Full-field Stress Distribution Research Articles

New high sensitivity approach for a quantitative visualization of the continuous whole-field stress evolution in digital photoelasticity

Digital photoelasticity is a widely used technique for experimental stress analysis on mechanical models subjected to loading conditions, due to its ability to reveal the stress information through color fringe patterns and consequently demodulate it computationally to achieve a quantitative evaluation. In this process, some limitations persist, such as, expertise dependence, experimental repeatability, sensitivity to load increments, and weak performance under experimental conditions, especially in time-dependent scenarios. In response to these weaknesses, the method “Quantitative Visualization of the Continuous Whole-Field Stress Evolution” introduced the ability to perform a complete demodulation of the fringe patterns generated in time-dependent applications, achieving high performance compared to conventional photoelasticity methods. This paper proposes a new highly sensitive approach for a quantitative visualization of the continuous whole-field stress evolution in digital photoelasticity by incorporating an inverse signal process and a multi-stage strategy. The algorithm aims to ensure the performance under high fringe order conditions while exhibiting high sensitivity in cases where the maximum stress obtained is less than one fringe order. The results presented validate its effectiveness in demodulating full-field stress distributions, especially in scenarios where the loading condition induces fringe orders less than one, thus contributing to the broader applicability of digital photoelasticity.

Image driven deep learning method with FFT solver for predicting the microscale full field stress of stochastic boundary composites

AbstractA novel image‐driven deep learning approach embedded with model‐data‐knowledge information can directly predict the full field stress distribution and mechanical properties of composites solely based on initial scanning geometry images. The fiber spatial distribution and morphological features are identified by Scanning Electron Microscopy (SEM) initially. An effective random fiber generation algorithm is further utilized to generate images database comprising equivalent geometric models of various microstructures. Subsequently, the geometry model images database is analyzed by fast Fourier transform (FFT) to produce the database including the elastic modulus parameters and full field stress distributions of composites with distinct microstructures. Finally, an innovative image‐learning comprehensive paradigm uniting convolutional neural networks and convolutional autoencoders is elaborated systematically to learn the inherent laws of geometry images and field images. The results show that the proposed method have capacity to effectively and accurately predict the elastic modulus and full field stress distributions combined with error analysis even for stochastic boundary composites. The proposed methodology is a symbiosis of cutting‐edge image learning and non‐destructive testing techniques for composites, which can directly use the local non‐destructive or scanning images of composite structural components to quickly obtain field information and further predict damage evolution online.Highlights Proposing a novel deep learning approach combined with FFT directly to predict stress distribution of stochastic boundary composites solely based on micro‐images. Adopting equivalent geometric models dispersed by higher pixels mesh density considering extreme thin interface. Incorporate adaptive algorithms for streamlined training optimization. An innovative integration of deep learning and non‐destructive testing technology for the stress distribution and properties prediction online.

Full-field measurement of residual stress in single-crystal diamond substrates based on Mueller matrix microscopy

In this work, a method has been proposed for fast-measuring full-field residual stress of diamond substrates based on Mueller Matrix (MM) microscopy. The measurement system features a polarization camera and a fixed compensator at 45° orientation, and real-time birefringence imaging can be performed. The magnitude and orientation of residual stress have been characterized by the stress-optical law. Optical-grade synthetic diamond substrates after laser-cutting and grinding have been measured. After laser-cutting samples exhibit a central region where stress orientation is shifted by −90° from the x-axis. After double-sided fine grinding, the average stress value is relatively low at 0.094 GPa, while single-sided fine grinding yields average stress of 0.142 Gpa, whereas double-sided rough grinding leads to 0.157 Gpa. Full-field stress distributions obtained from Raman images show consistent patterns. The research indicates that the MM-based method is a promising technique for detecting diamond substrate birefringence and characterizing its stress variation during fabrication.

A reconstruction method for structural stress distribution of wind turbine tower using optimised mathematical model

Wind turbine towers experience complex dynamic loads during actual operation, and these loads are difficult to accurately predict in advance, which may lead to inaccurate structural strength assessment during the structural design phase, thereby posing safety risks to the wind turbine tower. Therefore, a reconstruction method for structural stress distribution of wind turbine tower was developed based on modal expansion and linear superposition theory to estimate the full-field stress distribution of a tower, which can be used for online monitoring of structural strength. The dynamic stress distribution of the tower is assumed to be the superposition of several structural modal stress distributions, in the reconstruction method for structural stress distribution developed in this study. The modes with the greatest contribution to the wind turbine structural response were selected based on the modal effective mass, and used for the base functions of an initial mathematical model for the reconstruction of structural stress distribution of the tower, in which many candidate strain gauge locations and directions were considered. Then, the initial mathematical model was expressed as a linear system of equations. Two numerical examples were used to verify the accuracy and stability of the initial mathematical model for the reconstruction of structural stress distribution of the tower, and the reconstruction results indicate that the initial mathematical model combined with the Moore–Penrose inverse algorithm can provide stable and accurate reconstruction results. However, the initial mathematical model uses too many sensors, which is not conducive to engineering applications. Therefore, D-optimal and C-optimal design methods were used to reduce the dimensions of the initial mathematical model, optimise the system of equations, and determine the location, direction and number of strain gauges. Finally, the numerical examples of stress distribution reconstruction show that dimensionality reduction of the mathematical model leads to higher accuracy, in which the C-optimal design algorithm providing a more robust reconstruction outcome.

Stress intensity factors and full-field stresses for a hypocycloid-type crack within a thermo-elastic material

This study focuses on the failure analysis of a hypocycloid-type crack within a thermo-elastic material. Employing the conformal mapping method, analytical continuation theorem, and principle of superposition, the explicit general solution for stress intensity factors (SIFs) associated with an arbitrary-edged hypocycloid-type crack is determined analytically under the influence of remote homogeneous heat flux and mechanical load. The superposition method combines stress functions and SIFs for two distinct loading conditions. The outcomes of the normalized SIFs are affected by the magnitude and orientation of the heat flux and mechanical load. A full-field stress distribution is provided to account for variations in SIFs. Certain combinations of loads lead to maximum SIF values, rendering the system highly vulnerable to damage, while two specific scenarios inhibit crack propagation, thereby reducing the risk of structural failure.

A finite element-convolutional neural network model (FE-CNN) for stress field analysis around arbitrary inclusions

This study presents a data-driven finite element-machine learning surrogate model for predicting the end-to-end full-field stress distribution and stress concentration around an arbitrary-shaped inclusion. This is important because the model’s capacity to handle large datasets, consider variations in size and shape, and accurately replicate stress fields makes it a valuable tool for studying how inclusion characteristics affect material performance. An automatized dataset generation method using finite element simulation is proposed, validated, and used for attaining a dataset with one thousand inclusion shapes motivated by experimental observations and their corresponding spatially-varying stress distributions. A U-Net-based convolutional neural network (CNN) is trained using the dataset, and its performance is evaluated through quantitative and qualitative comparisons. The dataset, consisting of these stress data arrays, is directly fed into the CNN model for training and evaluation. This approach bypasses the need for converting the stress data into image format, allowing for a more direct and efficient input representation for the CNN. The model was evaluated through a series of sensitivity analyses, focusing on the impact of dataset size and model resolution on accuracy and performance. The results demonstrated that increasing the dataset size significantly improved the model’s prediction accuracy, as indicated by the correlation values. Additionally, the investigation into the effect of model resolution revealed that higher resolutions led to better stress field predictions and reduced error. Overall, the surrogate model proved effective in accurately predicting the effective stress concentration in inclusions, showcasing its potential in practical applications requiring stress analysis such as structural engineering, material design, failure analysis, and multi-scale modeling.

Inverse design of nonlinear mechanical metamaterials via video denoising diffusion models

The accelerated inverse design of complex material properties—such as identifying a material with a given stress–strain response over a nonlinear deformation path—holds great potential for addressing challenges from soft robotics to biomedical implants and impact mitigation. Although machine learning models have provided such inverse mappings, they are typically restricted to linear target properties such as stiffness. Here, to tailor the nonlinear response, we show that video diffusion generative models trained on full-field data of periodic stochastic cellular structures can successfully predict and tune their nonlinear deformation and stress response under compression in the large-strain regime, including buckling and contact. Key to success is to break from the common strategy of directly learning a map from property to design and to extend the framework to intrinsically estimate the expected deformation path and the full-field internal stress distribution, which closely agree with finite element simulations. This work thus has the potential to simplify and accelerate the identification of materials with complex target performance.

An electrochemical-mechanical coupled multi-scale modeling method and full-field stress distribution of lithium-ion battery

The rapid development of lithium-ion batteries has made the market more and more concerned about their lives. A large number of studies have shown that the alternating diffusion-induced stress caused by the cyclic charging and discharging processes can significantly shorten the service life of a battery. In recent years, scientists have tried to reveal the distributions and evolutions of the internal stress in lithium-ion batteries during operation by means of experiments and simulations, so as to propose guidance for their design and application. However, the existing numerical simulation framework is still limited to the particles, electrodes and battery units, rather than a battery cell. It is urgent to develop a method that can obtain the full-field stress distributions in commercial lithium-ion battery cells during working, so as to reveal the influence of stress on their lives, and further improve the efficiency of design and optimization. In this paper, an electrochemical-mechanical coupled multi-scale modeling method for lithium-ion batteries is proposed, which solves the technical problem of cross-scaled modeling and simulation from battery units to battery cells. Taking a pouch lithium-ion cell as an example, the lithium concentration distribution, potential distribution, and current density distribution of the battery unit, as well as the full-field displacement distribution, strain distribution and stress distribution of the battery cell during charging are obtained and analyzed. And the assumption, adaptability and potential applications of the method are discussed. It provides a new technical means and insight into the properties of lithium-ion batteries, and even solid-state batteries in the future.

Improved mechanical performance of Strombus gigas shell inspired artificial composites by regulating the laminated structure and interface bonding

Inspired by the cross-laminated hierarchical structure and flexible interface of high toughness Strombus gigas shell, the “fiber-metal-polymer” laminated composites with different laying modes including cross-laminated structure and interfacial properties were designed, and the corresponding damage and toughening mechanisms were investigated. It shows that the cross-laminated structure, accompanying soft interface modification by metal ultra-thin strip and polymer can optimize the full-field stress distribution and failure behavior, then achieve maximize energy absorption and ensure good strength (ultimate strain and toughness increased to 352% and 127.5%, respectively compared to unidirectional laminated material), which may provide optimization strategies for the design of lightweight composites.

A data-driven approach to full-field nonlinear stress distribution and failure pattern prediction in composites using deep learning

An image-based deep learning framework is developed to predict nonlinear stress distribution and failure pattern in microstructural representations of composite materials in this paper. The work is motivated by the complexity and computational cost of high-fidelity simulations of such materials. The proposed deep learning framework predicts the post-failure full-field stress distribution and the crack pattern in two-dimensional representations of the composites based on their microstructures. The deep learning framework contains two stacked fully-convolutional networks, namely, Generator 1 and Generator 2, trained sequentially. First, Generator 1 learns to translate the microstructural geometry to the full-field post-failure stress distribution. Then, Generator 2 learns to translate the output of Generator 1 to the failure pattern. A physics-informed loss function is also designed and incorporated to further improve the performance of the proposed framework and facilitate the validation process. The material of interest is selected to be a unidirectional carbon fiber-reinforced polymer composite. 4500 microstructural representations are synthetically generated and simulated using an efficient finite element framework to provide a sufficiently large data set for training and validating the deep learning framework. It is shown that the proposed deep learning approach can predict the composites’ post-failure full-field stress distribution and failure pattern, two of the most complex phenomena to simulate in computational solid mechanics, with an impressive accuracy of 90%.

Optical method for identification and quantification of full-field stress distributions and evolution in assembled lining structures based on additively printed models and phase-shifting methods

The accurate knowledge and characterization of the full-field stress distributions and evolution in assembled lining structures underlie the design, construction, and maintenance of tunnel linings. However, it is challenging for traditional field monitoring and laboratory experiments to identify directly and quantify accurately such distributions and evolution. Numerical simulations, as alternative solutions, are limited, as their results are significantly dependent on the accuracy of mechanical parameters, constitutive laws, failure criteria, mesh optimization, and boundary conditions, which are difficult to determine experimentally. In this study, a plane-stress-model-based photoelastic testing method was developed for the direct observation and quantification of the full-field stress distribution and evolution in an assembled lining structure based on additive manufacturing or three-dimensional printing technology and phase shifting methods. Three-dimensional printing techniques and stress- sensitive photopolymers were employed to fabricate transparent assembled models based on the information of real lining structures. The model split-merge technique, phase-shifting method, and unwrapping algorithm were combined to determine the full-field distribution of the principal stress difference and shear stress within the assembled segments. The proposed method was verified based on a comparison of the calculated and measured fringe orders at different loading stages. The experimental results indicated that the largest stress concentration was around the joint that connected the adjacent Segment L1 and basic Segment B1, which formed the potential critical failure zone of the assembled structure. An approximate X-shaped shear band was also identified. Comparisons of the results verified that the boundary and contact conditions, which are difficult to simulate, can lead to significantly different simulation results with respect to the distribution and evolution of the principal stress difference and shear stress. This study shows that the proposed method can effectively and quantitatively characterize the full-field stress distributions and evolution within complex assembled lining structures.

Bioinspired nacre-like GO-based fiber with improved strength and toughness by staggered layer structure regulation and interface modification

High-performance fiber materials are widely used in aerospace, automobile and other hi-tech fields due to their excellent mechanical properties. Here, inspired by natural organisms, a kind of bionic composite fiber with excellent mechanical properties, consisting of graphene oxide (GO) and thermoplastic polyurethane (TPU), was prepared by wet spinning method. In the composite fiber, the hard GO sheets and flexible TPU were arranged staggered to form a nacre-like "brick-mortar" layered structure. It shows that the strength and toughness of the composite fiber could be effectively improved by regulating the mass ratio of TPU to GO and the modification of their interfacial properties. Further study indicated that the full-field and local stress distribution can be optimized by regulating the proportion between TPU and GO, and the load transfer efficiency can be further improved by modifying the interface between them, then achieve excellent strength and toughness of the composite fiber. These results will provide useful guidance for the microstructure optimization and performance improvement of GO-based composite fiber.

The surface effects on solid and hollow nanowires under diametral loading

The size effects of energetic surfaces on the elastic behavior of solid and hollow nanowires are investigated under diametral loading for the first time. In order to model the diametral compression test on nanowires, the structural version of the locally-exact theory is developed for solid and hollow nanowires (LETNW) by considering energetic surfaces attached at the boundaries of bulk materials and modeled using the Gurtin-Murdoch model. The developed analytical solutions employ Fourier series representations of displacement fields in the cylindrical coordinate system that exactly satisfy the governing differential equations, facilitating rapid convergence of full-field stress distributions. The solution's accuracy is validated against the in-house finite-element (FE) program which is currently the computational standard, where excellent agreement is obtained. The surface effects on the local stresses are then illustrated by varying the surface parameters, loading angle, dimension of nanowires, as well as residual surface stress. The efficiency of the LETNW is attributed to its analytical nature and thus consumes much less execution time relative to the FE implementation. What's more, instabilities associated with the solution of stress fields are observed with surface properties in certain crystallographic orientations for both LETNW and FE approaches. Contrary to the LETNW technique, the bifurcation phenomenon is shown to depend on the finite-element mesh refinement. The locally-exact theory provides an alternative and independent way of identifying surface bifurcations in solid and hollow nanowires and hence is a good tool in assessing the finite-element method as well as other approaches’ predictive capability for this class of materials.

A mixed finite element based inverse approach for residual stress reconstruction

In this paper a full-field residual stress identification procedure is proposed and explored from partially measured residual elastic strain or stress within a PDE constrained optimization framework. At first, we have constructed a penalized least-square cost functional with an appropriate regularization term. We have taken data discrepancy term in energy norm while the regularization term is a complementary strain energy functional. We then construct an appropriate Lagrangian to impose the optimization constraint. It turns out that using first order optimality condition leads to standard two field mixed, of Hellinger-Reissner type, variational formulation with residual stress and Lagrangian variable as independent field variables. This allows us to use standard two and three dimensional mixed finite elements for approximation of the stress and Lagrangian variable. Using mixed finite element set-up, we then solved these equations to obtain full-field residual stress distribution. One key issue of the proposed formulation, as in case of any inverse problem, is the choice of penalization parameter. In this context, we have used modified L-curve based approach to choose optimal penalty parameter. Finally, we assess the numerical effectiveness of the proposed procedure against a few problems of engineering interest.

Static Residual Tensile Strength Response of GFRP Composite Laminates Subjected to Low-Velocity Impact

The dependency of the static residual tensile strength for the Glass Fiber-Reinforced Plastic (GFRP) laminates after impact on the impact energy level and indent shape is investigated. In this study, two different laminates, unidirectional, [0°2]s) and TRI (tri-axial, (±45°/0°)2]s), were prepared using the vacuum infusion method, and an impact indent on the respective laminates was created at different energy levels with pyramidal and hemispherical impactors. Impact damage patterns, such as matrix cracking, delamination, debonding and fiber breakage, could be observed on the GFRP laminates by a scanning electron microscope (SEM), and it is found that those were dependent on the impactor head shape and laminate structure. Residual in-plane tensile strength of the impacted laminates was measured and the reduction of the strength is found to be dependent upon the impact damage patterns. Furthermore, in this study, stress concentrations in the vicinity of the indents were determined from full-field stress distribution obtained by three-dimensional Digital Image Correlation (3D DIC) measurement. It was found that the stress concentration was associated with the reduction of the residual strength for the GFRP laminates.

A Non-Singular Analytical Technique for Reinforced Non-Circular Holes in Orthotropic Laminate

The intricacy in Lekhnitskii’s available single power series solution for stress distribution around hole edge for both circular and noncircular holes represented by a hole shape parameter ε is decoupled by introducing a new technique. Unknown coefficients in the power series in ε are solved by an iterative technique. Full field stress distribution is obtained by following an available method on Fourier solution. The present analytical solution for reinforced square hole in an orthotropic infinite plate is derived by completely eliminating stress singularity that depends on the concept of stress ratio. The region of validity of the present analytical solution on reinforcement area is arrived at based on a comparison with the finite element analysis. The present study will also be useful for deriving analytical solution for orthotropic shell with reinforced noncircular holes.

Quantification of continuous evolution of full-field stress associated with shear deformation of faults using three-dimensional printing and phase-shifting methods

Fault deformation or slip activated by underground mining, hydraulic fracture stimulation, and construction activities can cause devastating earthquakes or rockbursts. Fault deformability is significantly affected by the distribution and evolution of non-uniform stress around the faults. However, quantifying the continuous evolution of the full-field stress near natural rough faults using conventional methods is a challenging task due to the difficulties in discriminating and extracting stresses near a rough fault. This study proposes an optical characterization method to extract and quantify the continuous distributions and evolutions of the full-field principal stress difference and shear stress around a rough fault model. Three-dimensional (3D) printing technology and stress-sensitive photopolymers were utilized to fabricate a transparent rough fault model according to Barton's standard rough profiles. A planar testing device was designed to mimic geostress conditions and fault deformation. The conventional phase-shifting method and unwrapping algorithm were modified to quantify the continuous evolution of the principal stress difference and shear stress near rough faults. The effect of fault roughness on the distribution and evolution of the full-field stresses around the fault was also evaluated. A positive relationship between the undulating angle and the near-fault stress was established for the rough fault model. Results show that the proposed method works well for quantifying and visualizing full-field stress distribution and evolution during fault deformation.

Efficient Two-Way Shear Grillage Model Solution for Bridge RC Four-Pile Caps under Wall Loading

Reinforced concrete four-pile caps under wall loading occur in heavily loaded foundations in bridge construction. The failure mode of shear across the full width of the cap may occur in these deep structural elements. A statically determinate two-way grillage model, comprising orthogonal deep beam grillage elements obeying a predetermined test observing deflection pattern and boundary conditions, is established to solve the structure’s shear capacity. The model gives more accurate and faster solutions than the traditional strut-and-tie method and commercial nonlinear numerical modeling. A key step to solving the model is a linear constitutive (load-deflection) relationship developed for the grillage elements. The grillage model is verified against laboratory experiments for nine pile caps at the University of Southampton (UoS) with the results of a numerical modeling parametric study. A Visual Basic Userform-based design software is developed, incorporating the model and enabling engineers to obtain the shear capacity, full-field reinforcement stress distribution, and cap deflections within seconds.

Finite-volume homogenization and localization of nanoporous materials with cylindrical voids. Part 1: Theory and validation

Abstract Surface elasticity effects based on the Gurtin-Murdoch model are incorporated for the first time into a finite-volume based homogenization theory to enable analysis of materials with nanoscale cylindrical voids of circular and ellipsoidal cross-section in periodic arrays. In a departure from the previously employed enforcement of traction and displacement continuity conditions in a surface-average sense applied locally to each subvolume of the unit cell, the Young-Laplace equilibrium equations are implemented using a central-difference approach involving adjacent subvolumes, an approach both new to the finite-volume theory as well as necessary. In Part 1, the new computational capability is validated by published results on homogenized moduli, stress concentrations and full-field stress distributions in nanoporous aluminum obtained using elasticity-based and numerical approaches. Notably, numerical problems associated with singular-like stresses and associated instabilities experienced in finite-element solutions (as well as the elasticity solution of an elliptical void in an infinite matrix) are not as pronounced in the proposed approach, enabling determination of surface and full-field stresses in a wider range of pore radii. New results are generated in Part 2 aimed at demonstrating the effects of nanopore array type and aspect ratio of elliptical voids on homogenized moduli and local stress fields in a wide range of porosity volume fractions and radii. These results highlight the importance of adjacent pore interactions neglected in the classical micromechanics models , that remains to be quantified by numerical homogenization techniques.

Full-field fabric stress mapping by micro Raman spectroscopy in a yarn push-out test.

The full-field stress distribution of a two-dimensional plain fabric was mapped using micro Raman spectroscopy (MRS) through a novel yarn push-out test, simulating a quasi-static projectile impact on the fabric. The stress-strain relationship for a single yarn was established using a digital image correlation method in a single-yarn tensile test. The relationship between Raman peak shift and aramid Kevlar 49 yarn stress was established using MRS in a single-yarn tensile test. An out-of-plane loading test was conducted on an aramid Kevlar 49 plain fabric, and the yarn stress was measured using MRS. From the full-field fabric stress distribution, it can be observed that there is a cross-shaped distribution of high yarn stress; this result would be helpful in further studies on load transfer on a fabric during a projectile impact.