Predicted Displacement Fields Research Articles

Image-driven prediction of fatigue crack growth in metal materials via spatiotemporal neural network

This study proposes an image-driven model based on the SimVP spatiotemporal neural network (STNN) to predict the fatigue crack growth (FCG) in aluminum alloys. This methodology represents a novel usage of STNNs for FCG analysis. It does not require repetitive modeling, extensive computations, or conventional mechanical assumptions. The datasets used during this study were gathered from fatigue experiments with a variety of crack positions, angles, and load levels; they contained a total of 17,925 image frames obtained from DIC measurements. Subsequently, the displacement fields were interpolated onto uniform grids and then augmented, so they could be fitted into an STNN. The proposed method was validated using specimens with edge and central cracks subjected to loads equal to 15.0 % and 20.0 % of the ultimate load. The generalization capability of the proposed method was studied by predicting the FCG under load levels and crack angles outside the training set. In addition, its predictive capability was investigated for both short and long step sizes by employing datasets in which the image data were collected at varying intervals. The overall structural similarity index measurement values were greater than 0.968, and the root mean square errors were held within 0.025 mm. The predicted displacement fields, crack lengths, and crack growth rates agreed well with experimental measurements.

Comparison of linear and nonlinear stepwise μFE displacement predictions to digital volume correlation measurements of trabecular bone biopsies

Digital volume correlation (DVC) enables to evaluate the ability of μFE models in predicting experimental results on the mesoscale. In this study predicted displacement fields of three different linear and materially nonlinear μFE simulation methods were compared to DVC measured displacement fields at specific load steps in the elastic regime (StepEl) and after yield (StepUlt). Five human trabecular bone biopsies from a previous study were compressed in several displacement steps until failure. At every compression step, μCT images (resolution: 36 μm) were recorded. A global DVC algorithm was applied to compute the displacement fields at all loading steps. The unloaded 3D images were then used to generate homogeneous, isotropic, linear and materially nonlinear μFE models. Three different μFE simulation methods were used: linear (L), nonlinear (NL), and nonlinear stepwise (NLS). Regarding L and NL, the boundary conditions were derived from the interpolated displacement fields at StepEl and StepUlt, while for the NLS method nonlinear changes of the boundary conditions of the experiments were captured using the DVC displacement field of every available load step until StepEl and StepUlt. The predicted displacement fields of all μFE simulation methods were in good agreement with the DVC measured displacement fields (individual specimens: R2>0.83 at StepEl and R2>0.59 at StepUlt; pooled data: R2>0.97 at StepEl and R2>0.92 at StepUlt). At StepEl, all three simulation methods showed similar intercepts, slopes, and coefficients of determination while the nonlinear μFE models improved the prediction of the displacement fields slightly in all Cartesian directions at StepUlt (individual specimens: L: R2>0.59 and NL, NLS: R2>0.68; pooled data: L: R2>0.92 and NL, NLS: R2>0.94). Damaged/overstrained elements in L, NL, and NLS occurred at similar locations but the number of overstrained elements was overestimated when using the L simulation method. Considering the increased solving time of the nonlinear μFE models as well as the acceptable performance in displacement prediction of the linear μFE models, one can conclude that for similar use cases linear μFE models represent the best compromise between computational effort and accuracy of the displacement field predictions.

Flow rate–pressure drop relations for new configurations of slender compliant tubes arising in microfluidics experiments

We investigate the steady-state fluid–structure interaction between a Newtonian fluid flow and a deformable microtube in two novel geometric configurations arising in recent microfluidics experiments. The first configuration is a cylindrical fluidic channel surrounded by an annulus of soft material with a rigid outer wall, while the second one is a cylindrical fluidic channel extruded from a soft rectangular slab of material. In each configuration, we derive a mathematical theory for the nonlinear flow rate–pressure drop relation by coupling lubrication theory for the flow with linear elasticity for the inner tube wall’s deformation. Using the flow conduit’s axial slenderness and its axisymmetry, we obtain an analytical expression for the radial displacement in each configuration from a plane-strain configuration. The predicted displacement field, and the resulting closed-form flow rate–pressure drop relation, are each validated against three-dimensional direct numerical simulations via SimVascular’s two-way-coupled fluid–structure interaction solver, svFSI, showing good agreement. We also show that weak flow inertia can be easily incorporated in the derivation, further improving the agreement between theory and simulations for larger imposed flow rates.

A robust unsupervised neural network framework for geometrically nonlinear analysis of inelastic truss structures

In this study, a robust and simple unsupervised neural network (NN) framework is proposed to perform the geometrically nonlinear analysis of inelastic truss structures. The core idea is to employ the NN to directly estimate nonlinear structural responses without utilizing any time-consuming incremental-iterative algorithms as those done in standard finite element method (FEM). To achieve such an objective, the loss function built via the total potential energy principle under boundary conditions (BCs) is minimized in the suggested NN model whose weights and biases are considered as design variables. In our computational framework, spatial coordinates of truss nodes are treated as input data, whilst corresponding displacement degrees of freedom are taken account of output. At the beginning of each training step, feedforward is performed to get the predicted displacement field, and it is used to derive the loss function based on the physical law. Then, back-propagation is applied to update the parameters of the network. This adjustment, which is the so-called learning process, is repeated until the potential energy is minimized. Once the network is properly trained, the mechanical responses of inelastic structures can be easily obtained. The suggested methodology is also extremely simple to implement, while the unlabeled data is available, small in size, independent of sampling techniques, and without finite element analyses (FEAs). Several benchmark examples regarding geometrical and material nonlinear analysis of truss structures are tested to show the effectiveness and reliability of the proposed paradigm. Obtained outcomes indicate that the developed NN framework is robust and can be extended to apply for other structures.

Fundamental study for development of displacement field prediction method using deep learning techniques

In recent years, the Deep Energy Method defines a loss function based on the energy minimization principle and obtains approximate solutions to partial differential equations using deep learning techniques. This method has been developed and applied to the plate with a circular hole problem and the two-dimensional fracture mechanics analysis. In this paper, we investigated a method to predict the displacement field from displacement information of several points in the computational domain based on the concept of the Deep Energy Method. Compared with the result of the finite element analysis of the x and y directions, the total absolute errors of the predicted displacement field were 5.24% and 2.15%, respectively.

A continuum-kinematics-inspired peridynamic model of anisotropic continua: Elasticity, damage, and fracture

In this work, linearized elastic isotropic continuum-kinematics-inspired-peridynamics (CPD) is further generalized to study the elastic, damage, and fracture behavior of anisotropic continua, focusing on 3D transversely isotropic and 2D orthotropic body. The anisotropy is generated by changing the material properties, including the micromodulus, critical stretch, and critical micropotential energy of basic finite kinematic elements with their direction in the principal material axes in terms of eight-order double Fourier expansion. It is critically proven that the volumetric micromodulus of finite volume elements in the 3D case is independent of their direction, which is similarly applied to the areal micromodulus in the 2D case. For this reason, the 2D orthotropic CPD formulation characterized by three independent elastic moduli and the 3D transversely isotropic CPD formulation characterized by four independent elastic moduli are distinguished. The accuracy of the computational models applied to elastic analysis is assessed by comparing the predicted displacement fields with the results from finite element analysis. Quantitative simulation of an orthotropic lamina with a central rectangular hole under a tensile load, eccentric three-point bending test for orthotropic lamina, and compact tension test for cortical bone are performed to verify the ability of the proposed model to describe the damage and fracture behavior of anisotropic materials.

Unsupervised Image Registration for Video SAR

Existing approaches for SAR image registration focus on the global transformation correction between SAR images. However, there are often local deformations between images. Due to the time-changing viewpoint of video SAR, the images suffer a lot from local deformations, which can result in false alarms in moving target detection. This article presents an unsupervised image registration approach for the use of video SAR moving target detection, which has good registration performance and acceptable processing efficiency. The designed unsupervised learning-based framework is a cascade of two convolutional neural networks. The first network directly predicts the parameters of the rigid transformation between the reference and unregistered images, and recovers the global transformation between them. Then, the second network uses the reference image and the registered image from the first network as input and then predicts a displacement field. After that, we put a limitation on the predicted displacement field to prevent moving target shadows from being aligned. Finally, the displacement field with limitation is used to compensate local deformations between the two images. Processing results of real video SAR images have shown good performance of the proposed approach with convincing generation ability.

Progresses in the structural assessment of the central region of a HELIAS 5-B breeding blanket half sector

Abstract Within the framework of EUROfusion action, the HELIcal-axis Advanced Stellarator (HELIAS) is considered as a possible long-term alternative to a tokamak DEMOnstration power plant (DEMO). From the plasma physics point of view, the HELIAS 5-B is a very promising reactor concept. It consists in a large 5 field period stellarator reactor directly extrapolated from Wendelstein 7-X. Intense studies are currently ongoing at KIT in order to achieve a preliminary design of a breeding blanket (BB) for the HELIAS 5-B reactor which takes the outcomes from the pre-conceptual design of the tokamak DEMO BB into account. To this end, the Helium-Cooled Pebble Bed (HCPB) and the Water-Cooled Lithium Lead (WCLL) BB concepts have been considering, focusing on the investigation of the suitability of their main structural features to the stellarator geometry. In this regard, possible design constraints coming from the Remote Maintenance (RM) have to be fulfilled in order to better align the blanket segmentation. In the present work a more sophisticated structural assessment of the central region of a HELIAS 5-B BB half sector has been performed, paying attention to the predicted displacement field. The study has been aimed at the refinement of the numerical model so far adopted, investigating the impact of the major assumptions, such as Vacuum Vessel (VV) temperature and equivalent Young’s Modulus, on the obtained results. The results are herewith presented and critically discussed, giving some hints for the follow-up of this activity.

Three-dimensional traction microscopy accounting for cell-induced matrix degradation

Tractions exerted by cells on the extracellular matrix (ECM) are critical in many important physiological and pathological processes such as embryonic morphogenesis, wound healing, and cancer metastasis. Three-dimensional Traction Microscopy (3DTM) is a tool to quantify cellular tractions by first measuring the displacement field in the ECM in response to these tractions, and then using this measurement to infer tractions. Most applications of 3DTM have assumed that the ECM has spatially-uniform mechanical properties, but cells secrete enzymes that can locally degrade the ECM. In this work, a novel computational method is developed to quantify both cellular tractions and ECM degradation. In particular, the ECM is modeled as a hyperelastic, Neo-Hookean solid, whose material parameters are corrupted by a single degradation parameter. The feasibility of determining both the traction and the degradation parameter is first demonstrated by showing the existence and uniqueness of the solution. An inverse problem is then formulated to determine the nodal values of the traction vector and the degradation parameter, with the objective of minimizing the difference between a predicted and measured displacement field, under the constraint that the predicted displacement field satisfies the equation of equilibrium. The inverse problem is solved by means of a gradient-based optimization approach, and the gradient is computed efficiently using appropriately derived adjoint fields. The computational method is validated in-silico using a geometrically realistic neuronal cell model and synthetic traction and degradation fields. It is found that the method accurately recovers both the traction and degradation fields. Moreover, it is found that neglecting ECM degradation can yield significant errors in traction measurements. Our method can extend the range of context where tractions can be appropriately measured.

Three-dimensional traction microscopy with a fiber-based constitutive model

Tractions exerted by cells on their surroundings play an important role in many biological processes including stem cell differentiation, tumorigenesis, cell migration, cancer metastasis, and angiogenesis. The ability to quantify these tractions is important in understanding and manipulating these processes. Three-dimensional traction force microscopy (3DTFM) provides reliable means of evaluating cellular tractions by first measuring the displacement of fluorescent beads in response to these tractions in the surrounding matrix, and then using this measurement to compute the tractions. However, most applications of 3DTFM assume that the surrounding extra-cellular matrix (ECM) is non-fibrous, despite the fact that in many natural and synthetic environments the ECM contains a significant proportion of fibrous components. Motivated by this, we develop a computational approach for determining tractions, while accounting for the fibrous nature of the ECM. In particular, we make use of a fiber-based constitutive model in which the stress contains contributions from a distribution of nonlinear elastic fibers and a hyperelastic matrix. We solve an inverse problem with the nodal values of the traction vector as unknowns, and minimize the difference between a predicted displacement field, obtained by solving the equations of equilibrium in conjunction with the fiber-based constitutive model, and the measured displacement field at the bead locations. We employ a gradient-based minimization method to solve this problem and determine the gradient efficiently by solving for the appropriate adjoint field. We apply this algorithm to problems with experimentally observed cell geometries and synthetic, albeit realistic, traction fields to gauge its sensitivity to noise, and quantify the impact of using an incorrect constitutive model: the so-called model error. We conclude that the approach is robust to noise, yielding about 10% error in tractions for 5% displacement noise. We also conclude that the impact of model error is significant, where using a nonlinear exponential hyperelastic model instead of the fiber-based model, can lead to more than 100% error in the traction field. These results underline the importance of using appropriate constitutive models in 3DTFM, especially in fibrous ECM constructs.

Peridynamic Open-Hole Tensile Strength Prediction of Fiber-Reinforced Composite Laminate Using Energy-Based Failure Criteria

In the present study, peridynamic (PD) open-hole tensile (OHT) strength prediction of fiber-reinforced composite laminate using energy-based failure criteria is conducted. Spherical-horizon peridynamic laminate theory (PDLT) model is used. Energy-based failure criteria are introduced into the model. Delamination fracture modes can be distinguished in the present energy-based failure criteria. Three OHT testing results of fiber-reinforced composite laminate are chosen from literatures and used as benchmarks to validate the present PD composite model with energy-based failure criteria. It is shown that the PD predicted OHT strength fits the experimental results quite well. From the predicted displacement field, the fracture surface can be clearly detected. Typical damage modes of composite, fiber breakage, matrix crack, and delamination, are also illustrated in detail for each specimen. Numerical results in the present study validate the accuracy and reliability of the present PD composite model with energy-based failure criteria.

Elastic reconstruction of shear modulus and stress distribution for assessing abdominal aorta aneurysmal rupture risk

The necessity of surgical intervention of abdominal aorta aneurysms is based on a risk-reduction paradigm primarily relying on trans-abdominal ultrasound (US) measurements of the maximum diameter of an AAA. However, AAA diameter is only a rough estimate of rupture potential and elastographic estimates of material property changes and stresses within aortic tissue may be a better predictor. This work presents an elastic imaging technique to match model predicted displacement fields to those measured using clinical US. A linear elastic finite-element model is used and is assumed to be undergoing a quasi-static, plane strain deformation. This technique uses a regularization scheme to incorporate geometric segmentation information, as a penalty or soft prior, to counter the inherent ill-posedness of the inverse problem. In addition, displacement fields are measured and accumulated over the entire cardiac cycle and incorporated simultaneously in the reconstruction technique to improve the signal to noise of the recovered modulus distribution. Model predicted strain fields and modulus distributions are used to predict the relative stress induced over the cardiac cycle. Results of validation studies comparing modulus and stress fields performed using finite-element simulations of 3D and time dependent geometries, tissue-mimicking phantom simulations, and initial clinical results will be presented.

A comparison methodology for measured and predicted displacement fields in modal analysis

Recent advances in experimental mechanics have enabled full-field measurements of deformation fields and - particularly in the field of solid mechanics - methodologies have been proposed for utilizing these fields in the validation of computational models. However, the comparison of modal shapes and the path from the undeformed shape to the deformed shape at the extreme of a vibration cycle is not straightforward. Therefore a new method to compare vibration data from experiment to simulations is presented which uses full-field experimental data from the entire cycle of vibration. Here, the first three modes of vibration of an aerospace panel were compared, covering a frequency range of 14–59Hz and maximum out-of-plane displacements of 2mm. Two different comparison methodologies are considered; the first is the use of confidence bands, previously explored for quasi-static loading, the second is the use of a concordance correlation coefficient, which provides quantifiable information about the validity of the simulation. In addition, three different simulation conditions were considered, representing a systematic refinement of the model. It was found that meaningful conclusions can be drawn about the simulation by comparing individual components of deformation from the image decomposition process, such as the relative phase and magnitude. It was ultimately found that the best performing model did not entirely fall within the confidence bounds for all conditions, but returned a concordance correlation coefficient of nearly 70% for all three modes.

Dislocation characteristics of shear bands in metallic glasses

Using a digital image correlation technique, we measured the spatial displacement distribution around the shear band tip terminated in a deformed bulk metallic glass. The excellent agreement is found between the experimentally observed and theoretically predicted displacement fields for dislocations, which provides a direct evidence for the dislocation-like behaviour of the shear bands in metallic glasses.

Towards the mechanical characterization of abdominal wall by inverse analysis

The aim of this study is to characterize the passive mechanical behaviour of abdominal wall in vivo in an animal model using only external cameras and numerical analysis. The main objective lies in defining a methodology that provides in vivo information of a specific patient without altering mechanical properties. It is demonstrated in the mechanical study of abdomen for hernia purposes. Mechanical tests consisted on pneumoperitoneum tests performed on New Zealand rabbits, where inner pressure was varied from 0mmHg to 12mmHg. Changes in the external abdominal surface were recorded and several points were tracked. Based on their coordinates we reconstructed a 3D finite element model of the abdominal wall, considering an incompressible hyperelastic material model defined by two parameters. The spatial distributions of these parameters (shear modulus and non linear parameter) were calculated by inverse analysis, using two different types of regularization: Total Variation Diminishing (TVD) and Tikhonov (H1). After solving the inverse problem, the distribution of the material parameters were obtained along the abdominal surface. Accuracy of the results was evaluated for the last level of pressure.Results revealed a higher value of the shear modulus in a wide stripe along the craneo-caudal direction, associated with the presence of linea alba in conjunction with fascias and rectus abdominis. Non linear parameter distribution was smoother and the location of higher values varied with the regularization type. Both regularizations proved to yield in an accurate predicted displacement field, but H1 obtained a smoother material parameter distribution while TVD included some discontinuities. The methodology here presented was able to characterize in vivo the passive non linear mechanical response of the abdominal wall.

A reference material for establishing uncertainties in full-field displacement measurements

A simple reference material for establishing the minimum measurement uncertainty of optical systems for measuring 3D surface displacement fields in deforming objects is described and its use demonstrated by employing 3D digital image correlation as an exemplar technique. The reference material consists of a stepped bar, whose dimensions can be scaled to suit the application, and that can be clamped rigidly at its thick end to create an idealized cantilever. The cantilever was excited at resonance to generate out-of-plane displacements and, in a separate experiment, loaded statically in-plane to provide in-plane displacement fields. The displacements were measured using 3D digital image correlation and compared to the predicted displacement fields derived from tip deflections obtained using a calibrated transducer that provided traceability to the national standard for length. The minimum measurement uncertainties were evaluated by comparing the measured and predicted displacement fields, taking account of the uncertainties in the input parameters for the predictions. It was found that the minimum measurement uncertainties were less than 3% for the Cartesian components of displacement present during static in-plane bending and less than 3 µm for out-of-plane displacements during dynamic loading. It was concluded that this reference material was more straightforward to use, more versatile and yielded comparable results relative to an earlier design.

Effects of age and diabetes on scleral stiffness.

The effects of diabetes on the collagen structure and material properties of the sclera are unknown but may be important to elucidate whether diabetes is a risk factor for major ocular diseases such as glaucoma. This study provides a quantitative assessment of the changes in scleral stiffness and collagen fiber alignment associated with diabetes. Posterior scleral shells from five diabetic donors and seven non-diabetic donors were pressurized to 30 mm Hg. Three-dimensional surface displacements were calculated during inflation testing using digital image correlation (DIC). After testing, each specimen was subjected to wide-angle X-ray scattering (WAXS) measurements of its collagen organization. Specimen-specific finite element models of the posterior scleras were generated from the experimentally measured geometry. An inverse finite element analysis was developed to determine the material properties of the specimens, i.e., matrix and fiber stiffness, by matching DIC-measured and finite element predicted displacement fields. Effects of age and diabetes on the degree of fiber alignment, matrix and collagen fiber stiffness, and mechanical anisotropy were estimated using mixed effects models accounting for spatial autocorrelation. Older age was associated with a lower degree of fiber alignment and larger matrix stiffness for both diabetic and non-diabetic scleras. However, the age-related increase in matrix stiffness was 87% larger in diabetic specimens compared to non-diabetic controls and diabetic scleras had a significantly larger matrix stiffness (p = 0.01). Older age was associated with a nearly significant increase in collagen fiber stiffness for diabetic specimens only (p = 0.06), as well as a decrease in mechanical anisotropy for non-diabetic scleras only (p = 0.04). The interaction between age and diabetes was not significant for all outcomes. This study suggests that the age-related increase in scleral stiffness is accelerated in eyes with diabetes, which may have important implications in glaucoma.

Volume digital image correlation to assess displacement field in compression loaded bread crumb under X-ray microtomography

Abstract In this study, we present an original approach to assess structural changes during bread crumb compression using a mechanical testing bench coupled to 3D X-ray microtomography. X-ray images taken at different levels of compression of the bread crumb are processed using image analysis. A subset-based digital volume correlation method is used to achieve the 3D displacement field. Within the limit of the approach, deterministic search strategy is implemented for solving subset displacement in each deformed image with regards to the undeformed one. The predicted displacement field in the transverse directions shows differences that depend on local cell arrangement as confirmed by finite element analysis. The displacement component in the loading direction is affected by the magnitude of imposed displacement and shows more regular change. Large displacement levels in the compression direction are in good agreement with the imposed experimental displacement. The results presented here are promising in a sense of possible identification of local foam properties. New insights are expected to achieve better understanding of structural heterogeneities in the overall perception of the product. Industrial relevance Texture evaluation of cereal product is an important aspect for testing consumer acceptability of new designed products. Mechanical evaluation of backed products is a systemic route for determining texture of cereal based product. From the industrial viewpoint, mechanical evaluation allows saving both time and cost compared to panel evaluation. We demonstrate that better understanding of structural changes during texture evaluation can be achieved in addition to texture evaluation. Sensing structural changes during bread crumb compression is achievable by combining novel imaging technique and processing based on image analysis. We present thus an efficient way to predict displacements during compression of freshly baked product. This method can be used in different practical situations such as in plants or labs at the cost of having access to 3D imaging facilities.

Improved reconstruction of 4D-MR images by motion predictions.

The reconstruction of 4D images from 2D navigator and data slices requires sufficient observations per motion state to avoid blurred images and motion artifacts between slices. Especially images from rare motion states, like deep inhalations during free-breathing, suffer from too few observations. To address this problem, we propose to actively generate more suitable images instead of only selecting from the available images. The method is based on learning the relationship between navigator and data-slice motion by linear regression after dimensionality reduction. This can then be used to predict new data slices for a given navigator by warping existing data slices by their predicted displacement field. The method was evaluated for 4D-MRIs of the liver under free-breathing, where sliding boundaries pose an additional challenge for image registration. Leave-one-out tests for five short sequences of ten volunteers showed that the proposed prediction method improved on average the residual mean (95%) motion between the ground truth and predicted data slice from 0.9mm (1.9mm) to 0.8mm (1.6mm) in comparison to the best selection method. The approach was particularly suited for unusual motion states, where the mean error was reduced by 40% (2.2mm vs. 1.3mm).

Temperature and Displacement Fields Measurements to Assist the Numerical Simulation of the Welding-Brazing Process of Thin Automotive Parts

Car manufacturers use many different mechanical or thermo-mechanical processes to assemble thin metal sheets. Each of these processes may induce –more or less localizedundesirable deformations of the assembled sheets. The numerical simulation of these deformations via the use of predictive thermo-mechanical finite element analyses may help and reduce development time and cost. To validate such complex non-linear numerical simulations by comparison of the numerical results with experimental evidence, it is necessary to develop well-controlled and highly instrumented tests. Welding-brazing is one the various assembly processes involving a heat source used by car manufacturers to assemble thin –typically 0.7 to 1mm thick- metal sheets. Predictive heat transfer simulations of this process require accurate modelling of both the heat source and the boundary conditions imposed onto the assembled sheets –including the contact between the sheets. Using ABAQUS general-purpose finite element code for this study, the welding-brazing heat source is modelled as the combination of a 3D volumetric source corresponding to the welding-brazing joint, and a 2D surface source corresponding to the heat flux emitted by the laser beam onto the sheets in the vicinity of the joint. Besides, the contact between the sheets is modelled by a thermal resistance depending on the pressure between the sheets when they are in contact, or the distance between them when they are apart. Identification of heat source and contact models is derived from the results of weldingbrazing tests instrumented with thermocouples and infrared cameras. Micrographic observations in the vicinity of the welding-brazing joint are used to (partially) validate the numerical predictions of the Heat Affected Zone (HAZ). After validation of this heat transfer numerical analysis, the thermo-mechanical analysis of the process will be validated by comparison of the predicted displacement fields with the results of 3D Digital Image Correlation (stereo-correlation) measurements made during the welding-brazing tests.