Homogeneous Material Research Articles

Effective Multi-Layered Structure Design with Carbon-Based Hybrid Polymer Nanocomposites Using Evolutionary Algorithms

Electromagnetic wave-absorbing materials (EMAMs) and structures are crucial in aerospace and electronic communications due to their ability to absorb electromagnetic waves. The development of materials that are lightweight, sustainable, and cost-effective, exhibiting high-performance absorption across a broad frequency spectrum, is therefore important. However, homogeneous electromagnetic absorbing materials require assistance to meet all these criteria. Therefore, developing multi-layer absorbing coatings is essential for enhancing performance. The present study uses 21 different composites of varying weight fractions of polypropylene, graphene nanoplatelets, and multiwall carbon nanotubes nanocomposites to develop multi-layer absorbing materials and optimize their performance. These multi-layer carbon polymer nanocomposites were meticulously constructed using evolutionary algorithms like Non-sorted Genetic Algorithm-II and Particle Swarm Optimization to achieve ultra-broadband electromagnetic wave absorption capabilities. Among the designed electromagnetic absorbing materials, a two-layer model, i.e., 1.5 wt% MWCNT/PP/epoxy with a thickness of 1.052 mm and 2.7% GNP/PP/epoxy with a thickness of 4.456 mm totaling 5.506 mm, was identified as optimal using NSGA-II. The structure has exhibited exceptional absorption performance with a minimum reflection loss of −21 dB and a qualified bandwidth extending to 4.2 GHz. PSO validated and optimized this structure, confirming NSGA-II’s efficiency and effectiveness in quickly obtaining optimal solutions. This broadband absorber design combines the structure design and material functioning through additive manufacturing, allowing it to absorb well over a wide frequency range.

Functionally Graded Impact Attenuator Using Bonded Construction

ABSTRACTAutomotive collisions are one of the major causes of death in the European Union, especially in childhood and adolescence. However, improvements in vehicle safety cannot be achieved only by increasing the size and dimensions of the structures, as this demands more materials and more costly manufacturing processes, which leads to an increased resource expenditure and lowered sustainability. Moreover, the increase of the structure size raises the vehicle's weight, leading to added fuel consumption, which cannot be accepted considering modern environmental regulations. To solve these issues, the application of bonded joints using the combination of several adherends materials, such as steel and aluminium alloys and fibber‐reinforced polymers with crash‐resistant adhesives presents itself as a novel solution, allowing to attain enhanced joint strength, energy absorption and weight reduction. The present works introduce a novel concept of an impact attenuator using bonded, geometrically optimized using the concept of functionally graded adherends to maximize energy absorption by ensuring that a load‐bearing path is kept during impact, converting the impact energy into the plastic deformation of panels with variable mechanical properties, tailored to withstand specific load cases, fulfilling a gap in the literature regarding impact absorption devices that combines graded materials and bonded construction. The results obtained present an increase in the energy absorption values of the graded impact attenuators above 200% when compared to the homogenous materials.

Spectrum of the Maxwell Equations for a Flat Interface Between Homogeneous Dispersive Media

The paper determines and classifies the spectrum of a non-self-adjoint operator pencil generated by the time-harmonic Maxwell problem with a nonlinear dependence on the frequency for the case of two homogeneous materials joined at a planar interface. We study spatially one-dimensional and two-dimensional reductions in the whole space R and R2. The dependence on the spectral parameter, i.e. the frequency, is in the dielectric function and we make no assumptions on its form. These function values determine the spectral sets. In order to allow also for non-conservative media, the dielectric function is allowed to be complex, yielding a non-self-adjoint problem. The whole spectrum consists of eigenvalues and the essential spectrum, but the various standard types of essential spectra do not coincide in all cases. The main tool for determining the essential spectra are Weyl sequences.

NMR-Based Investigation of Pore–Fracture Structure Heterogeneity in Deep Coals of Different Macrolithotypes in the Daning-Jixian Block, Ordos Basin

Deep coalbed methane (CBM) demonstrates significant production potential, and a fervent exploration and development boom is currently underway in China. The permeability of coal reservoirs is heavily influenced by pore–fracture structure heterogeneity. Some researches have been conducted on deep coals’ pore–fracture structure; however, these studies mostly consider coal as a homogeneous material, neglecting the heterogeneity of the macrolithotypes within the coal. In this study, 33 deep coals with burial depths of more than 2000 m were obtained from the Daning-Jixian block of the Ordos Basin, covering all macrolithotypes: bright coal (BC), semi-bright coal (SBC), semi-dull coal (SDC), and dull coal (DC). These samples were subjected to three sets of NMR tests in dry, fully saturated, and irreducible water conditions, with the pore–fracture structure characteristics being analyzed. The results demonstrate that the sampled deep coals’ pore–fracture structure is highly heterogeneous, with transitional pores being dominant, followed by mesopores, “macropores and fractures”, and micropores. The NMR T2C ranges from 0.61 to 2.44 ms, with an average of 1.19 ms; a higher T2C value indicates more developed micropores. The ranges for producible water porosity (φpr) and producible water saturation (Spr) are 0.31–7.24% (avg. 2.42%) and 6.97–71.47% (avg. 31.06%), respectively. Both of them exhibit a high positive correlation with the total volumes of “macropores and fractures” and mesopores. Compared to SDC and DC, the BC and SBC, especially the former, overall contain more “macropores and fractures” and mesopores, fewer transitional pores and micropores, and higher φpr and Spr. These findings suggest that regions with abundant BC and SBC should be prioritized during deep CBM exploration and production due to the inherently superior permeability and gas extraction potential of BC and SBC, and these coals are likely to require less intensive stimulation to achieve higher recovery rates and could provide more sustainable gas production over time.

Optimal local truncation error method on unfitted Cartesian meshes for solution of 3-D wave and heat equations for heterogeneous materials

In the paper we develop the optimal local truncation error method (OLTEM) with the non-diagonal and diagonal mass matrices on unfitted Cartesian meshes for the 3-D time-dependent wave and heat equations for heterogeneous materials with irregular interfaces. 27-point stencils that are similar to those for linear finite elements are used with OLTEM. There are no unknowns for OLTEM on interfaces between different materials; the structure of the global discrete equations is the same for homogeneous and heterogeneous materials. The calculation of the unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations, includes the use of the interface conditions and the entire PDE in derivations, and yields the optimal fourth order of accuracy of OLTEM with the non-diagonal mass matrix. This is two order higher than for linear finite elements with similar 27-point stencils. OLTEM with the diagonal mass matrix includes the rigorous calculation of the diagonal mass matrix and provides the optimal second order of accuracy. The 3-D numerical results for heterogeneous materials with irregular interfaces show that at the same number of degrees of freedom, OLTEM is even much more accurate than high-order (up to the 7-th order - the highest order in the commercial code COMSOL) finite elements with much wider stencils. Compared to linear finite elements with similar 27-point stencils, at an accuracy of 0.1% OLTEM decreases the number of degrees of freedom by 550–7300 times. This leads to a huge reduction in computation time.A new 3-D post-processing procedure has been developed with OLTEM for the calculation of the spatial derivatives of time-dependent numerical solutions. The spatial derivatives for each grid point are calculated with the help of one compact 27-point stencil (the same as that in basic computations). In contrast to known post-processing procedures, the new approach includes also the use of the time derivatives of the function, the interface conditions and the original PDE. The spatial derivatives of the OLTEM solutions calculated with the new post-processing procedure are much more accurate compared to those obtained by high-order (up to the 7-th order) finite elements with much wider stencils. At an accuracy of 0.1% for the spatial derivatives, OLTEM decreases the number of degrees of freedom by 1.9⋅106–6⋅109 times compared to linear finite elements. The new post-processing procedure can be equally applied to the calculation of the partial derivatives obtained by other numerical methods as well as to the numerical results for other PDEs.Due to the huge reduction in the computation time compared to existing methods and the use of trivial unfitted Cartesian meshes that are independent of irregular geometry, the proposed technique does not require remeshing for the shape change of irregular geometry and it will be effective for many design and optimization problems as well as for multiscale problems without the scale separation.

Laser interaction with undercritical foams of different spatial structures

The interaction of high-power laser pulses with undercritical foams produced by different techniques but with the same average density is studied at the PALS laser facility. The spatial–temporal evolution of X-ray emission is observed using an X-ray streak camera, electron and ion temperatures are measured by X-ray spectroscopy, and hot-electron production is characterized by monochromatic X-ray imaging. Transmission of a femtosecond laser probe pulse through foams is observed in the near and far fields. In spite of large differences in pore size and foam structure, the velocity of ionization front propagation is quite similar for all the foams studied and is slower than that in a homogeneous material of the same average density. The ion temperature in the plasma behind the ionization front is a few times higher than the electron temperature. Hot-electron production in plastic foams with small pores is strongly suppressed compared with that in solid targets, whereas in foams produced by additive manufacturing, it is significantly increased to the level observed in bare copper foil targets.

Vibrational Analysis of Building Structures with Irregularities

This paper presents a mathematical model for predicting vibrations in lightweight, timber-based floor/ceiling structures, enhanced to account for irregularities in joist shape and stiffness, as well as floor stiffness. Building on a prior model that assumed precise geometry and homogeneous material properties, the study now incorporates real timber measurements via the power spectral density of irregularities to incorporate their impact on the system’s vibrational response, including mid-frequency vibrations. Existing results underscore the critical role of component connections in shaping vibration behavior, while the present paper gives new principles for building a model to assess how uncertainties in these connections or material properties affect the overall structural response. This new model maintains the property of efficient computation so that irregularities in the components may be included in the design stage to improve the mid-frequency performance of lightweight, timber-framed structures.

A comparative study on Arc- and vacuum induction-melting for Ti16.6Zr16.6Hf16.6Co10Ni20Cu20 high entropy shape memory Alloy Production

Arc-melting (AM) as a primary method for casting high entropy alloys (HEAs) ensures rapid alloy screening with minimal material input, high cost-effectiveness, and high cooling rates. However, the limitations of AM on a laboratory scale, particularly its constrained sample size and the necessity for remelting steps to ensure homogeneity, hampers thorough mechanical and functional testing of bulk materials. Therefore, this study features a comparative analysis between AM and vacuum induction-melting (VIM) techniques for High Entropy Shape Memory Alloys (HE-SMAs) production, focusing on the senary alloy Ti16.6Zr16.6Hf16.6Co10Ni20Cu20, known for its potential functional applications and high sensitivity to material inhomogeneity. The alloy’s composition, including high-melting point elements like Hf, Ti and Zr, makes it a well-suited candidate for assessing the capabilities of VIM in producing homogeneous bulk materials. The employment of binary pre-alloys in both AM and VIM processes reduced the necessity for remelting steps and ensured better initial quality for subsequent heat treatments. A homogenization treatment at 900 °C for 100 h of an AM-produced senary alloy showed only slight improvements compared to the same alloy produced via VIM, largely due to the slow diffusion of the larger Hf and Zr atoms from the dendrites into the solid solution. This suggests that VIM can achieve comparable levels of homogenization in substantially less time than required for AM-treated samples. The findings finally indicate that by using VIM, when combined with binary pre-alloys, one achieves more homogeneous alloys with reduced heat-treatment time, making it a viable method for HE-SMA production.

Ground motion characteristics of subshear and supershear ruptures in the presence of sediment layers

SUMMARY We investigate the impact of sediment layers on ground motion characteristics during subshear and supershear rupture growth. Our findings suggest that sediment layers may lead to local supershear propagation, affecting ground motion, especially in the fault parallel (FP) direction. In contrast to homogeneous material models, we find that in the presence of sediment layers, a larger fault normal (FN) compared to FP particle velocity jump, reflects shear propagation at depth but does not rule out shallow supershear propagation. Conversely, a large FP compared to FN particle velocity jump indicates supershear propagation at depth. In the presence of a shallow layer, we also uncover a non-monotonic behaviour in the sediment’s influence on supershear transition and ground motion characteristics. During supershear propagation at depth we observe that sediment layers contribute to enhancing FP velocity pulses while minimally affecting the FN component. Furthermore, in the limit of global supershear propagation we identify local supersonic propagation within the sediment layers that significantly alters the velocity field around the rupture tip as observed on the free surface, creating both dilatational and shear Mach cones. In all our models with sediments we also find a significant enhancement in the fault vertical component of ground velocity. This could have particular implications for hazard assessments, such as in applications related to linear infrastructure, or a higher propensity to tsunami wave generation. Our research unravels the importance of considering heterogeneous subsurface material distribution in our physical models as they can have drastic implications on earthquake source physics.

Estimating nonlinear anisotropic properties of healthy and aneurysm ascending aortas using magnetic resonance imaging.

An ascending aortic aneurysm is an often asymptomatic localized dilatation of the aorta. Aortic rupture is a life-threatening event that occurs when the stress on the aortic wall exceeds its mechanical strength. Therefore, patient-specific finite element models could play an important role in estimating the risk of rupture. This requires not only the geometry of the aorta but also the nonlinear anisotropic properties of the tissue. In this study, we presented a methodology to estimate the mechanical properties of the aorta from magnetic resonance imaging (MRI). As a theoretical framework, we used finite element models to which we added noise to simulate clinical data from real patient geometry and different properties of healthy and aneurysmal aortic tissues collected from the literature. The proposed methodology considered the nonlinear properties, the zero pressure geometry, the heart motion, and the external tissue support. In addition, we analyzed the aorta as a homogeneous material and as a heterogeneous model with different properties for the ascending and descending parts. The methodology was also applied to pre-surgical,in vivo MRI data of a patient who underwent surgery during which an aortic wall sample was obtained. The results were compared with those obtained from ex vivo biaxial test of the patient's tissue sample. The methodology showed promising results after successfully recovering the nonlinear anisotropic material properties of all analyzed cases. This study demonstrates that the variable used during the optimization process can affect the result. In particular, variables such as principal strains were found to obtain more realistic materials than the displacement field.

Refined speckle contrast estimation in OCT based on compensation of scattering-related distortions of speckle pattern parameters

Abstract Speckle contrast (SC) parameters in optical coherence tomography (OCT) scans are formed by the interplay of several factors—local level of optical wave backscattering by the material inhomogeneities, parameters of spatial distribution of the latter and the degree of cumulative optical wave attenuation during its fourth-and-back propagation. For the optical wavelengths used in OCT, this attenuation is usually dominated by the influence of scattering in the visualized turbid tissues rather than by absorption. For sufficiently high concentrations of scatterers (at least a few scatterers in the coherence volume) characterized by comparable scattering strengths and a fairly homogeneous distribution in space, the interference of locally scattered waves should be characterized by a Rayleigh distribution of speckle amplitudes, for which the local SC tends to 0.52. Equivalently, in terms of speckle intensities, the local SC tends to unity. Local spatial inhomogeneities or strongly uneven scattering strengths lead to the appearance of increased values of SC, which may serve as a diagnostic feature of some tissue components in OCT images. At the same time, in comparison to surface speckles formed by coherent-light scattering from rough surfaces, OCT-beam attenuation during its fourth-and-back propagation may introduce intensity inhomogeneities in OCT scans even for homogeneous tissue areas. This effect results in artefactual distortion of the visible SC in comparison with the above-mentioned expected value. Moreover, the presence of individual strong scatterers may additionally non-locally distort SC values due to the appearance of elongated shadows below such scatterers, which causes lateral inhomogeneities in OCT scans. Here, we propose a refined SC parameter, which is cleaned from distorting scattering-related effects in both axial and lateral directions. Depth-resolved estimation of the optical attenuation coefficient is used to restore attenuation-free OCT scans, for which the refined SC is estimated. The efficiency of the proposed approach is demonstrated using both digital OCT phantoms with highly controlled properties and experimental OCT data.

Hybrid dark-field and attenuation contrast retrieval for laboratory-based X-ray tomography

X-ray dark-field imaging highlights sample structures through contrast generated by sub-resolution features within the inspected volume. Quantifying dark-field signals generally involves multiple exposures for phase retrieval, separating contributions from scattering, refraction, and attenuation. Here, we introduce an approach for non-interferometric X-ray dark-field imaging that presents a single-parameter representation of the sample. This fuses attenuation and dark-field signals, enabling the reconstruction of a unified three-dimensional volume. Notably, our method can obtain dark-field contrast from a single exposure and employs conventional back projection algorithms for reconstruction. Our approach is based on the assumption of a macroscopically homogeneous material, which we validate through experiments on phantoms and on biological tissue samples. The methodology is implemented on a laboratory-based, rotating anode X-ray tube system without the need for coherent radiation or a high-resolution detector. Utilizing this system with streamlined data acquisition enables expedited scanning while maximizing dose efficiency. These attributes are crucial in time- and dose-sensitive medical imaging applications and unlock the ability of dark-field contrast with high-throughput lab-based tomography. We believe that the proposed approach can be extended across X-ray dark-field imaging implementations beyond tomography, spanning fast radiography, directional dark-field imaging, and compatibility with pulsed X-ray sources.

Modeling abscission of cacti branches

During evolution, various functional principles have evolved that allow plants to create predetermined breaking points for the spatially defined abscission of organs. In the plant family of cacti, some species, such as Cylindropuntia bigelovii, have fragile branch–branch junctions that serve vegetative reproduction, while in other species, such as Opuntia ficus-indica, they are very stable. The fracture behavior of these junctions has been thoroughly characterized anatomically and mechanically, the data being the prerequisite for the performance of cactus-inspired phase field simulations. We have found that models composed of homogeneous materials or material systems with low elastic modulus contrast (analogous to Cylindropuntia bigelovii) exhibit a fracture mode where cracks initiation occurs at the epidermis of the junction notch. In comparison, heterogeneous material systems with high elastic modulus contrast (similar to Opuntia ficus-indica) show fracture nucleation along the inner vascular bundles, with an increase in the maximum fracture energy by a factor of 2.2. In the high contrast heterogeneous models, the V-notch and stiffening of the dermal tissue (“periderm”) have a negligible effect on their fracture behavior. In addition, the fracture morphologies of these models resemble the rough junction fracture sites found experimentally. The knowledge gained about the geometric influences and the importance of the contrasts in the mechanical properties of the individual materials in the overall system can be transferred as functional principles to bioinspired engineering composites in order to program their fracture behavior.

An adaptive mesh refinement algorithm for crack propagation with an enhanced thermal–mechanical local damage model

This paper presents a computationally effective approach for crack propagation under mechanical and thermal loads based on an adaptive mesh refinement (AMR) approach tailored for our recently developed enhanced local damage model. The mesh-dependent issue encountered in the classical local theories is effectively mitigated by incorporation of fracture energy and element characteristic length into the damage evolution function. Our previous research has demonstrated that being equipped by a novel equivalent strain derived from the bi-energy norm concept and a new damage criterion recently proposed by Mazars et al., the model provides results comparable to the reference experimental data as well as other numerical models based on non-local/gradient damage and phase field method. In the framework of computational efficiency using finite elements, we significantly enhance the performance of our enhanced local model by considering adaptive mesh refinement (AMR). The finite element mesh is locally refined in the damaged zone, and the mesh refinement is conducted on-the-fly during the analysis. For that purpose, the damage parameter whose information is stored at integration points is selected as an indicator to mark whether an element should be refined or not after every loading step. For quadrilateral element mesh, a quad-tree technique is utilized, meaning that each marked element is further divided into four smaller quadrilateral elements. The so-called hanging nodes appear during the process, and the elements are thus treated as n-gons and are constructed by the Laplace shape functions, instead of the usual Lagranges shape functions. To show the accuracy and effectiveness of the proposed scheme, several numerical examples involving homogeneous and heterogeneous materials are studied. In these examples, the damage is induced either by only mechanical loads or by both mechanical and thermal loads.

Second-order nonlocal shifts of scattered wave-packets: What can be measured by Goos–Hänchen and Imbert–Fedorov effects?

The scattering of wavepackets with arbitrary energy dispersion on surfaces has been analyzed. Expanding up to second order in scattering shifts, it is found that besides the known Goos–Hänchen or Imbert–Fedorov spatial offset, as well as the Wigner delay time, new momentum and frequency shifts appear. Furthermore, the width of the scattered wave packet becomes modified as well, which can lead to a shrinking of pulses by multiple scattering. For a model of dielectric material characterized by a longitudinal and transverse dielectric function the shifts are calculated analytically. From the Goos–Hänchen and Imbert–Fedorov shifts one can access the longitudinal and transversal dielectric function. Perfectly aligned crystal symmetry axes with respect to scattering beam shows no Imbert–Fedorov effect. It is found that the Goos–Hänchen and Imbert–Fedorov effect are absent for homogeneous materials. Oppositely it is found that the Wigner delay time and the shrinking of the temporal pulse width allows to access the dielectric function independent on the beam geometry.

Torsion and Extension of Functionally Graded Mooney–Rivlin Cylinders

We analytically study finite torsional and extensional deformations of rubberlike material circular cylinders with the two material moduli in the Mooney–Rivlin relation assumed to be continuous functions of the undeformed radius. It is shown that under null resultant axial load on the end faces the cylinder length increases upon twisting. Furthermore, when the two moduli are affine functions of the radius the inhomogeneity parameters can be found to have the maximum shear stress occur at a pre-determined interior point. Whereas the radial stress is finite at the center of a cross-section of a homogeneous material cylinder, it may have large values for an inhomogeneous material cylinder. The closed-form solutions provided herein for the two moduli having affine, power-law and exponential functions of the radius should benefit numerical analysts verify their algorithms and engineers design soft material robots for improving their performance under torsional loads.

Influence of Mechanical Activation on the Evolution of TiSiCN Powders for Reactive Plasma Spraying

In modern materials science and surface engineering, reactive plasma spraying (RPS) holds a key position due to its ability to create high-quality coatings with unique properties. The effectiveness of this process is largely determined by the physicochemical characteristics of the initial powder materials. This study examines the effects of mechanical activation for two compositions in the TiSiCN system and their impact on the quality and performance characteristics of RPS-produced coatings. It is shown that mechanical activation induces significant changes in the crystalline structure of the powders, reducing their particle size and increasing their specific surface area, thereby enhancing the reactivity of the materials during mechanochemical reactions. These changes contribute to the formation of dense and durable coatings with improved hardness and thermal stability. Thermogravimetric analysis (TGA) results confirm that the powders retain stable thermal properties and exhibit resistance to oxidation and decomposition. X-ray structural analysis reveals multiphase structures, including TiC, SiC, and TiCN, with the TiCN phase playing a key role in ensuring coating hardness. Additionally, SEM analysis showed that the TiSiCN-2-2 coating possesses a denser and more homogeneous structure with minimal pores and microcracks, providing superior mechanical strength and wear resistance compared to TiSiCN-1-2. Cross-sectional micrographs further revealed that the TiCN + Si coating has a greater average thickness (39.87 μm) and more uniform distribution compared to Ti + SiC (35.48 μm), indicating better application control and a more homogeneous material structure. Mechanical activation significantly influences the properties of powders, allowing for the determination of optimal parameters for RPS, which is a highly efficient method for creating coatings with unique performance characteristics.

NU-NeRF: Neural Reconstruction of Nested Transparent Objects with Uncontrolled Capture Environment

The geometry reconstruction of transparent objects is a challenging problem due to the highly noncontinuous and rapidly changing surface color caused by refraction. Existing methods rely on special capture devices, dedicated backgrounds, or ground-truth object masks to provide more priors and reduce the ambiguity of the problem. However, it is hard to apply methods with these special requirements to real-life reconstruction tasks, like scenes captured in the wild using mobile devices. Moreover, these methods can only cope with solid and homogeneous materials, greatly limiting the scope of the application. To solve the problems above, we propose NU-NeRF to reconstruct nested transparent objects without requiring a dedicated capture environment or additional input. NU-NeRF is built upon a neural signed distance field formulation and leverages neural rendering techniques. It consists of two main stages. In Stage I, the surface color is separated into reflection and refraction. The reflection is decomposed using physically based material and rendering. The refraction is modeled using a single MLP given the refraction and view directions, which is a simple yet effective solution of refraction modeling. This step produces high-fidelity geometry of the outer surface. In stage II, we use explicit ray tracing on the reconstructed outer surface for accurate light transport simulation. The surface reconstruction is executed again inside the outer geometry to obtain any inner surface geometry. In this process, a novel transparent interface formulation is used to cope with different types of transparent surfaces. Experiments conducted on synthetic scenes and real captured scenes show that NU-NeRF is capable of producing better reconstruction results than previous methods and achieves accurate nested surface reconstruction under an uncontrolled capture environment.

The mechanical response of polymeric gyroid structures in an optimised orthotic insole.

This study aims to explore the mechanical behaviour of polymeric gyroid structures under compression within the context of orthotic insoles, focussing on custom optimisation for lower peak plantar pressures. This research evaluates the compressive response of gyroid structures using a combination of experimental testing and numerical modelling. Stereolithography was used to manufacture gyroid samples for experimental tests, and explicit finite element analysis was used to model the gyroid's response numerically. Hyperfoam, first-order polynomial, and second-order polynomial hyperelastic constitutive models were considered to homogenise the mechanical response of the structure. The homogenised properties of the structure were then implemented in an optimisation algorithm to obtain the optimal gyroid structure for a given subject by minimising the standard distribution of plantar pressures. Findings indicate that the compressive response polymeric gyroid structures can be represented with a homogeneous material. The hyperfoam model was chosen due to its accuracy and interpolation quality. The optimisation process successfully identified configurations that maximise the mechanical advantages of gyroid lattices, demonstrating significant improvements in plantar pressure distributions. The optimised insole showed a 30% reduction in the standard deviation of the plantar pressure and a 10% reduction in the peak stress. The optimisation method reduced peak pressures by 12.2 kPa compared to a traditional medium-density Poron orthotic insole, and 94.3 kPa compared barefoot conditions. The mechanical response of gyroid structures has successfully been modelled, analysed and homogenised. The study concludes that custom gyroid-based orthotic insoles offer a promising solution for personalised foot care.

Engineering a vanillate-producing strain of Pseudomonas sp. NGC7 corresponding to aromatic compounds derived from the continuous catalytic alkaline oxidation of sulfite lignin

IntroductionLignin is a promising resource for obtaining aromatic materials, however, its heterogeneous structure poses a challenge for effective utilization. One approach to produce homogeneous aromatic materials from lignin involves the application of microbial catabolism, which is gaining attention. This current study focused on constructing a catabolic pathway in Pseudomonas sp. NGC7 to produce vanillate (VA) from aromatic compounds derived from the chemical depolymerization of sulfite lignin.ResultsAlkaline oxidation of sulfite lignin was performed using a hydroxide nanorod copper foam [Cu(OH)2/CF]-equipped flow reactor. The flow reactor operated continuously for 50 h without clogging and it yielded a sulfite lignin stream containing acetovanillone (AV), vanillin (VN), and VA as the major aromatic monomers. The catabolic pathway of Pseudomonas sp. NGC7 was optimized to maximize VA production from aromatic monomers in the sulfite lignin stream derived from this oxidation process. Pseudomonas sp. NGC7 possesses four gene sets for vanillate O-demethylase, comprising the oxygenase component (vanA) and its oxidoreductase component (vanB). Among these, the vanA4B4 gene set was identified as the key contributor to VA catabolism. To facilitate the conversion of AV to VA, AV-converting enzyme genes from Sphingobium lignivorans SYK-6 were introduced. The ΔvanA4B4 strain, harboring these AV-converting genes, produced VA from the sulfite lignin stream with 91 mol%. Further disruption of vanA1B1, vanA2B2, vanA3B3, and a vanillin reductase gene, in addition to vanA4B4, and introduction of a 5-carboxyvanillate decarboxylase gene from S. lignivorans SYK-6 to utilize 5-carboxyvanillin and 5-carboxyvanillate from the sulfite lignin stream for VA production achieved a VA yield of 103 mol%.ConclusionDeveloping methods to overcome lignin heterogeneity is essential for its use as a raw material. Consolidating continuous alkaline oxidation of lignin in a Cu(OH)2/CF-packed flow reactor and biological funneling using an engineered catabolic pathway of Pseudomonas sp. NGC7 is a promising approach to produce VA for aromatic materials synthesis. NGC7 possesses a higher adaptability to various aromatic compounds generated from the alkaline oxidation of lignin and its natural ability to grow on p-hydroxyphenyl, guaiacyl, and syringyl compounds underscores its potential as a bacterial chassis for VA production from a wide range of lignin-derived aromatic compounds.Graphical