Forward Deformation Research Articles

Critical analysis of the prediction of stress relaxation from forward creep of Type 316H austenitic stainless steel

This work evaluates the effectiveness of using forward creep deformation laws to predict the observed relaxation behaviour of 316H austenitic stainless steel. A summary of empirical creep methods, forward and stress relaxation experimental data were given. A primary and secondary creep strain rate (RCC-MR) model and an average creep strain rate model are combined with derived material constants to predict a group of stress relaxation tests at temperatures from 475°C to 600°C. The RCC-MR primary creep model predicted the stress relaxation behaviour soundly and the average creep strain rate model underestimated all of the stress relaxation data. The difference between stress relaxations predicted using strain hardening and time hardening versions of the RCC-MR equations are small. Factors affecting the predictions; including limitations in data range, data scatter, selection of a forward creep model, application of a forward model to stress relaxation and difference between forward creep and stress relaxation and are discussed.

Physical Models for Simulation and Reconstruction of Human Tissue Deformation Fields in Dynamic MRI

Medical image registration can be formulated as a tissue deformation problem, where parameter estimation methods are used to obtain the inverse deformation. However, there is limited knowledge about the ability to recover an unknown deformation. The main objective of this study is to estimate the quality of a restored deformation field obtained from image registration of dynamic MR sequences. We investigate the behavior of forward deformation models of various complexities. Further, we study the accuracy of restored inverse deformations generated by image registration. We found that the choice of 1) heterogeneous tissue parameters and 2) a poroelastic (instead of elastic) model had significant impact on the forward deformation. In the image registration problem, both 1) and 2) were found not to be significant. Here, the presence of image features were dominating the performance. We also found that existing algorithms will align images with high precision while at the same time obtain a deformation field with a relative error of 40%. Image registration can only moderately well restore the true deformation field. Still, estimation of volume changes instead of deformation fields can be fairly accurate and may represent a proxy for variations in tissue characteristics. Volume changes remain essentially unchanged under choice of discretization and the prevalence of pronounced image features. We suggest that image registration of high-contrast MR images has potential to be used as a tool to produce imaging biomarkers sensitive to pathology affecting tissue stiffness.

Effect of deformation mode and grain size on Bauschinger behavior of annealed copper

The present investigation looks into the effect of forward deformation mode, monotonic and cyclic, but asymmetric, on the Bauschinger phenomenon of annealed polycrystalline copper in terms of different Bauschinger parameters for 2.5–18% unidirectional tensile strain. Apart from the amount of deformation, the Bauschinger phenomenon has also been looked into as a function of stress rate used for forward deformation and also the grain size. It is found that Bauschinger effect is less pronounced when the forward deformation is carried out through asymmetric cyclic loading as compared to monotonic loading. This difference in the Bauschinger effect is attributed to lower back stress developed during asymmetric cyclic loading as compared to monotonic deformation. In the present investigation very negligible influence of stress rate on Bauschinger effect has been observed. On the other hand, for both monotonic and asymmetric cyclic deformation it is observed that Bauschinger effect is more in case of fine grain size.

Toward adaptive radiotherapy for head and neck patients: Uncertainties in dose warping due to the choice of deformable registration algorithm.

The aims of this work were to evaluate the performance of several deformable image registration (DIR) algorithms implemented in our in-house software (NiftyReg) and the uncertainties inherent to using different algorithms for dose warping. The authors describe a DIR based adaptive radiotherapy workflow, using CT and cone-beam CT (CBCT) imaging. The transformations that mapped the anatomy between the two time points were obtained using four different DIR approaches available in NiftyReg. These included a standard unidirectional algorithm and more sophisticated bidirectional ones that encourage or ensure inverse consistency. The forward (CT-to-CBCT) deformation vector fields (DVFs) were used to propagate the CT Hounsfield units and structures to the daily geometry for "dose of the day" calculations, while the backward (CBCT-to-CT) DVFs were used to remap the dose of the day onto the planning CT (pCT). Data from five head and neck patients were used to evaluate the performance of each implementation based on geometrical matching, physical properties of the DVFs, and similarity between warped dose distributions. Geometrical matching was verified in terms of dice similarity coefficient (DSC), distance transform, false positives, and false negatives. The physical properties of the DVFs were assessed calculating the harmonic energy, determinant of the Jacobian, and inverse consistency error of the transformations. Dose distributions were displayed on the pCT dose space and compared using dose difference (DD), distance to dose difference, and dose volume histograms. All the DIR algorithms gave similar results in terms of geometrical matching, with an average DSC of 0.85 ± 0.08, but the underlying properties of the DVFs varied in terms of smoothness and inverse consistency. When comparing the doses warped by different algorithms, we found a root mean square DD of 1.9% ± 0.8% of the prescribed dose (pD) and that an average of 9% ± 4% of voxels within the treated volume failed a 2%pD DD-test (DD2%-pp). Larger DD2%-pp was found within the high dose gradient (21% ± 6%) and regions where the CBCT quality was poorer (28% ± 9%). The differences when estimating the mean and maximum dose delivered to organs-at-risk were up to 2.0%pD and 2.8%pD, respectively. The authors evaluated several DIR algorithms for CT-to-CBCT registrations. In spite of all methods resulting in comparable geometrical matching, the choice of DIR implementation leads to uncertainties in dose warped, particularly in regions of high gradient and/or poor imaging quality.

ICONE23-1582 Atomistic simulation of yield and plastic deformation in bulk nanostructured metals

The influence of dislocation density on yield strength, which is a key factor in the anomalous deformation behavior in UFG metals, was investigated by huge scale atomistic simulations. Polycrystalline models with intragulanular Frank-Read sources were constructed to elucidate the relationship between the inter- and intra-granular plastic deformation processes and the mechanical properties. Then the uniaxial tension and compression were applied to the polycrystalline copper. Consequently it was found that Frank-Read sources were activated prior to intergranular dislocation emission, and the yield event of the whole system seems to occur when some dislocation sources activated. The yield stress is strongly influenced by the number of intragranular dislocation sources, i.e., dislocation density. Additionally, the Bauschinger effect of UFG metals is caused by the change in dislocation density in the process of forward and backward deformation.

Unlocking stranded resources in naturally fractured reservoirs using a novel approach to structural reconstructions and palaeostress field modelling: an example from the Hoton field, southern North Sea, UKCS

Abstract Remaining resources in mature basins, such as the southern North Sea (SNS), are often associated with complex or unconventional reservoirs. Unlocking the value of these resources requires non-conventional approaches to the description and the development of the reservoir. Originally developed as a conventional reservoir, the Hoton field in the SNS delivers economic rates from a tight and fractured Lower Leman Sandstone. The northern part of the field is developed via a trilateral producer, but the field's southern half, which appraisal drilling showed to consist of poor-quality rock, was deemed too tight for development. Roughly 40% of the field's resource of dry gas lies within the southern part of the field with no plans to develop it. A reassessment of the southern area's potential using geomechanical tools suggests that it also could deliver commercial well rates, similar to those experienced in the northern area of the field. A combination of structural restorations using Dynel2D and forward deformation modelling using Poly3D produces palaeostress predictions, which are used to constrain a discrete fracture network model. From these, well profiles are generated that suggest that a development well into the southern part of the field can recover about half of the currently stranded resource.

Progressive offset and surface deformation along a seismogenic blind thrust in the Po Plain foredeep (Southern Alps, Northern Italy)

AbstractHere we present, for the first time in the Po Plain foredeep (Northern Italy), the middle to late Pleistocene growth history of an outcropping secondary fold and related faults, whose progressive deformation over an intermediate time window (105 years) is driven by an underlying seismogenic blind thrust. We trenched and logged an outcropping decametric secondary anticline, related to a deeper blind compressional structure, which deforms fluvial sediments and an overlying loess‐paleosol sequence. Folded units were dated, using radiocarbon and optically stimulated luminescence methods, to the late Pleistocene–Holocene and tentatively correlated with glacial‐interglacial phases occurring during the time interval from marine isotope stage 6 to the present. A multistep retrodeformation of the fold allowed us to calculate uplift rates for this secondary and shallow anticline, varying between 0.02 and 0.1 mm/yr since circa 200 kyr. Trishear forward deformation modeling of the fold indicates that the amplification of the observed fold could be caused by two shallow thrusts formed through a break‐backward activation. This generated a decametric surface fold whose most recent growth was associated with bending‐moment normal faulting in the crestal and forelimb region. Our observations demonstrate that near‐surface compressive tectonics can be caused by blind thrusting, via a complex array of fault and folds: upward strain propagation and generation of shallow low‐angle thrust and related folding seem to be mainly due to secondary fold‐related faulting, according to an out‐of‐syncline thrusting mechanism.

Metal Average Deformation Velocity and Forward Slip Model for Longitudinal Profiled Plate Rolling Process

Based on the characteristics of longitudinal profiled plate rolling process, longitudinal profiled plate rolling process is a non-stable rolling process. The rule of volume flow rate has not applied to the longitudinal profiled plate rolling process. So, forward slip model and metal average deformation velocity of conventional rolling do not apply to longitudinal profiled plate rolling process. Forward slip model and metal average deformation velocity of longitudinal profiled plate rolling process are deduced by according to the definition of forward slip and metal average deformation velocity.

Analysis of deformation characteristic in multi-way loading forming process of aluminum alloy cross valve based on finite element model

The deformation characteristic in the forming process of aluminum alloy 7075 cross valve under multi-way loading was investigated by numerical simulation method. The results indicate that there exist 4 deformation patterns in the multi-way loading forming process of cross valve, such as forward extrusion, backward extrusion, forward-lateral extrusion and backward-lateral extrusion; one or several patterns occur at different forming stages depending on loading path. In general, the main deformation pattern is forward extrusion or backward extrusion at the initial stage; the main deformation pattern is backward extrusion at the intermediate stage, and the backward extrusion and forward-lateral extrusion occur at the final stage. In order to improve the cavity fill and reduce the forming defects, the lateral extrusion deformation should be increased at the initial and intermediate stages, and the forward extrusion deformation at the final forging stage should be reduced or avoided.

A framework for deformable image registration validation in radiotherapy clinical applications.

Quantitative validation of deformable image registration (DIR) algorithms is extremely difficult because of the complexity involved in constructing a deformable phantom that can duplicate various clinical scenarios. The purpose of this study is to describe a framework to test the accuracy of DIR based on computational modeling and evaluating using inverse consistency and other methods. Three clinically relevant organ deformations were created in prostate (distended rectum and rectal gas), head and neck (large neck flexion), and lung (inhale and exhale lung volumes with variable contrast enhancement) study sets. DIR was performed using both B‐spline and diffeomorphic demons algorithms in the forward and inverse direction. A compositive accumulation of forward and inverse deformation vector fields was done to quantify the inverse consistency error (ICE). The anatomical correspondence of tumor and organs at risk was quantified by comparing the original RT structures with those obtained after DIR. Further, the physical characteristics of the deformation field, namely the Jacobian and harmonic energy, were computed to quantify the preservation of image topology and regularity of spatial transformation obtained in DIR. The ICE was comparable in prostate case but the B‐spline algorithm had significantly better anatomical correspondence for rectum and prostate than diffeomorphic demons algorithm. The ICE was 6.5 mm for demons algorithm for head and neck case when compared to 0.7 mm for B‐spline. Since the induced neck flexion was large, the average Dice similarity coefficient between both algorithms was only 0.87, 0.52, 0.81, and 0.67 for tumor, cord, parotids, and mandible, respectively. The B‐spline algorithm accurately estimated deformations between images with variable contrast in our lung study, while diffeomorphic demons algorithm led to gross errors on structures affected by contrast variation. The proposed framework offers the application of known deformations on any image datasets, to evaluate the overall accuracy and limitations of a DIR algorithm used in radiation oncology. The evaluation based on anatomical correspondence, physical characteristics of deformation field, and image characteristics can facilitate DIR verification with the ultimate goal of implementing adaptive radiotherapy. The suitability of application of a particular evaluation metric in validating DIR is dependent on the clinical deformation observed.PACS numbers: 87.57 nj, 87.55‐x,87.55 Qr

Crustal deformations in the epicentral area of the West Bohemia 2008 earthquake swarm in central Europe

In West Bohemia, central Europe, during October 2008 an earthquake swarm of 25,000 shocks with a maximum event of ML ∼ 3.7–3.8 occurred at depths of 7–11 km. In 2007, annual GPS campaigns were launched. During the co‐seismic phase, displacements of a few centimeters were detected at GPS sites. Maximum displacement was revealed at the KOPA site, which subsided by 167 mm. The epicentral area is covered by eluvium of 4–10 m thick, and is located in undulating pastures and well‐forested valleys where visible surface soil effects could not be observed. To test possible fault manifestations, rough geomorphologic, geoelectric, and geochemical surveys were performed. GPS and seismic data, with geologic materials, were used to build a forward model for surface displacements, crustal deformations, and shear and normal stress fields. The fields enabled us to better determine crustal deformations and stresses that appeared within the seismic cycle, during the pre‐, co‐, and post‐seismic phases. During the co‐seismic phase, modeled fault motions along N‐S faults located within the epicentral zone reached 0.6–1 mm/day. Possible structural block rotations were comprised of these motions. A dominant role for stress accumulation, release, and relaxation was assigned to the Mariánské Lázně fault zone and the Nový Kostel zone. Strain loads slowly, and when local PT conditions with an action of deep magmatic fluids reach instability, the strain is released and stress balancing occurs. The process leads to the reversible motions known for silent earthquakes. A forward crustal deformation model for West Bohemia is also presented within.

Pitfalls among the promises of mechanics-based restoration: Addressing implications of unphysical boundary conditions

Mechanics-based restoration has been seen by some in the structural geology community as a panacea – a new technology that melds the retrodeformational merits of kinematic balancing with principles of continuum mechanics. The method has been touted for its ability to simulate complex 3D systems without assumptions of plane strain, allowing for heterogeneous fault slip distributions and mechanical interaction of fault segments. It has been suggested as a means to predict distributions of geologic strain and associated small-scale structures; however, we demonstrate that the kinematics of restoration models may differ significantly from forward deformation. Restoration models are governed by boundary conditions that are different from the forces driving forward geologic deformation. Models may be improved by supplementing restoration boundary conditions with loads that attempt to reverse tectonic strain, but unphysical artifacts persist. Mechanics-based restoration may be an appropriate tool for traditional applications of kinematic models including validation of structural interpretation and modeling geometric evolution; however, more subtle features, particularly strain distribution, should be treated with skepticism. Restoration models may provide insights to the initial configuration of forward mechanical models with physically appropriate boundary conditions and non-linear material behavior. Forward models provide the best means for simulating deformation and predicting subsidiary structures.

The SISMA prototype system: integrating Geophysical Modeling and Earth Observation for time-dependent seismic hazard assessment

An innovative approach to seismic hazard assessment is illustrated that, based on the available knowledge of the physical properties of the Earth structure and of seismic sources, on geodetic observations, as well as on the geophysical forward modeling, allows for a time-dependent definition of the seismic input. According to the proposed approach, a fully formalized system integrating Earth Observation data and new advanced methods in seismological and geophysical data analysis is currently under development in the framework of the Pilot Project SISMA, funded by the Italian Space Agency. The synergic use of geodetic Earth Observation data (EO) and Geophysical Forward Modeling deformation maps at the national scale complements the space- and time-dependent information provided by real-time monitoring of seismic flow (performed by means of the earthquake prediction algorithms CN and M8S) and permits the identification and routine updating of alerted areas. At the local spatial scale (tens of km) of the seismogenic nodes identified by pattern-recognition analysis, both GNSS (Global Navigation Satellite System) and SAR (Synthetic Aperture Radar) techniques, coupled with expressly developed models for interseismic phase, allow us to retrieve the deformation style and stress evolution within the seismogenic areas. The displacement fields obtained from EO data provide the input for the geophysical modeling, which eventually permits to indicate whether a specific fault is in a “critical state.” The scenarios of expected ground motion (shakemaps) associated with the alerted areas are then defined by means of full waveforms modeling, based on the possibility to compute synthetic seismograms by the modal summation technique (neo-deterministic hazard assessment). In this way, a set of deterministic scenarios of ground motion, which refer to the time interval when a strong event is likely to occur within the alerted area, can be defined both at national and at local scale. The considered integrated approach opens new routes in understanding the dynamics of fault zones as well as in modeling the expected ground motion. The SISMA system, in fact, provides tools for establishing warning criteria based on deterministic and rigorous forward geophysical models and hence allows for a well-controlled real-time prospective testing and validation of the proposed methodology over the Italian territory. The proposed approach complements the traditional probabilistic approach for seismic hazard estimates, since it supplies routinely updated information useful in assigning priorities for timely mitigation actions and hence it is particularly relevant to Civil Defense purposes.

Constitutive equations that describe creep stress relaxation for 316H stainless steel at 550°C

The prediction of the stress relaxation behaviour of welding induced residual stresses in thick section 316H austenitic stainless steel welded component provides an input for quantifying reheat crack initiation observed in the heat affected zone. The cracks occur after service at a temperature range from 490 to 520°C. The present work reviews some of the widely applied stress relaxation models. The relative strengths and weaknesses of these existing models are discussed. An improved constitutive equation derived from a forward uniaxial creep deformation law is proposed. The relative importance of the parameters selected in the new constitutive model, when compared with experimental data, is discussed. The importance of a better understanding of the role of the internal stress and its measurement is highlighted.

Constitutive equations that describe creep stress relaxation for 316H stainless steel at 550°C

The prediction of the stress relaxation behaviour of welding induced residual stresses in thick section 316H austenitic stainless steel welded component provides an input for quantifying reheat crack initiation observed in the heat affected zone. The cracks occur after service at a temperature range from 490 to 520°C. The present work reviews some of the widely applied stress relaxation models. The relative strengths and weaknesses of these existing models are discussed. An improved constitutive equation derived from a forward uniaxial creep deformation law is proposed. The relative importance of the parameters selected in the new constitutive model, when compared with experimental data, is discussed. The importance of a better understanding of the role of the internal stress and its measurement is highlighted.

Biaxial elastic–viscoplastic behavior of Nafion membranes

Durability is a major limitation of current proton exchange membrane fuel cells. Mechanical stress due to hygro-thermal cycling is one failure mechanism of the polymer electrolyte membrane (PEM). In a fuel cell the PEM is highly constrained in the membrane plane and relatively unconstrained in the through-thickness direction, leading to primarily biaxial loading upon hygro-thermal cycling. The rate, temperature, and hydration dependent elastic–viscoplastic mechanical behavior of Nafion, the benchmark PEM, has been extensively investigated in uniaxial tension in prior work which also served as a data basis for a three dimensional constitutive model. Here, the important effects of the biaxiality of the loading conditions on the elastic–viscoplastic Nafion stress–strain behavior are investigated for the first time via experiments and simulation. Biaxial stress–strain behaviors were shown to exhibit similar features to uniaxial behavior including linear elasticity followed by a highly non-linear transition to yield followed by post-yield strain hardening with highly non-linear unloading and reloading; these features were each quantitatively dependent on the biaxiality of the loading conditions. The constitutive model was found to successfully quantitatively predict the loading behavior and its dependence on biaxiality. The constitutive model was also found to predict the magnitude of the yield shoulder during unloading and reloading, but to underestimate the gradual nature of both the forward and reverse plastic deformation processes as well as the strain recovery at zero load. These errors are consistent with those seen in the uniaxial model indicating that the framework used to incorporate the uniaxial behavior into a three dimensional model is capable of predicting the biaxial deformation response of the membrane.

Low-energy tensile-impact behavior of superelastic NiTi shape memory alloy wires

Superelastic property of shape memory alloys (SMAs) is becoming increasingly important for impact applications due to their large recoverable strains and high capacity to dissipate energy. In this work, tensile behavior of superelastic NiTi SMA wires at impact strain rates was studied by instrumented tensile-impact technique, which allows to obtain material properties on the order of 1–10 2 s −1. The results show that even at impact strain rates, martensite can be induced by tension in NiTi. At impact, a plateau stress appears during transformations similar to that at quasi-static strain rates, but 100–150 MPa higher in stress. This is due to the higher temperatures achieved during the deformation due to the close to adiabatic nature of the impact event. The influence of the strain rate over the mechanical behavior of NiTi was spread to the quasi-static strain rates so that the evolution of several parameters was also studied on the range 10 −5–10 2 s −1. Therefore, forward stress-induced martensitic (SIM) transformation stresses ( σ Ms and σ Mf) and deformation energy ( E d) increase with strain rate, but they are strain rate independent from 10 −1 s −1 at least until 10 2 s −1. Reverse SIM transformation stresses ( σ As and σ Af), recoverable strain energy ( E r), and dissipated energy ( W d) depend mainly on maximum strain achieved during the deformation, but for strains corresponding to a load–unload cycle with complete SIM transformation, σ As, σ Af and E r are higher at impact than at quasi-static strain rates, and W d shows similar values at very low strain rates and at impact.

SU-FF-I-101: Inverse Consistency Deformable Image Registration On Partially Matched Images

Purpose: For many RT applications, deformable image registrations (DIR) are often carried out between two images that only match partially. In addition, it is often desirable to use inverse consistency DIR to improve accuracy and to compute both the forward and backward deformation vector fields (DVF) simultaneously and consistently. Inverse consistency is especially important for adaptive radiotherapy applications because doses and structures need to be remapped between the planning image and the daily image using both forward and backward DVFs. Image mismatching (superior‐inferior coverage difference, field‐of‐view (FOV) cutoff, etc) makes it difficult for inverse consistency DIR algorithms which normally need both images to have matched image content and dimensions. Therefore, we propose a method in this study to perform inverse consistency DIR for these image mismatch situations. Method: Our method is based on the inverse consistency optical flow algorithm (Yang, PMB, 2008). The idea of allowing image mismatching is to extend the image volumes and define the extension voxel (outside the original image volume) values as NaN (not‐a‐number). NaN values are transparent to all floating‐point arithmetic computations in the DIR computation, including re‐sampling, interpolation, etc. With the NaN voxels, registrations are carried out with one additional rule that a NaN voxel can match any voxel. In this way, the matched sections of the images are registered properly, and the mismatched sections of the images are registered to NaN voxels. Results: We demonstrate the proposed method with Tomotherapy MVCT images with FOV cutoff problems and smaller volumetric coverage. Our results suggest that the proposed method could significantly improve image registration accuracy, especially near or in the mismatched image regions. Conclusion: This proposed method makes it possible to obtain inverse consistent DVFs on partially matched images that are usually difficult to register otherwise.

Forward modeling synsedimentary deformation associated with a prograding steep-sloped carbonate margin

Differential compaction associated with prograding and aggrading steep-sloped carbonate margins leads to penecontemporaneous and post-depositional modifications of stratal geometries and tensile and shear stress concentrations that might result in brittle deformation. In an effort to investigate controls on these deformation processes, we employ a step-wise gravity loaded elastic model that captures pre-failure displacement and stress field patterns for a depositional geometry based on the Permian Capitan depositional system, Guadalupe Mountains, West Texas and New Mexico, USA. We consider four model geometries with varying progradation to aggradation (P/A) ratios, from strongly prograding (P/A = 10) to strongly aggrading (P/A = 0.1). The strongly prograding case (P/A = 10) is used for sensitivity analysis that investigates the effects of varying rock mechanical properties of basin and platform facies. Model results yield relatively consistent patterns of deformation and stress that include: (1) a region of enhanced subsidence centered near the platform margin, (2) basinward displacement of the platform margin that decreases down slope, and (3) positive maximum Coulomb stress and positive (tensile) stress, both in-plane and out-of-plane, near the platform margin and in adjacent slope and platform facies. The patterns of deformation for the strongly progradational model are strikingly similar to present day stratal geometries of the Capitan depositional system that are often inferred to be primarily depositional in origin. Model results suggest that these geometries are established immediately upon deposition and may therefore affect the stratal architecture of the margin, but significant additional deformation also occurs during subsequent platform growth. We interpret the regions of positive Coulomb stress and tensile stress as areas likely to fail by faulting or jointing, respectively. This inference is corroborated by field observations of early-formed brittle deformation features in the Capitan margin. Our geomechanical models of the Capitan margin suggest that early-formed deformation is an integral part of the general steep-sloped carbonate system.

A simple fixed‐point approach to invert a deformation fielda)

Inversion of deformation fields is applied frequently to map images, dose, and contours between the reference frame and the study frame. A prevailing approach that takes the negative of the forward deformation as the inverse deformation is oversimplified and can cause large errors for large deformations or deformations that are composites of several deformations. Other approaches, including Newton's method and scatter data interpolation, either require the first derivative or are very inefficient. Here we propose an iterative approach that is easy to implement, converges quickly to the inverse when it does, and works for a majority of cases in practice. Our approach is rooted in fixed-point theory. We build a sequence to approximate the inverse deformation through iterative evaluation of the forward deformation. A sufficient but not necessary convergence condition (Lipschitz condition) and its proof are also given. Though this condition guarantees the convergence, it may not be met for an arbitrary deformation field. One should always check whether the inverse exists for the given forward deformation field by calculating its Jacobian. If nonpositive values of the Jacobian occur only for few voxels, this method will usually converge to a pseudoinverse. In case the iteration fails to converge, one should switch to other means of finding the inverse. We tested the proposed method on simulated 2D data and real 3D computed tomography data of a lung patient and compared our method with two implementations in the Insight Segmentation and Registration Toolkit (ITK). Typically less than ten iterations are needed for our method to get an inverse deformation field with clinically relevant accuracy. Based on the test results, our method is about ten times faster and yet ten times more accurate than ITK's iterative method for the same number of iterations. Simulations and real data tests demonstrated the efficacy and the accuracy of the proposed algorithm.