Isotropic Behavior Research Articles

A strain rate-dependent distortional hardening model for nonlinear strain paths

In this paper, a strain rate-dependent distortional hardening model is firstly proposed to describe strain rate-dependent material behaviors under linear and nonlinear strain paths changes in 0≤θpathchange≤180∘. The proposed model is formulated based on the simplified strain rate-independent distortional hardening model (Choi and Yoon, 2023). Any yield function could be used for the strain rate-dependent isotropic and anisotropic yielding. For the linear strain path, the strain rate-dependent isotropic hardening behavior could be explained by two state variables representing rate-dependent yielding and convergence rate of flow stress under monotonically increasing loading condition, respectively. For the nonlinear strain paths, the strain rate-dependent material behaviors such as Bauschinger effect, yield surface contraction, permanent softening, and nonlinear transient behavior could be described by modifying the evolution equations of the simplified strain rate-independent distortional hardening model with a logarithmic term of strain rate. For the verification purpose, it was used the strain-rate dependent tension-compression experiments of TRIP980 and TWIP980 (Joo et al., 2019). In addition, a high speed U-draw bending test was conducted with original and pre-strained specimens. The springback prediction in high speed U-draw bending test was performed by using strain rate-independent isotropic, strain rate-dependent isotropic-kinematic and distortional hardening models. It is identified that the proposed model showed the most accurate prediction for the pre-strained specimen where the possible bilinear and trilinear path change in 0≤θpathchange≤180∘ is observed while it showed the same accuracy for the original specimen where main strain path change occur in forward-reverse manner (θpathchange=180∘).

Magnetic properties and I‐V characteristics of DC magnetron sputtered [Co (0.2 nm)/Ni (0.4 nm)]10 thin films

AbstractA set of [Co(0.2 nm)/Ni(0.4 nm)]10 multilayers (MLs) thin films were fabricated on silicon and glass substrate under various distinct conditions (i) as‐prepared films without an under‐layer, (ii) films with a copper [Cu(2 nm)] underlayer (UL), (iii) films with an in situ annealed Ta/Cu UL during sputtering, and (iv) films with post‐annealing treatment, by using a DC magnetron sputtering machine. The [Co/Ni] MLs thin films prepared under various conditions exhibit in‐plane magnetic anisotropic behavior except as‐prepared films which show isotropic behavior. The maximum saturation magnetization was observed in the as‐prepared films prepared on both silicon and glass substrate. The Ta/Cu UL in situ annealing followed by post‐annealing films exhibit highest coercivity, moderate saturation magnetization but lowest squareness in contrast to the films deposited under other conditions. The I‐V curves of the films show diode like behavior with breakdown voltage of 42, 58, 14, and 21 V for [Co/Ni] MLs under four different conditions.

Arctic temperature effects on the mechanical properties and failure modes of photopolymer resin for sandwich composite core' materials

The increased marine activity in the Arctic Circle presents significant challenges for naval structures operating in extreme conditions, such as temperatures as low as -60°C (Arctic temperature, AT). This study uniquely investigates the potential of Formlabs' “Durable resin” as a core material for sandwich composites. It focuses explicitly on its mechanical response under these extreme Arctic conditions, a largely unexplored area in current materials research. Durable resin's quasi-static tensile, flexural, and compressive behaviors were tested at both room temperature (RT) and AT. Finite element models were developed to explain observed failure mechanisms. At AT, the resin showed isotropic behavior with notable improvements, including a 318% increase in tensile modulus, 322% rise in ultimate tensile strength, 450% increase in flexural modulus, and 460% improvement in compressive modulus, though strain at failure decreased. Failure modes varied by temperature: tensile and flexural fractures consistently occurred at the midsection, while compressive samples at AT failed via axial splitting, compared to barreling at RT. This study's findings contribute to the foundational understanding needed to develop materials that endure extreme Arctic environments, underscoring the promise of Durable resin for Arctic exploration despite its reduced ductility under AT conditions.

Extrusion‐Based Additive Manufacturing of Cranial Implants Using High‐Performance Polymers: A Comparative Study on Mechanical Performance and Dimensional Accuracy

Fused filament fabrication (FFF) offers great potential to fabricate patient‐specific implants to treat large size defects resulting from craniectomy. Such cranial implants impose critical requirements on material and design. So far, the field has focused on printing cranial implants from polyetheretherketone (PEEK), which is semicrystalline in nature and, therefore, not ideal for FFF because of warping and nonhomogeneous crystallization. Consequently, this work aims at exploring alternative amorphous high‐performance polymers. The tensile and flexural mechanical properties of printed samples from PEEK, polyetherketoneketone (PEKK), and polyphenylsulfone (PPSU) according to ISO standards are compared. Testing of specimens obtained from three orthogonal build directions reveals nearly isotropic mechanical behavior (e.g. ultimate tensile strength differed no more than 8% between print orientations). This enables printing of patient‐specific cranial implants in vertical orientation with minimal support structures, which result in dimensional accuracies in the clinically acceptable range for craniofacial reconstructions. Mechanical assessment via an in‐house designed indentation set‐up shows that both PEKK and PPSU should be considered valid alternatives to PEEK for cranial implants. This work showcases the maturity of FFF for high‐performance polymers and leverages it for complex patient‐specific geometries such as a cranial implant.

Lattice Structures-Mechanical Description with Respect to Additive Manufacturing.

Lattice structures, characterized by their repetitive, interlocking patterns, provide an efficient balance of strength, flexibility, and reduced weight, making them essential in fields such as aerospace and automotive engineering. These structures use minimal material while effectively distributing stress, providing high resilience, energy absorption, and impact resistance. Composed of unit cells, lattice structures are highly customizable, from simple 2D honeycomb designs to complex 3D TPMS forms, and they adapt well to additive manufacturing, which minimizes material waste and production costs. In compression tests, lattice structures maintain stiffness even when filled with powder, suggesting minimal effect from the filler material. This paper shows the principles of creating finite element simulations with 3D-printed specimens and with usage of the lattice structure. The comparing of simulation and real testing is also shown in this research. The efficiency in material and energy use underscores the ecological and economic benefits of lattice-based designs, positioning them as a sustainable choice across multiple industries. This research analyzes three selected structures-solid material, pure latices structure, and boxed lattice structure with internal powder. The experimental findings reveal that the simulation error is less than 8% compared to the real measurement. This error is caused by the simplified material model, which is considering the isotropic behavior of the used material PA12GB (not the anisotropic model). The used and analyzed production method was multi jet fusion.

Transversely isotropic elastoplastic behaviour in a mechanically loaded rotating disk

This article deals with the study of transversely isotropic elastoplastic behaviour in a mechanical loaded rotating disk by using transition theory and generalised strain measure. Magnesium material disk requires higher value of angular speed to yield at the inner surface as compared to the disk made of beryl material. With the effect of mechanical loading, angular speed also increases at the inner surface of the disk made of magnesium/beryl. Upon the introduction of mechanical loading, the rotating disk made of beryl material requires maximum radial stress at the inner surface as compared to disk made of magnesium material. The beryl material disk is more convenient than that of magnesium material.

Variation of Gilbert damping constant via interface induced magnetic anisotropy in LSMO/PMN-PT heterostructures

The field of spintronics is emerging at blistering pace due to its promising room-temperature applications in low-power logic-based devices. In this work, we investigate the suitability of ferromagnetic (FM) La0.7Sr0.3MnO3 (LSMO) thin film/ferroelectric (FE) Pb(Mg0.33Nb0.67)O3-PbTiO3 (PMN-PT) heterostructures for spintronic device applications through characterizing the static and dynamic magnetic properties. Due to the magnetoelastic coupling at the interface, LSMO/PMN-PT(001) is found to exhibit a 4-fold symmetry of magnetic anisotropy, while LSMO/PMN-PT(111) shows isotropic behavior at room temperature. The direction dependent Gilbert damping constant (α) estimated for the LSMO/PMN-PT(001) sample clearly shows that its values are smaller along the magnetically hard axis than along the easy axis, while no significant variation is observed for the LSMO/PMN-PT(111) sample. The electric field induced variation of α also demonstrate that the Gilbert damping is closely related to the magnetic anisotropy. The present results clearly indicate that it will be possible to realize electric field controlled spin dynamics in FM/FEs to develop futuristic spintronic devices.

Enhancing wear resistance of aluminum 6061 composites with fly ash: A sustainable approach for industrial applications

This study investigated the benefits of adding fly ash as a reinforcement material. The benefits included cost-effectiveness, improved quality, isotropic behavior, and environmental advantages. To improve self-lubrication and wettability behavior, Al6061 alloy composites were fabricated with different amounts of fly ash (0%, 2%, 4%, 6%, and 8% by weight), along with a fixed amount of graphite (3wt.%) and magnesium (2wt.%). Wear tests were conducted using Taguchi’s Design of Experiment (DoE) approach on the composites. The optimized composition with 6% fly ash exhibited the least wear rate under the test conditions of load = 10 N, sliding velocity = 3 m/s, and sliding distance = 2 km. SEM images revealed a uniform distribution of fly ash and graphite reinforcement in the matrix, contributing to enhanced wear resistance. The composites exhibited fewer scratches and plastically deformed surfaces, indicating a decrease in wear rate and increased wear resistance with higher fly ash content. ANOVA were used, and four parameters were identified to be critical, Composition at 34%, Sliding Distance at 27%, load at 23%, and Sliding Velocity at 12% contribution with a statistical confidence of 95%. This research contributes to developing cost-effective and environmentally sustainable materials with improved mechanical properties. It makes them suitable for various industrial applications, such as the automotive industry, where wear resistance is essential.

Research of Acoustic Emission Characteristics and Applicability of Artificial Intelligence for Source Localization

Within this research, the deployment of artificial intelligence for the localization of acoustic emissions (AE) is being investigated. In detail, series of experiments were conducted on a plate of granite with homogeneous and isotropic material behavior. Acoustic emissions could be generated by the breaking of pencil leads, as well as the impact of rice grains and steel balls on 81 specific positions with a distance of 50 mm in both horizontal axes to each other. The response of the system was recorded using 16 acoustic emission sensors, of which 8 sensors were positioned on each surface side of the plate. In further steps the data could be processed, so that the resulting characteristic signal features could be translated into spec-trograms and furthermore being used as input for the artificial intelligence. Additionally, the corresponding source locations appeared as labels. Both, the signal features as well as the labels, could be implemented in the process of supervised learning using a convolutional neural network (CNN). The results of this network indicated a validation accuracy of over 99% as well as a low loss value by classifying the inserted features to the right labels. Thus demonstrates the excellent applicability of artificial intelligence for the source localization of acoustic emission (AE).

Isotropic compression behavior of salinized unsaturated agricultural soil: An experimental and constitutive investigation

Salinity-induced soil degradation is a significant challenge in coastal reclamation areas, impacting agricultural productivity and infrastructure development. Variations in soil compression and deformation caused by changes in salinity warrant further investigation, particularly for agricultural applications. This study explores the relationship between soil pore water salinity and compressibility by conducting isotropic compression tests on salinized unsaturated agricultural soils treated with distilled water, 0.5 mol/L and 1 mol/L sodium chloride (NaCl) and calcium chloride (CaCl2) solutions. The results demonstrate that the type and concentration of salts significantly affect the compression behavior of these soils. The constitutive parameters were calibrated based on the experimental data. To account for osmotic suction, Barcelona Basic Model (BBM) was adjusted. The findings indicate that as pore water salinity increases, soil compressibility decreases, reflected by a compression index (Cc), and higher pre-consolidation stress (py). This modification aimed to quantify the impact of pore water salinity on soil compression. To validate the constitutive model, a numerical analysis of an isotropic compression test was carried out. This study contributes to our understanding of the isotropic compression behavior of coastal saline soil, proposes a constitutive framework for predicting soil responses under different salt conditions, and provides theoretical support for engineering construction in coastal reclamation areas.

Combined analytical and numerical modelling of the electrical conductivity of 3D printed carbon nanotube-cementitious nanocomposites

This study explores the electrical properties of 3D-printed carbon nanotube (CNT)-cementitious nanocomposites using a dual modelling approach that integrates micromechanics with finite element (FE) analysis for self-sensing applications. 3D-printed cementitious structures are prone to early crack formation, and incorporating CNTs enhances the material’s electrical conductivity, enabling a built-in health monitoring system. Given the critical impact of CNT dispersion, waviness, and orientation on the electrical conductivity, a theoretical model was developed to incorporate these factors. Experimental tests were conducted to evaluate the material’s conductivity and mechanical performance, and to validate the model. The results show that CNTs align with the printing direction at a 3D-printed layer’s surface, while maintaining isotropic behaviour at the core. Additionally, although the CNTs aggregate, they do not entangle with each other, instead creating conductive networks within the bundles. Moreover, the CNTs are not straight but wavy, which affects the material’s electrical conductivity. Based on the experimental results and the analytical model, a finite element model was developed to predict the conductivity of printed layers, accounting for varying CNT orientations throughout the layer. The results indicate that the model overestimates 3D-printed materials’ conductivity, suggesting that further studies are needed to account for interlayer effects on the measurements.

Stress-strain curve estimation from micropillar compression with transverse contraction effect

The Focused Ion Beam (FIB) technique and the associated compression testing capabilities provide versatile access to understanding the microstructural behaviour of materials. Among many objectives, determining the stress-strain relationship from experimental or numerical force-displacement data remains a fundamental challenge. However, for micropillers under compression, the inside deformation constraint is complex like in components and the transformation of a measured force-displacement curve into an accurate uniaxial stress-strain curve is not straightforward. In this context, in a previous numerical based analysis for perfect volume constancy or incompressibility the determination of reliable and accurate stress-strain curves from nonlinear load-deformation curves of micropillers was already verified. In the case of transverse contractions, however, numerical simulations of micropillers provide unexpected force-displacement behaviour, i.e. their force-displacement curves are almost superimposing and are very close to the force-displacements for incompressibility. This effect implies, that transverse contraction would have no contributions in micropillar compression. In contrast, independent simulations using a single finite element accurately explore the true uniaxial stress-strain behaviour for the whole range of transverse contractions. These are considered as the reference behaviour and are also treated by an analytical expression. With the presented new stress-strain estimation approach, including transverse contraction, any force-displacement curve from a micropillar under compression can be stepwise corrected. The first step of the new stress-strain curve estimation method, including transverse contraction, is carried out in the same way as in the preceding analysis for incompressibility, followed by further steps to obtain the final true stress-strain curve. Although the presented numerical analysis is exemplarily performed for the behaviour of fused silica, but the stress-strain approach is in the same manner generally applicable for a material behaviour with other stress-strain curves. The assumption behind is isotropic and nonlinear material behaviour.

Structural Optimization of a Large-Scale 3D-Printed High-Altitude Propeller Blade with Experimental Validation

This paper presents a structural optimization of a 3D-printed thermoplastic-core propeller blade for high-altitude unmanned aerial vehicles using a genetic algorithm. It aims to minimize the weight of the blade by creating longitudinal holes and spars and to minimize the blade tip deflection during operation at an altitude of 16 km. The objective is to check the validity of a 3D-printed material modeling approach for large-scale and more complex 3D-printed parts, such as hollow twisted blades. The approach is based on attentively selecting the printing parameters that reduce the anisotropy of the 3D-printed parts. The linear isotropic behavior of 3D-printed Polylactic Acid and Acrylonitrile Butadiene Styrene M30 tensile samples, which have been tested at ambient and low temperatures (−60°C), is utilized to numerically predict the experimental deformation and natural frequencies of 3D-printed substitute and twisted full blades with good accuracy. The validated linear isotropic model of each material is then used to evaluate the objectives and the constraints of the two-objective optimization process using one-way fluid–structure interaction. Four optimized blades have been selected from the Pareto fronts as candidates, printed, and tested in bending and vibration. The numerical and experimental results of the candidate blades in terms of deformation and natural frequencies are in good agreement, proving the validity of the present macroscale approach for large-scale hollow twisted blades.

Investigation on the effects of deposition strategy on the mechanical characteristics and microstructure of austenitic stainless steel 308LSi manufactured via wire arc additive manufacturing

This study examines the impact of deposition strategy on ASS 308LSi thin-walled structure manufactured via the Wire Arc Additive Manufacturing (WAAM) technique on the microstructural characteristics, tensile strength, microhardness, Charpy impact testing, and fracture morphology of the WAAM 308LSi. The analysis of the microstructure reveals that the deposition strategy promotes transitioning from columnar to equiaxed fine grain structure. The tensile strength results show that specimens with a 45° deposition strategy exhibit lower anisotropy and higher tensile properties compared to those with a 0° deposition strategy, with improvements of 33.1% in the transverse direction and 26.7% in the longitudinal deposition directions, respectively. The microhardness in WAAM SS308LSi demonstrates variations in the bottom, middle, and top regions, with the highest average value observed at a 45° deposition strategy (213.3 ± 6.5 HV, 201.1 ± 10.7 HV, and 191.5 ± 5.2 HV) as well. The impact testing results indicate that the highest absorbed energy occurs at a 45° deposition strategy, with 75 ± 4.2 J and 74 ± 4.0 J for the transverse and longitudinal directions, respectively. The fractures observed during testing exhibit ductile characteristics, with the presence of dimples and particles. This study demonstrates the significant potential of the 45° deposition strategy with the implementation of double-sided substrate deposition, resulting in a refined microstructure, nearly isotropic behavior, and excellent mechanical performance.

Alternating current electrophoretic deposition of maleic anhydride modified chitosan on Ti implants to combat biofilm formation

Chitosan, a cationic biopolymer, holds promise for diverse applications, including dental implant surface modification, due to its biocompatibility, non-toxicity, and antimicrobial properties. However, its limited water solubility at neutral pH complicates its use in alternating current electrophoretic deposition (AC-EPD). This study explores the novel use of water-soluble maleic anhydride modified chitosan (MA-CS) in AC-EPD to create antimicrobial coatings on titanium substrates. We optimize AC-EPD parameters for uniform MA-CS coatings and compare AC-EPD with conventional dipping. AC-EPD MA-CS coatings exhibit enhanced surface topography and amphiphilic, isotropic behavior, while other MA-CS-treated samples display anisotropic, monopolar behavior. We assess AC-EPD MA-CS-coated metallic substrates' biofunctionality, focusing on protein adsorption and antimicrobial properties. These coatings effectively adsorb proteins through diverse interactions with bovine serum albumin. To combat peri-implant diseases, we evaluate antimicrobial activity against oral bacterial communities, showing that AC-EPD successfully concentrates water-soluble MA-CS on titanium without compromising its biological performance. In summary, this study highlights AC-EPD as a versatile, efficient method for depositing polysaccharides in biomedical applications. It offers the potential for enhancing dental implant surface antimicrobial properties, addressing peri-implant diseases, and promoting overall dental health.

Data-driven methods for computational mechanics: A fair comparison between neural networks based and model-free approaches

We present a comparison between two approaches to modelling hyperelastic material behaviour using data. The first approach is a novel approach based on Data-driven Computational Mechanics (DDCM) that completely bypasses the definition of a material model by using only data from simulations or real-life experiments to perform computations. The second is a neural network (NN) based approach, where a neural network is used as a constitutive model. It is trained on data to learn the underlying material behaviour and is implemented in the same way as conventional models. The DDCM approach has been extended to include strategies for recovering isotropic behaviour and local smoothing of data. These have proven to be critical in certain cases and increase accuracy in most cases. The NN approach contains certain elements to enforce principles such as material symmetry, thermodynamic consistency, and convexity. In order to provide a fair comparison between the approaches, they use the same data and solve the same numerical problems with a selection of problems highlighting the advantages and disadvantages of each approach. Both the DDCM and the NNs have shown acceptable performance. The DDCM performed better when applied to cases similar to those from which the data is gathered from, albeit at the expense of generality, whereas NN models were more advantageous when applied to wider range of applications.

Mechanical modeling of the petiole-lamina transition zone of peltate leaves

Plant leaves have to deal with various environmental influences. While the mechanical properties of petiole and lamina are generally well studied, only few studies focused on the properties of the transition zone joining petiole and lamina. Especially in peltate leaves, characterised by the attachment of the petiole to the abaxial side of the lamina, the 3D leaf architecture imposes specific mechanical stresses on the petiole and petiole-lamina transition zone. Several principles of internal anatomical organisation have been identified. Since the mechanical characterisation of the transition zone by direct measurements is difficult, we explored the mechanical properties and load-bearing mechanisms by finite-element simulations. We simulate the petiole-lamina transition zone with five different fibre models that were abstracted from CT data. For comparison, three different load cases were defined and tested in the simulation. In the proposed model, the fibres are represented in a smeared sense, where we considered transverse isotropic behavior in elements containing fibres. In a pre-processing step, we determined the fibre content, direction, and dispersion and fed them into our model. The simulations show that initially, matrix and fibres carry the load together. After relaxation of the stresses in the matrix, the fibres carry most of the load. Load dissipation and stiffness differ according to fibre arrangement and depend, among other things, on orientation and cross-linking of the fibres and fibre amount. Even though the presented method is a simplified approach, it is able to show the different load-bearing capacities of the presented fibre arrangements. Statement of significanceIn plant leaves, the petiole-lamina transition zone is an important structural element facilitating water and nutrient transport, as well as load dissipation from the lamina into the petiole. Especially in peltate leaves, the 3D leaf architecture imposes specific mechanical stresses on the petiole-lamina transition zone. This study aims at investigating its mechanical behavior using finite-element simulations. The proposed continuum mechanical anisotropic viscoelastic material model is able to simulate the transition zone under different loads while also considering different fibre arrangements. The simulations highlight the load-bearing mechanisms of different fibre organisations, show the mechanical significance of the petiole-lamina transition zone and can be used in the design of a future biomimetic junction in construction.

An experimental investigation into crashworthiness of filament wound intra-yarn hybrid glass/jute epoxy composites tubes under quasi-static axial and lateral compression

The increasing demand for sustainable materials in the automotive industry has driven the research towards exploration of natural fiber composites for crash structures. This study investigates the quasi-static axial and lateral crushing behavior of hybrid glass/jute fiber epoxy tubes. Intra-yarn hybrid mixing ratios of jute and glass fibers were tested to evaluate the feasibility of using natural fibers as eco-friendly alternatives to traditional synthetic composites. A total of five different configurations were fabricated using filament winding process. The experimental results were analyzed for collapsing behavior, failure modes, and energy absorption characteristics. The hybrid epoxy tubes revealed fiber-matrix fracturing, local buckling, and delamination as three primary failure modes under crushing tests. The hybrid configuration with 25 % jute fiber and 75 % glass fiber demonstrated optimal crashworthiness performance, achieving the highest specific energy absorption (SEA) values of 15.85 J/g under axial loading and 2.96 J/g under lateral loading. The configurations with higher jute content of 50 % and 75 %, showed decreasing SEA and crush force efficiency (CFE) values, with brittle fracturing and delamination as dominant failure modes, indicating a trade-off between weight and energy absorption efficiency. The neat glass fiber configuration maintained nearly consistent CFE values of 0.55 and 0.56, between axial and lateral loadings respectively, demonstrating isotropic behavior in energy absorption. Conversely, the neat jute fiber configuration improved SEA to 12.14 J/g under axial loading but exhibited significant limitations under lateral loading, with SEA decreasing to 0.69 J/g. Visual examination of crushed samples highlighted local buckling in GF configurations and brittle fracturing in hybrid and neat jute fiber configurations. The scanning electron microscope (SEM) analysis provided detailed insights into the microstructural characteristics and failure mechanisms, highlighting the inter-laminar debonding between the jute and glass fibers in hybrid configuration. By evaluating the combined effects of hybridization and loading conditions, the present study contributes to developing eco-friendly and efficient materials for automotive safety, aligning with industry sustainability goals.

First-principles investigation of lanthanides diffusion in HCP zirconium via vacancy-mediated transport

The diffusion of lanthanide fission products plays an important role in the growth of the fuel-cladding chemical interaction (FCCI) region in metallic fuels. The use of a Zr interdiffusion barrier may mitigate the transport of lanthanides from the fuel to the cladding, but the efficacy of such a liner is not yet known. In this paper, the stability and vacancy-mediated diffusion of La, Ce, Pr, and Nd in hexagonal close-packed (HCP) Zr is investigated via density functional theory (DFT) calculations and self-consistent mean field (SCMF) analysis. DFT is used to calculate the formation, binding, and migration energies of vacancies and vacancy-solute pairs. The DFT energetics are used in the KineCluE code to calculate the Onsager transport coefficients. La is found to be the fastest diffusing species in HCP Zr and experiences an almost isotropic diffusion behavior. The other three species (Ce, Pr, and Nd) demonstrate anisotropic diffusion where the diffusion in the basal planes is significantly faster than that along the c-axis. The calculated lanthanide diffusivities in HCP Zr are fitted to an Arrhenius relation and the activation energies and prefactors are reported for the first time. Furthermore, the vacancy drag and the segregation tendencies were analyzed using the calculated off-diagonal transport coefficients. According to our vacancy-mediated diffusion model, lanthanides are expected to be enriched at vacancy sinks at low temperatures, while at high temperatures, lanthanides are depleted at sinks and will preferably diffuse into the bulk. The enrichment/depletion transition temperature depends on the diffusion direction (basal or axial) and hence will be controlled by the grain texture and orientation.

Hierarchical triply periodic minimal surface shell lattices with superior isotropic elasticity: Design guidelines, fabrication, and validation

Hierarchical triply periodic minimal surface (TPMS) shell lattices exhibit a wide range of tailorable properties that can be fine-tuned by lattice design. Recent advances in additive manufacturing towards high resolution enable the precise fabrication of hierarchical TPMS lattices. However, the isotropic behavior of hierarchical TPMS lattices has received little attention. In this study, we focus on the design of hierarchical TPMS lattices to explore their superior isotropic elasticity. By considering three unique geometric parameters of hierarchical TPMS: cell length ratio, relative density, and order number, multiple representative isotropic hierarchical TPMS lattices can be achieved at the same given relative density, which significantly expands its design space. The resultant lattices retain a minimal mid-surface and exhibit a large range of tailorable stiffness. To validate their isotropic elasticity, high-precision laser powder bed fusion was adopted to fabricate representative isotropic lattices and their anisotropic counterparts. Morphology observation and micro-CT scan show that the fabricated samples are dense, and their geometries are highly consistent with the designed models. Quasi-static compression tests further confirm the isotropic elasticity in the new designs. Moreover, a prediction rule was proposed to assess whether an isotropic hierarchical TPMS lattice can be obtained from two selected single-level lattices, which significantly enhances the design efficiency. As a result, the design method and principles can be summarized in this study to provide effective design guidelines to swiftly create hierarchical shell lattices with superior isotropic elasticity.