memory storage and energy devices. The current work investigates the HEA Al 1.3 CoCrCuFeNi, which has been previously shown to be single-phase at high temperatures, but undergoes phase separation at lower temperatures, transforming the structural and the functional properties. This phase separation is investigated at high temperatures with in-situ small angle neutron scattering (SANS) and scanning transmission electron microscopy (EDS). These techniques show that increasing the temperature up to 800°C, the microstructure of the HEA adiabatically disorders and abruptly homogenizes near 700°C, which is consistent with spinodal decomposition. Overall, the microstructural evolution proceeds mainly by the atomistic redistribution of the constituent elements within simple crystal lattices, producing coherent phase mixtures.

36 MATERIALS SCIENCE↗

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗