Distribution Of Material Properties Research Articles

Machine learning powered predictive modelling of complex residual stress for nuclear fusion reactor design

Fusion In-vessel components, assembled and maintained using laser welding, one of the most promising techniques, exhibit complex distributions of residual stress, microstructures, and material properties. These residual stresses can compromise structural integrity and lifespan of critical components. Although using advanced experimental measurements can evaluate the residual stress for individual case, extending the measurements to massive number of components are costly and time-consuming. Traditional machine learning (ML) models struggle to account for the heterogeneity and anisotropy of these stress distributions. Here, we develop a novel ML framework based on the Eurofer97 steel, the structural material for in-vessel components. The ML framework is trained on high-resolution residual stress data derived from recently-developed evaluation techniques. Combining with microstructures, the model enables prediction of heterogenous and anisotropic residual stress distribution. It successfully predicts the compressive residual stress in fusion zone (∼−200 MPa) balanced by tensile residual stress in heat affected zone (∼300 MPa), aligning closely with experimental results with the R-squared value of 0.989 and the mean square error of 10−4. Unlike experiments that take hours, the ML model provides predictions within seconds. It offers valuable insights into residual stress prediction for various joints, enhancing the reliability and lifetime prediction of in-vessel components.

Large-amplitude nonlinear vibrations characteristics of bi-directional functionally graded plate having microstructure defects in hygro-thermal environment

The present article investigates the nonlinear hygro-thermal vibration characteristics of bi-directional functionally graded plates (BFGP) with microstructural defects. The distribution of material properties is anticipated to vary gradually along both thickness and length directions according to the modified power-law distribution. A novel expression has been developed to solve for the nonlinear temperature variation along the thickness of the BFGP. The micro-structural defects in terms of porosity have been incorporated in the formulation using a newly developed porosity model for a BFGP. A refined non-polynomial trigonometric higher-order shear deformation theory (HSDT) with a von Karman sense of geometric nonlinearity has been employed for the vibration response of BFGP. The finite element formulation has been carried out utilizing the C0 continuous Lagrangian quadrilateral element with nine nodes and eight degrees of freedom per node. The equations of motion have been derived using a variational approach. Various validation and comparative studies have been conducted to substantiate the current formulation's authenticity. The effect of the geometric nonlinearity, boundary constraints, volume fraction index along thickness (n) and volume fraction index along length (q), porosity index, temperature, and moisture concentration difference on the vibration frequency ratios (VFR) has been covered in depth. The VFR is more sensitive to the volume fraction indices (VFI) ' n′ than 'q'. Incorporating porosity decreases the VFR of BFGP, but it increases at higher amplitude ratios when BFGP becomes more porous. The VFR of BFGP exhibits nonlinear behavior with increasing moisture concentration and also varies non-linearly with the rise in amplitude ratio due to the hygro-thermal environment.

Interfacial dynamic impermeable crack analysis in dissimilar piezoelectric materials by a new interaction integral

Dynamic intensity factors (IFs) provide an important parameter for assessing the failure risk of an interfacial crack for piezoelectric composites exposed to electromechanical impact loadings. In the present research, a new dynamic interaction integral (I-integral) is built for computing the dynamic stress IFs (SIFs) and electric displacement IF (EDIF) of an interfacial crack located in dissimilar inhomogeneous piezoelectric media. Through proper selection of auxiliary variables, the domain expression of I-integral for the inhomogeneous piezoelectric bi-materials does not need to take into account any derivative term for any piezoelectric material property. Further, after rigorous theoretical derivation, the resulting I-integral is still valid for complex models where the integration domain contains other multiple interfaces, regardless of whether the extra materials are straight or curved. Incorporating the modified extended finite element approach, the accuracy is confirmed by checking the dynamic IFs extracted from the I-integral with referenced results. The domain-independence is tested by varying ranges of integration domains for inhomogeneous piezoelectric bi-materials and multi-interface piezoelectric composites. Finally, typical examples are employed to discuss the influences of the direction and magnitude of electric impact loading, combination of polarizations, inhomogeneous degree of piezoelectric bi-materials and complex distribution of diverse material properties on the dynamic IFs.

Effect of the parameters of metal forming processes on the behaviour of thin-walled structures

Abstract The parameters of metal forming processes affect the distribution of material properties through the workpiece. In particular, sheet rolling and drawing processes induce the through thickness gradient of material properties in sheets that are used in thin-walled structures. The present paper studies the effect of this gradient on the product in the shape of two developable shells (circular cylinder and developable helicoids with different screwing degree) obtained from a plane metal workpiece by parabolic bending. The possibility of manufacturing any developable product without creases and tears from a thin metal workpiece is theoretically proved and the influence of metal forming process on the resulting stress-strain in the workpiece is examined. The results of the research can be implemented in different engineering fields as marine design, civil engineering, air-space industry, and in a range of manufacturing processes.

Experimental and numerical investigations on dynamic response of butt-welded plates subjected to blast load

Experimental and numerical investigations on the small-size butt-welded plates subjected to air blast loads were conducted to highlight the effect of welded joints on the blast proof structures. The inherent characteristics of welded joints, including geometry, mechanical properties and welding residual stress were evaluated and discussed in the computation of blast loading. The geometry shape was assessed through macrographic of the welded joints. The distribution of mechanical and thermal physics property was determined through basic experiments using the specimens extracted from different zones of a welded joint. Welding residual stress was calculated in a thermo-mechanical coupled model. Conventional Weapons Effects Program (CONWEP) is more economic but limited compared with Arbitrary-Lagrangian–Eulerian (ALE) method. ALE and CONWEP methods were applied to simulate the air blast load applied on the plates. Effectiveness and efficiency of the methods were discussed. The results of the two programs could both coincide well with the experiment measurements. The models under six conditions were calculated to uncouple and discuss the effect of material property distribution and welding residual stress on the dynamic response of the welded structure. Permanent deflections were considered to assess the capacity of welded structures. Welding residual stress fields and the local weak materials are advantageous to the bending deformation. The phenomenological expressions of permanent deflection across thickness under different welding conditions were established based on simulation results. The effect of aspect ratio of the welded structures was also be discussed.

Cut‐Cell Microstructures for Two‐scale Structural Optimization

AbstractTwo‐scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is widely used in many fabrication applications to achieve a target deformation behavior for a variety of objects. The main idea of this approach is to optimize the distribution of material properties in the object partitioned into relatively coarse cells, and then replace each cell with microstructure geometry that mimics these material properties. In this paper, we focus on adapting this approach to complex shapes in situations when preserving the shape's surface is essential.Our approach extends any regular (i.e. defined on a regular lattice grid) microstructure family to complex shapes, by enriching it with tiles adapted to the geometry of the cut‐cell. We propose a fully automated and robust pipeline based on this approach, and we show that the performance of the regular microstructure family is only minimally affected by our extension while allowing its use on 2D and 3D shapes of high complexity.

Surrogation and Bayesian updating of a finite element model of the Leaning Tower of Pisa

Numerical models play a crucial role in the study and understanding of cultural heritage structures, serving as valuable tools for predicting their behavior under diverse and prospective scenarios. They are however affected by various uncertainties, which impact can be mitigated through the calibration of model parameters. For heritage structures, where testing is usually restricted to the use of non-destructive techniques, and often unable to directly assess the inherent heterogeneity of the materials, a calibration approach can prove particularly useful to obtain a working model. This work applies a Bayesian model updating procedure to material-related uncertainties affecting a recently developed finite element model of the Leaning Tower of Pisa also comprising the underlying soil layers. A general Polynomial Chaos Expansion-based surrogation of the model was employed to evaluate the sensitivity of modal properties and ease the computational burden that comes with the probabilistic framing of the updating problem. Material property distributions were then updated, taking advantage of modal data from a newly installed sensor network which allowed the most up-to-date dynamic identification of the monument. The results represent the first probabilistic model-based assessment of material uncertainties in a three-dimensional finite element model of the Leaning Tower of Pisa. They shed some light into the value of specific modal information, while the use of analytical surrogation paves the way for the future design of a real-time updating procedure for monitoring and damage detection.

Physics-Informed Machine Learning for Structural Damage Diagnosis in Aluminium Plates

Damage diagnosis plays a crucial role in Structural Health Monitoring (SHM) by facilitating the identification, localization, and estimation of the extent of defects in structures. Lamb waves, known for their sensitivity to defects, are widely employed in SHM methods for thin-walled structures. Most of those traditional methods require extracting damage indices from Lamb wave signals. This operation involves substantial post-processing and implies that part of the diagnostic information is lost. To solve those limitations and improve the damage diagnosis accuracy, machine learning methods have recently been proposed in the literature. However, the reluctance of the industrial sector to adopt conventional black-box models due to their lack of explainability poses a challenge. This study proposes a physics-informed machine-learning approach to address the limitations of standard black-box methods. Particularly, a Physics-Informed Neural Network (PINN) is implemented to predict the density of an aluminium plate based on measurements of plate displacements caused by Lamb wave excitation. This is made possible by the implementation of a specific loss function, which leverages physical knowledge in the form of the partial differential equation governing Lamb waves. Predicting the plate density based on measured displacements eliminates the need for artificial damage indices, utilizing the density variation itself to detect and localize damage. Additionally, the outputs of the PINN, rooted in physics equations, offer enhanced explainability compared to standard black-box models. The versatility of this framework extends to predicting material properties distributions for components, and efforts will be directed towards adapting the method for composite materials, where the approach may pose additional challenges.

Effect of cement volume on biomechanical response of a spine segment treated with a PEEK polymer implant: a finite element comparative study with vertebroplasty.

In the current study, a 3D finite element study was performed to investigate the biomechanical response of an osteoporotic spine segment treated with a novel transpedicular implant (V-STRUT©, Hyprevention, France) made of PEEK (polyetheretherketone) material combined with either injections of 2, 3, 4, 5 and 6 cc of cement. The objective was to assess numerically the biomechanical performance of the implant in combination with different doses of the injected bone cement and to compare its performance with the gold standard vertebroplasty (VP) technique. A female (69yo) was selected and a 3D finite element model of an osteoporotic spine segment was built based on a Computed Tomography (CT) scan performed from T12 to L2 with corresponding intervertebral discs and ligaments. A heterogeneous distribution of bone material properties was assigned to the bone using grey scale levels. Bilateral ellipsoid geometries of the inserted cement were retained for the V-STRUT and VP models based on experimental observation performed on different patients treated with the V-STRUT device. The current study demonstrated an optimal dose of 4 cc of bilaterally injected cement for the V-STRUT and VP techniques to restore the treated segment and confirmed that the V-STRUT device in combination with bone cement is superior to VP alone in establishing the normal stiffness and in reducing the applied stress to the immediately adjacent vertebral levels.

Buckling behavior of rotor blade sandwich panels with spatially distributed material uncertainties

The study evaluates the impact of material uncertainties on the buckling behavior of sandwich panels in wind turbine rotor blades. The analysis is limited to linear buckling and is performed using stochastic finite element Monte Carlo simulation on a rectangular and flat submodel of the rotor blade’s trailing edge panel. The finite element model of the panels is simply supported on all edges. To generate the spatial material property distributions, the Karhunen-Loève expansion is used in combination with Latin hypercube sampling. The results compare the effects of various correlation lengths of the spatial distributions. The buckling loads vary in correlation to the average panel stiffness caused by the random distributions. The spatial distribution has a less dominant effect, reducing the mean value of the buckling load results. The amount of reduction in buckling load is highest when the correlation length of the distribution is close to the harmonic half-wave of the dominant buckling shape.

Free vibration Analysis of Beams with Functional Gradient Materials with Cracks

The article presents the development of a dynamic model for a functionally graded material (FGM) beam incorporating cracks. Initially, it assumes an exponential distribution of material properties along the thickness direction of the beam and simulates the opening crack using a zero-mass rotational spring model. This approach enables the calculation of bending stiffness and local flexibility at the cracked section. Subsequently, drawing upon Timoshenko beam theory and von Kármán geometric nonlinear theory, the study formulates the energy equation of the beam and establishes the partial differential control equations for the cracked FGM using Hamilton's principle. The method of separation of variables is employed to discretize the partial differential motion equations into ordinary differential motion equations. Beam functions serve as mode functions, whose unknown coefficients are determined according to the boundary and continuity conditions, thereby yielding the natural frequencies and mode shapes of the cracked FGM beam. Numerical analysis is conducted to evaluate the impact of boundary conditions, the relative position of cracks, and the length-to-thickness ratio on the natural frequencies of the cracked FGM beam.

Mechanical and elemental characterization of ant mandibles: consequences for bite mechanics.

Mandible morphology has an essential role in biting performance, but the mandible cuticle can have regional differences in its mechanical properties. The effects of such a heterogeneous distribution of cuticle material properties in the mandible responses to biting loading are still poorly explored in chewing insects. Here, we tested the mechanical properties of mandibles of the ant species Formica cunicularia by nanoindentation and investigated the effects of the cuticular variation in Young's modulus (E) under bite loading with finite-element analysis (FEA). The masticatory margin of the mandible, which interacts with the food, was the hardest and stiffest region. To unravel the origins of the mechanical property gradients, we characterized the elemental composition by energy-dispersive X-ray spectroscopy. The masticatory margin possessed high proportions of Cu and Zn. When incorporated into the FEA, variation in E effectively changed mandible stress patterns, leading to a relatively higher concentration of stresses in the stiffer mandibular regions and leaving the softer mandible blade with relatively lower stress. Our results demonstrated the relevance of cuticle E heterogeneity in mandibles under bite loading, suggesting that the accumulation of transition metals such as Cu and Zn has a relevant correlation with the mechanical characteristics in F. cunicularia mandibles.

Analytical modeling of acoustic exponential materials and physical mechanism of broadband anti-reflection

Spatially exponential distributions of material properties are ubiquitous in many natural and engineered systems, from the vertical distribution of the atmosphere to acoustic horns and anti-reflective coatings. These media seamlessly interface different impedances, enhancing wave transmission and reducing internal reflections. This work advances traditional transfer matrix theory by integrating analytical solutions for acoustic exponential materials, which possess exponential density and/or bulk modulus, offering a more accurate predictive tool and revealing the physical mechanism of broadband anti-reflection for sound propagation in such non-uniform materials. Leveraging this method, we designed an acoustic dipole array that effectively mimics exponential mass distribution. Through experiments with precisely engineered micro-perforated plates, we demonstrate an ultra-low reflection rate of about 0.86% across a wide frequency range from 420 Hz to 10,000 Hz. Our modified transfer matrix approach underpins the design of exponential materials, and our layering strategy for stacking acoustic dipoles suggests a pathway to more functional gradient acoustic metamaterials.

Development of a piezo stack – Laser doppler vibrometer sensing approach for characterizing shear wave dispersion and local viscoelastic property distributions

Laser Doppler vibrometry and wavefield analysis have recently shown great potential for nondestructive evaluation, structural health monitoring, and studying wave physics. However, there are limited studies on these approaches for viscoelastic soft materials, especially, very few studies on the laser Doppler vibrometer (LDV)-based acquisition of time–space wavefields of dispersive shear waves in viscoelastic materials and the analysis of these wavefields for characterizing shear wave dispersion and evaluating local viscoelastic property distributions. Therefore, this research focuses on developing a piezo stack-LDV system and shear wave time–space wavefield analysis methods for enabling the functions of characterizing the shear wave dispersion and the distributions of local viscoelastic material properties. Our system leverages a piezo stack to generate shear waves in viscoelastic materials and an LDV to acquire time–space wavefields. We introduced space-frequency-wavenumber analysis and least square regression-based dispersion comparison to analyze shear wave time–space wavefields and offer functions including extracting shear wave dispersion relations from wavefields and characterizing the spatial distributions of local wavenumbers and viscoelastic properties (e.g., shear elasticity and viscosity). Proof-of-concept experiments were performed using a synthetic gelatin phantom. The results show that our system can successfully generate shear waves and acquire time–space wavefields. They also prove that our wavefield analysis methods can reveal the shear wave dispersion relation and show the spatial distributions of local wavenumbers and viscoelastic properties. We expect this research to benefit engineering and biomedical research communities and inspire researchers interested in developing shear wave-based technologies for characterizing viscoelastic materials.

Properties of biomolecular condensates defined by Activator of G-protein Signaling 3.

Activator of G-protein signaling 3 (AGS3; also known as GPSM1), a receptor-independent activator of G-protein signaling, oscillates among defined subcellular compartments and biomolecular condensates (BMCs) in a regulated manner that is likely related to the functional diversity of the protein. We determined the influence of cell stress on the cellular distribution of AGS3 and core material properties of AGS3 BMCs. Cellular stress (oxidative, pHi and thermal) induced the formation of AGS3 BMCs in HeLa and COS-7 cells, as determined by fluorescent microscopy. Oxidative stress-induced AGS3 BMCs were distinct from G3BP1 stress granules and from RNA processing BMCs defined by the P-body protein Dcp1a. Immunoblots indicated that cellular stress shifted AGS3, but not the stress granule protein G3BP1 to a membrane pellet fraction following cell lysis. The stress-induced generation of AGS3 BMCs was reduced by co-expression of the signaling protein Gαi3, but not the AGS3-binding partner DVL2. Fluorescent recovery following photobleaching of individual AGS3 BMCs indicated that there are distinct diffusion kinetics and restricted fluidity for AGS3 BMCs. These data suggest that AGS3 BMCs represent a distinct class of stress granules that serve as a previously unrecognized signal processing node.

General analysis of the dissipation of strain energy in circular columns

This theoretical paper is concerned with general analysis of the strain energy dissipation in columns of circular cross-section. The columns are under longitudinal displacements that vary continuously with time. The columns exhibit non-linear viscoelastic behavior that is studied by mechanical models constructed by using non-linear springs and dashpots. Besides, the columns are functionally graded along the radius of the cross-sections. A simple expression for the dissipated strain energy in the columns under consideration is derived. The expression holds for columns having portions with different radius of the cross-section. Also, the expression derived is applicable for columns built-up by concentric layers. Results indicating how the dissipated strain energy is influenced by various factors (distribution of material properties, geometry of the columns and loading) are presented. These results are found by using a non-linear viscoelastic model with one spring and one dashpot. A check-up is performed by determining the dissipated strain energy through subtracting the strain energy in the spring of viscoelastic model from the whole strain energy in the column.

Physics-informed neural network reconciles Australian displacements and tectonic stresses

Stress orientation information is invaluable to evaluate active tectonic forces within the Earth’s crust. The global dataset provided by the World Stress Map offers a rich resource of stress indicators, facilitating the calibration of mechanical models to extract complete stress and displacement fields. However, traditional inversion processes are hampered by the manual tuning of geomechanical properties and boundary conditions to reconcile simulations with observations. In this study, we introduce ML-SEISMIC (machine learning for stress estimation integrating satellite image and computational modelling), a physics-informed deep neural network approach to autonomously align stress orientation data with an elastic model. It nearly completely bypasses the need for explicit boundary condition inputs and yields comprehensive distributions of material properties, displacements, and stress tensors. Application of this methodology to Australia, coupled with precise global navigation satellite systems observations, unveils a robust and scale-independent interpolation framework. Additionally, it pinpoints regions where stress orientation reinterpretation is warranted. Our results present a streamlined yet powerful process, offering a substantial leap forward in geodynamic investigations. This approach promises to unify velocity and stress orientation observations with physical models, ushering in a new era of insights into Earth’s dynamic processes.

Design of equi-strength annular disks made of functionally graded materials

This research proposes a robust method for designing functionally graded disks subject to internal and external pressures. The design objective is to find the profile of equi-strength disks. The von Mises yield criterion controls the initiation of plastic yielding. The yield stress and Young’s modulus are entirely arbitrary functions of the polar radius. Poisson’s ratio is constant. The solution is facilitated using the dimensionless yield stress as an independent variable instead of the polar radius. In particular, a numerical technique is only required to solve two ordinary differential equations. Moreover, one of these equations is independent of the other. Therefore, the equations can be solved individually, simplifying the solution method. The limitation imposed by the thickness gradient on the acceptability of plane stress conditions is considered. Particular designs are proposed assuming that the power function describes the radial distribution of material properties. A critical condition that allows for deriving relatively simple design solutions is emphasized. It is shown that this condition is satisfied for many specific material property distributions used in the literature.

DEVELOPMENT OF AN OPEN-SOURCE FINITE ELEMENT ANKLE MODEL FOR IN-SILICO INVESTIGATION OF THE ANKLE JOINT

AbstractObjectivesThis abstract provides an update on the Open Ankle Models being developed at the University of Bath. The goal of this project is to create three fully open-source finite element (FE) ankle models, including bones, ligaments, and cartilages, appropriate musculoskeletal loading and boundary conditions, and heterogeneous material property distribution for a standardised representation of ankle biomechanics and pre-clinical ankle joint analysis.MethodsA computed tomography (CT) scan data (pixel size of 0.815 mm, and slice thickness of 1 mm) was used to develop the 3D geometry of the bones (tibia, talus, calcaneus, fibula, and navicular). Each bone was given the properties of a heterogeneous elastic material based on the CT greyscale. The density values for each bone element were calculated using a linear empirical relation, ρ= 0.0405 + (0.000918) HU and then power law equations were utilised to get the Young's Modulus value for each bone element [1]. At the bone junction, a thickness of cartilage ranging from 0.5–1 mm, and was modelled as a linear material (E=10 MPa, ν=0.4 [2]). All ligament insertions and positions were represented by four parallel spring elements, and the ligament stiffness and material attributes were applied in accordance with the published literature [2]. The ankle model was subjected to static loading (balance standing position). Four noded tetrahedral elements were used for the discretization of bones and cartilages. All degrees of freedom were restricted at the proximal ends of the tibia and fibula. The ground reaction forces were applied at the underneath of the calcaneus bone. The interaction between the cartilages and bones was modelled using an augmented contact algorithm with a sliding elastic contact between each cartilage. A tied elastic contact was used between the cartilages and the bone. FEbio 2.1.0 (University of Utah, USA) was used to construct the open-source ankle model.ResultsWhen the double-legged stance phase loading condition was taken into consideration, stress at the antero-medial tibial wall (ranged from 1 to 7 MPa) was found to be similar to the prior work [2], indicating bulk of the load transfer was through this region. The maximum principal strain was predicted at the different regions on bones around the ankle joint. The proximal surface of the talus, and tibial distal surface were shown to have the highest maximum principal strains followed by antero-medial walls of the tibia bone, at the proximal location.ConclusionsThe present open 3D FE model of the ankle will assist researchers in better understanding ankle biomechanics, precisely predicting load transfer, and examining the ankle to address unmet clinical needs for this joint. The results of the current investigation are realistic in terms of load transfer and stress-strain distribution across the ankle joint and well comparable to those reported in the literature [2]. However, sensitivity and ankle instability simulations will be performed in future work to investigate the model's reliability and robustness.Declaration of Interest(b) declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research reported:I declare that there is no conflict of interest that could be perceived as prejudicing the impartiality of the research project.

A black-box optimization strategy for customizable global elastic deformation behavior of unit cell-based tri-anti-chiral metamaterials

Metamaterials are a class of materials with a distinctive unit cell-based periodic architecture, often resulting in unique mechanical properties. The potential of metamaterials can be further improved by using gradients of unit cell parameters and thereby creating a specific distribution of material properties in a part. This design freedom comes with the challenge of finding new suitable design and optimization strategies. In this study, a Finite Element simulation-based optimization framework to create a predefined deformation behavior of unit cell-based metamaterials is presented. The framework consists of a numerical homogenization method to create an efficient linear elastic material representation, an interpolation scheme for a fast correlation of unit cell parameters with homogenized material properties and a black-box based optimization part. The framework is tested on a tri-anti-chiral metamaterial with additional geometric parameters and a newly developed transition unit cell. Several specified lateral deformations of simple 2D rectangular test specimens under tensile load are used as primary optimization targets and the homogenized results are validated against Finite Element simulations of fully modeled tri-anti-chiral structures. In addition, the effect of the design space and the number of design variables is studied and several combinations of optimization objectives and constraints are tested.