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Zdeněk P Bažant - One of the best experts on this subject based on the ideXlab platform.
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impact comminution of solids due to local kinetic energy of high Shear Strain rate i continuum theory and turbulence analogy
Journal of The Mechanics and Physics of Solids, 2014Co-Authors: Zdeněk P Bažant, Ferhun C CanerAbstract:The modeling of high velocity impact into brittle or quasibrittle solids is hampered by the unavailability of a constitutive model capturing the effects of material comminution into very fine particles. The present objective is to develop such a model, usable in finite element programs. The comminution at very high Strain rates can dissipate a large portion of the kinetic energy Of an impacting missile. The spatial derivative of the energy dissipated by comminution gives a force resisting the penetration, which is superposed on the nodal forces obtained from the static constitutive model in a finite element program. The present theory is inspired partly by Grady's model for expansive comminution due to explosion inside a hollow sphere, and partly by analogy with turbulence. In high velocity turbulent flow, the energy dissipation rate gets enhanced by the formation of micro-vortices (eddies) which dissipate energy by viscous Shear stress. Similarly, here it is assumed that the energy dissipation at fast deformation of a confined solid gets enhanced by the release of kinetic energy of the motion associated with a high-rate Shear Strain of forming particles. For simplicity, the shape of these particles in the plane of maximum Shear rate is considered to be regular hexagons. The particle sizes are assumed to be distributed according to the Schuhmann power law. The condition that the rate of release of the local kinetic energy must be equal to the interface fracture energy yields a relation between the particle size, the Shear Strain rate, the fracture energy and the mass density. As one experimental justification, the present theory agrees with Grady's empirical observation that, in impact events, the average particle size is proportional to the (-2/3) power of the Shear Strain rate. The main characteristic of the comminution process is a dimensionless number B-a (Eq. (37)) representing the ratio of the local kinetic energy of Shear Strain rate to the maximum possible Strain energy that can be stored in the same volume of material. It is shown that the kinetic energy release is proportional to the (2/3)-power of the Shear Strain rate, and that the dynamic comminution creates an apparent material viscosity inversely proportional to the (1/3)-power of that rate. After comminution, the interface fracture energy takes the role of interface friction, and it is pointed out that if the friction depends on the slip rate the aforementioned exponents would change. The effect of dynamic comminution can simply be taken into account by introducing the apparent viscosity into the material constitutive model, which is what is implemented in the paper that follows. (C) 2013 Elsevier Ltd. All rights reserved.
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impact comminution of solids due to local kinetic energy of high Shear Strain rate ii microplane model and verification
Journal of The Mechanics and Physics of Solids, 2014Co-Authors: Ferhun C Caner, Zdeněk P BažantAbstract:Abstract The new theory presented in the preceding paper, which models the dynamic comminution of concrete due to very high Shear Strain rate, is now compared to recent test data on the penetration of projectiles through concrete walls of different thicknesses, ranging from 127 to 254 mm. These data are analyzed by an explicit finite element code using the new microplane constitutive model M7 for concrete, which was previously shown to provide the most realistic description of the quasi-static uni-, bi- and tri-axial test data with complex loading path and unloading. Model M7 incorporates the quasi-static Strain rate effects due viscoelasticity and to the rate of cohesive crack debonding based on activation energy of bond ruptures, which are expected to extend to very high rates. Here model M7 is further enhanced by apparent viscosity capturing the energy dissipation due to the Strain-rate effect of comminution. The maximum Shear Strain rates in the computations are of the order of 105 s−1. The simulations document that, within the inevitable uncertainties, the measured exit velocities of the projectiles can be matched quite satisfactorily and the observed shapes of the entry and exit craters can be reproduced correctly.
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impact comminution of solids due to local kinetic energy of high Shear Strain rate ii microplane model and verification
Journal of The Mechanics and Physics of Solids, 2014Co-Authors: Ferhun C Caner, Zdeněk P BažantAbstract:The new theory presented in the preceding paper, which models the dynamic comminution of concrete due to very high Shear Strain rate, is now compared to recent test data on the penetration of projectiles through concrete walls of different thicknesses, ranging from 127 to 254 mm. These data are analyzed by an explicit finite element code using the new microplane constitutive model M7 for concrete, which was previously shown to provide the most realistic description of the quasi-static uni-, bi- and tri-axial test data with complex loading path and unloading. Model M7 incorporates the quasi-static Strain rate effects due viscoelasticity and to the rate of cohesive crack debonding based on activation energy of bond ruptures, which are expected to extend to very high rates. Here model M7 is further enhanced by apparent viscosity capturing the energy dissipation due to the Strain-rate effect of comminution. The maximum Shear Strain rates in the computations are of the order of 10(5) s(-1). The simulations document that, within the inevitable uncertainties, the measured exit velocities of the projectiles can be matched quite satisfactorily and the observed shapes of the entry and exit craters can be reproduced correctly. (C) 2014 Published by Elsevier Ltd.
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comminution of solids caused by kinetic energy of high Shear Strain rate with implications for impact shock and shale fracturing
Proceedings of the National Academy of Sciences of the United States of America, 2013Co-Authors: Zdeněk P Bažant, Ferhun C CanerAbstract:Although there exists a vast literature on the dynamic comminution or fragmentation of rocks, concrete, metals, and ceramics, none of the known models suffices for macroscopic dynamic finite element analysis. This paper outlines the basic idea of the macroscopic model. Unlike static fracture, in which the driving force is the release of Strain energy, here the essential idea is that the driving force of comminution under high-rate compression is the release of the local kinetic energy of Shear Strain rate. The density of this energy at Strain rates >1,000/s is found to exceed the maximum possible Strain energy density by orders of magnitude, making the Strain energy irrelevant. It is shown that particle size is proportional to the −2/3 power of the Shear Strain rate and the 2/3 power of the interface fracture energy or interface Shear stress, and that the comminution process is macroscopically equivalent to an apparent Shear viscosity that is proportional (at constant interface stress) to the −1/3 power of this rate. A dimensionless indicator of the comminution intensity is formulated. The theory was inspired by noting that the local kinetic energy of Shear Strain rate plays a role analogous to the local kinetic energy of eddies in turbulent flow.
Jonathan Ophir - One of the best experts on this subject based on the ideXlab platform.
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axial Shear Strain distributions in an elliptical inclusion model experimental validation and in vivo examples with implications to breast tumor classification
Ultrasound in Medicine and Biology, 2010Co-Authors: Arun K Thittai, Belfor Galaz, Jonathan OphirAbstract:Recently, we reported on the axial-Shear Strain fill-in of the interior of loosely bonded stiff elliptical inclu- sions in a soft backgroundat non-normal orientations, and the lack of fill-in in firmly bonded inclusions at any orien- tation. In this paper, we report on the experimental validation of the simulation studies using tissue-mimicking gelatin-based phantoms. We also show a few confirmatory examples of the existence of these phenomena in benign vs. malignant breast lesions in vivo. Phantom experiments showed that axial-Shear Strain zones caused by firmly bonded elliptical inclusions occurred only outside of the inclusion, as predicted by the simulation. By contrast, the axial-Shear Strain zones filled in the interior of loosely bonded elliptical inclusions at non-normal orientations. The axial-Shear Strain elastograms obtained from the in vivo cases appeared to be in general agreement with our experimental results. The results reported in this paper may have important clinical implications. Specifically, axial-Shear Strain fill-in inside an inclusion may be auniquesignature of stiff, loosely bonded, ellipsoidal or elongated inclusions at non-normal orientations. Thus, it may be useful as a marker of benignity of benign breast lesions (e.g., fibroadenomas) that are generally stiff, elongated and loosely bonded to the host tissues. (E-mail: Jonathan.Ophir@ uth.tmc.edu) 2010 World Federation for Ultrasound in Medicine & Biology.
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breast tumor classification using axial Shear Strain elastography a feasibility study
Physics in Medicine and Biology, 2008Co-Authors: Arun Thitaikumar, Louise M Mobbs, Christina M Kraemerchant, Brian S. Garra, Jonathan OphirAbstract:Recently, the feasibility of visualizing the characteristics of bonding at an inclusion-background boundary using axial-Shear Strain elastography was demonstrated. In this paper, we report a feasibility study on the utility of the axial-Shear Strain elastograms in the classification of in vivo breast tumor as being benign or malignant. The study was performed using data sets obtained from 15 benign and 15 malignant cases that were biopsy proven. A total of three independent observers were trained, and their services were utilized for the study. A total of 9 cases were used as training set and the remaining cases were used as testing set. The feature from the axial-Shear Strain elastogram, namely, the area of the axial-Shear region, was extracted by the observers. The observers also outlined the tumor area on the corresponding sonogram, which was used to normalize the area of the axial-Shear Strain region. There are several observations that can be drawn from the results. First, the result indicates that the observers consistently (~82% of the cases) noticed the characteristic pattern of the axial-Shear Strain distribution data as predicted in the previous simulation studies, i.e. alternating regions of positive and negative axial-Shear Strain values around the tumor–background interface. Second, the analysis of the result suggests that in approximately 57% of the cases in which the observers did not visualize tumor in the sonogram, the elastograms helped them to locate the tumor. Finally, the analysis of the result suggests that for the discriminant feature value of 0.46, the number of unnecessary biopsies could be reduced by 56.3% without compromising on sensitivity and on negative predictive value (NPV). Based on the results in this study, feature values greater than 0.75 appear to be indicative of malignancy, while values less than 0.46 to be indicative of benignity. Feature values between 0.46 and 0.75 may result in an overlap between benign and malignant cases.
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visualization of bonding at an inclusion boundary using axial Shear Strain elastography a feasibility study
Physics in Medicine and Biology, 2007Co-Authors: Thomas A. Krouskop, Arun Thitaikumar, Brian S. Garra, Jonathan OphirAbstract:Ultrasound elastography produces Strain images of compliant tissues under quasi-static compression. In axial-Shear Strain elastography, the local axial-Shear Strain resulting from application of quasi-static axial compression to an inhomogeneous material is imaged. The overall hypothesis of this work is that the pattern of axial-Shear Strain distribution around the inclusion/background interface is completely determined by the bonding at the interface after normalization for inclusion size and applied Strain levels, and that it is feasible to extract certain features from the axial-Shear Strain elastograms to quantify this pattern. The mechanical model used in this study consisted of a single stiff circular inclusion embedded in a homogeneous softer background. First, we performed a parametric study using finite-element analysis (FEA) (no ultrasound involved) to identify possible features that quantify the pattern of axial-Shear Strain distribution around an inclusion/background interface. Next, the ability to extract these features from axial-Shear Strain elastograms, estimated from simulated pre- and post-compression noisy RF data, was investigated. Further, the feasibility of extracting these features from in vivo breast data of benign and malignant tumors was also investigated. It is shown using the FEA study that the pattern of axial-Shear Strain distribution is determined by the degree of bonding at the inclusion/background interface. The results suggest the feasibility of using normalized features that capture the region of positive and negative axial-Shear Strain area to quantify the pattern of the axial-Shear Strain distribution. The simulation results showed that it was feasible to extract the features, as identified in the FEA study, from axial-Shear Strain elastograms. However, an effort must be made to obtain axial-Shear Strain elastograms with the highest signal-to-noise ratio (SNRasse) possible, without compromising the resolution. The in vivo results demonstrated the feasibility of producing and extracting features from the axial-Shear Strain elastograms from breast data. Furthermore, the in vivo axial-Shear Strain elastograms suggest an additional feature not identified in the simulations that may potentially be used for distinguishing benign from malignant tumors—the proximity of the axial-Shear Strain regions to the inclusion/background interface identified in the sonogram.
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signal to noise ratio contrast to noise ratio and their trade offs with resolution in axial Shear Strain elastography
Physics in Medicine and Biology, 2007Co-Authors: Thomas A. Krouskop, Arun Thitaikumar, Jonathan OphirAbstract:In axial-Shear Strain elastography, the local axial-Shear Strain resulting from the application of quasi-static axial compression to an inhomogeneous material is imaged. In this paper, we investigated the image quality of the axial-Shear Strain estimates in terms of the signal-to-noise ratio (SNRasse) and contrast-to-noise ratio (CNRasse) using simulations and experiments. Specifically, we investigated the influence of the system parameters (beamwidth, transducer element pitch and bandwidth), signal processing parameters (correlation window length and axial window shift) and mechanical parameters (Young's modulus contrast, applied axial Strain) on the SNRasse and CNRasse. The results of the study show that the CNRasse (SNRasse) is maximum for axial-Shear Strain values in the range of 0.005–0.03. For the inclusion/background modulus contrast range considered in this study (<10), the CNRasse (SNRasse) is maximum for applied axial compressive Strain values in the range of 0.005%–0.03%. This suggests that the RF data acquired during axial elastography can be used to obtain axial-Shear Strain elastograms, since this range is typically used in axial elastography as well. The CNRasse (SNRasse) remains almost constant with an increase in the beamwidth while it increases as the pitch increases. As expected, the axial shift had only a weak influence on the CNRasse (SNRasse) of the axial-Shear Strain estimates. We observed that the differential estimates of the axial-Shear Strain involve a trade-off between the CNRasse (SNRasse) and the spatial resolution only with respect to pitch and not with respect to signal processing parameters. Simulation studies were performed to confirm such an observation. The results demonstrate a trade-off between CNRasse and the resolution with respect to pitch.
Ferhun C Caner - One of the best experts on this subject based on the ideXlab platform.
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impact comminution of solids due to local kinetic energy of high Shear Strain rate i continuum theory and turbulence analogy
Journal of The Mechanics and Physics of Solids, 2014Co-Authors: Zdeněk P Bažant, Ferhun C CanerAbstract:The modeling of high velocity impact into brittle or quasibrittle solids is hampered by the unavailability of a constitutive model capturing the effects of material comminution into very fine particles. The present objective is to develop such a model, usable in finite element programs. The comminution at very high Strain rates can dissipate a large portion of the kinetic energy Of an impacting missile. The spatial derivative of the energy dissipated by comminution gives a force resisting the penetration, which is superposed on the nodal forces obtained from the static constitutive model in a finite element program. The present theory is inspired partly by Grady's model for expansive comminution due to explosion inside a hollow sphere, and partly by analogy with turbulence. In high velocity turbulent flow, the energy dissipation rate gets enhanced by the formation of micro-vortices (eddies) which dissipate energy by viscous Shear stress. Similarly, here it is assumed that the energy dissipation at fast deformation of a confined solid gets enhanced by the release of kinetic energy of the motion associated with a high-rate Shear Strain of forming particles. For simplicity, the shape of these particles in the plane of maximum Shear rate is considered to be regular hexagons. The particle sizes are assumed to be distributed according to the Schuhmann power law. The condition that the rate of release of the local kinetic energy must be equal to the interface fracture energy yields a relation between the particle size, the Shear Strain rate, the fracture energy and the mass density. As one experimental justification, the present theory agrees with Grady's empirical observation that, in impact events, the average particle size is proportional to the (-2/3) power of the Shear Strain rate. The main characteristic of the comminution process is a dimensionless number B-a (Eq. (37)) representing the ratio of the local kinetic energy of Shear Strain rate to the maximum possible Strain energy that can be stored in the same volume of material. It is shown that the kinetic energy release is proportional to the (2/3)-power of the Shear Strain rate, and that the dynamic comminution creates an apparent material viscosity inversely proportional to the (1/3)-power of that rate. After comminution, the interface fracture energy takes the role of interface friction, and it is pointed out that if the friction depends on the slip rate the aforementioned exponents would change. The effect of dynamic comminution can simply be taken into account by introducing the apparent viscosity into the material constitutive model, which is what is implemented in the paper that follows. (C) 2013 Elsevier Ltd. All rights reserved.
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impact comminution of solids due to local kinetic energy of high Shear Strain rate ii microplane model and verification
Journal of The Mechanics and Physics of Solids, 2014Co-Authors: Ferhun C Caner, Zdeněk P BažantAbstract:Abstract The new theory presented in the preceding paper, which models the dynamic comminution of concrete due to very high Shear Strain rate, is now compared to recent test data on the penetration of projectiles through concrete walls of different thicknesses, ranging from 127 to 254 mm. These data are analyzed by an explicit finite element code using the new microplane constitutive model M7 for concrete, which was previously shown to provide the most realistic description of the quasi-static uni-, bi- and tri-axial test data with complex loading path and unloading. Model M7 incorporates the quasi-static Strain rate effects due viscoelasticity and to the rate of cohesive crack debonding based on activation energy of bond ruptures, which are expected to extend to very high rates. Here model M7 is further enhanced by apparent viscosity capturing the energy dissipation due to the Strain-rate effect of comminution. The maximum Shear Strain rates in the computations are of the order of 105 s−1. The simulations document that, within the inevitable uncertainties, the measured exit velocities of the projectiles can be matched quite satisfactorily and the observed shapes of the entry and exit craters can be reproduced correctly.
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impact comminution of solids due to local kinetic energy of high Shear Strain rate ii microplane model and verification
Journal of The Mechanics and Physics of Solids, 2014Co-Authors: Ferhun C Caner, Zdeněk P BažantAbstract:The new theory presented in the preceding paper, which models the dynamic comminution of concrete due to very high Shear Strain rate, is now compared to recent test data on the penetration of projectiles through concrete walls of different thicknesses, ranging from 127 to 254 mm. These data are analyzed by an explicit finite element code using the new microplane constitutive model M7 for concrete, which was previously shown to provide the most realistic description of the quasi-static uni-, bi- and tri-axial test data with complex loading path and unloading. Model M7 incorporates the quasi-static Strain rate effects due viscoelasticity and to the rate of cohesive crack debonding based on activation energy of bond ruptures, which are expected to extend to very high rates. Here model M7 is further enhanced by apparent viscosity capturing the energy dissipation due to the Strain-rate effect of comminution. The maximum Shear Strain rates in the computations are of the order of 10(5) s(-1). The simulations document that, within the inevitable uncertainties, the measured exit velocities of the projectiles can be matched quite satisfactorily and the observed shapes of the entry and exit craters can be reproduced correctly. (C) 2014 Published by Elsevier Ltd.
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comminution of solids due to kinetic energy of high Shear Strain rate implications for shock and shale fracturing
Shale Energy Engineering 2014: Technical Challenges Environmental Issues and Public Policy, 2014Co-Authors: Zdene K P Bažant, Ferhun C CanerAbstract:This paper outlines the basic idea of a macroscopic model on the dynamic comminution or fragmentation of rocks, concrete, metals, and ceramics. The essential idea is that the driving force of comminution under high-rate Shear and compression with Shear is the release of the local kinetic energy of Shear Strain rate. The density of this energy at Strain rates >1,000/s is found to exceed the maximum possible Strain energy density by orders of magnitude, making the Strain energy irrelevant. It is shown that particle size is proportional to the −2/3 power of the Shear Strain rate and the 2/3 power of the interface fracture energy or interface Shear stress, and that the comminution process is macroscopically equivalent to an apparent Shear viscosity that is proportional (at constant interface friction) to the −1/3 power of this rate. A dimensionless indicator of the comminution intensity is formulated. The theory was inspired by noting that the local kinetic energy of Shear Strain rate plays a role analogous to the local kinetic energy of eddies in turbulent flow.
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comminution of solids caused by kinetic energy of high Shear Strain rate with implications for impact shock and shale fracturing
Proceedings of the National Academy of Sciences of the United States of America, 2013Co-Authors: Zdeněk P Bažant, Ferhun C CanerAbstract:Although there exists a vast literature on the dynamic comminution or fragmentation of rocks, concrete, metals, and ceramics, none of the known models suffices for macroscopic dynamic finite element analysis. This paper outlines the basic idea of the macroscopic model. Unlike static fracture, in which the driving force is the release of Strain energy, here the essential idea is that the driving force of comminution under high-rate compression is the release of the local kinetic energy of Shear Strain rate. The density of this energy at Strain rates >1,000/s is found to exceed the maximum possible Strain energy density by orders of magnitude, making the Strain energy irrelevant. It is shown that particle size is proportional to the −2/3 power of the Shear Strain rate and the 2/3 power of the interface fracture energy or interface Shear stress, and that the comminution process is macroscopically equivalent to an apparent Shear viscosity that is proportional (at constant interface stress) to the −1/3 power of this rate. A dimensionless indicator of the comminution intensity is formulated. The theory was inspired by noting that the local kinetic energy of Shear Strain rate plays a role analogous to the local kinetic energy of eddies in turbulent flow.
Arun Thitaikumar - One of the best experts on this subject based on the ideXlab platform.
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breast tumor classification using axial Shear Strain elastography a feasibility study
Physics in Medicine and Biology, 2008Co-Authors: Arun Thitaikumar, Louise M Mobbs, Christina M Kraemerchant, Brian S. Garra, Jonathan OphirAbstract:Recently, the feasibility of visualizing the characteristics of bonding at an inclusion-background boundary using axial-Shear Strain elastography was demonstrated. In this paper, we report a feasibility study on the utility of the axial-Shear Strain elastograms in the classification of in vivo breast tumor as being benign or malignant. The study was performed using data sets obtained from 15 benign and 15 malignant cases that were biopsy proven. A total of three independent observers were trained, and their services were utilized for the study. A total of 9 cases were used as training set and the remaining cases were used as testing set. The feature from the axial-Shear Strain elastogram, namely, the area of the axial-Shear region, was extracted by the observers. The observers also outlined the tumor area on the corresponding sonogram, which was used to normalize the area of the axial-Shear Strain region. There are several observations that can be drawn from the results. First, the result indicates that the observers consistently (~82% of the cases) noticed the characteristic pattern of the axial-Shear Strain distribution data as predicted in the previous simulation studies, i.e. alternating regions of positive and negative axial-Shear Strain values around the tumor–background interface. Second, the analysis of the result suggests that in approximately 57% of the cases in which the observers did not visualize tumor in the sonogram, the elastograms helped them to locate the tumor. Finally, the analysis of the result suggests that for the discriminant feature value of 0.46, the number of unnecessary biopsies could be reduced by 56.3% without compromising on sensitivity and on negative predictive value (NPV). Based on the results in this study, feature values greater than 0.75 appear to be indicative of malignancy, while values less than 0.46 to be indicative of benignity. Feature values between 0.46 and 0.75 may result in an overlap between benign and malignant cases.
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visualization of bonding at an inclusion boundary using axial Shear Strain elastography a feasibility study
Physics in Medicine and Biology, 2007Co-Authors: Thomas A. Krouskop, Arun Thitaikumar, Brian S. Garra, Jonathan OphirAbstract:Ultrasound elastography produces Strain images of compliant tissues under quasi-static compression. In axial-Shear Strain elastography, the local axial-Shear Strain resulting from application of quasi-static axial compression to an inhomogeneous material is imaged. The overall hypothesis of this work is that the pattern of axial-Shear Strain distribution around the inclusion/background interface is completely determined by the bonding at the interface after normalization for inclusion size and applied Strain levels, and that it is feasible to extract certain features from the axial-Shear Strain elastograms to quantify this pattern. The mechanical model used in this study consisted of a single stiff circular inclusion embedded in a homogeneous softer background. First, we performed a parametric study using finite-element analysis (FEA) (no ultrasound involved) to identify possible features that quantify the pattern of axial-Shear Strain distribution around an inclusion/background interface. Next, the ability to extract these features from axial-Shear Strain elastograms, estimated from simulated pre- and post-compression noisy RF data, was investigated. Further, the feasibility of extracting these features from in vivo breast data of benign and malignant tumors was also investigated. It is shown using the FEA study that the pattern of axial-Shear Strain distribution is determined by the degree of bonding at the inclusion/background interface. The results suggest the feasibility of using normalized features that capture the region of positive and negative axial-Shear Strain area to quantify the pattern of the axial-Shear Strain distribution. The simulation results showed that it was feasible to extract the features, as identified in the FEA study, from axial-Shear Strain elastograms. However, an effort must be made to obtain axial-Shear Strain elastograms with the highest signal-to-noise ratio (SNRasse) possible, without compromising the resolution. The in vivo results demonstrated the feasibility of producing and extracting features from the axial-Shear Strain elastograms from breast data. Furthermore, the in vivo axial-Shear Strain elastograms suggest an additional feature not identified in the simulations that may potentially be used for distinguishing benign from malignant tumors—the proximity of the axial-Shear Strain regions to the inclusion/background interface identified in the sonogram.
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signal to noise ratio contrast to noise ratio and their trade offs with resolution in axial Shear Strain elastography
Physics in Medicine and Biology, 2007Co-Authors: Thomas A. Krouskop, Arun Thitaikumar, Jonathan OphirAbstract:In axial-Shear Strain elastography, the local axial-Shear Strain resulting from the application of quasi-static axial compression to an inhomogeneous material is imaged. In this paper, we investigated the image quality of the axial-Shear Strain estimates in terms of the signal-to-noise ratio (SNRasse) and contrast-to-noise ratio (CNRasse) using simulations and experiments. Specifically, we investigated the influence of the system parameters (beamwidth, transducer element pitch and bandwidth), signal processing parameters (correlation window length and axial window shift) and mechanical parameters (Young's modulus contrast, applied axial Strain) on the SNRasse and CNRasse. The results of the study show that the CNRasse (SNRasse) is maximum for axial-Shear Strain values in the range of 0.005–0.03. For the inclusion/background modulus contrast range considered in this study (<10), the CNRasse (SNRasse) is maximum for applied axial compressive Strain values in the range of 0.005%–0.03%. This suggests that the RF data acquired during axial elastography can be used to obtain axial-Shear Strain elastograms, since this range is typically used in axial elastography as well. The CNRasse (SNRasse) remains almost constant with an increase in the beamwidth while it increases as the pitch increases. As expected, the axial shift had only a weak influence on the CNRasse (SNRasse) of the axial-Shear Strain estimates. We observed that the differential estimates of the axial-Shear Strain involve a trade-off between the CNRasse (SNRasse) and the spatial resolution only with respect to pitch and not with respect to signal processing parameters. Simulation studies were performed to confirm such an observation. The results demonstrate a trade-off between CNRasse and the resolution with respect to pitch.
Terence G Langdon - One of the best experts on this subject based on the ideXlab platform.
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three dimensional Shear Strain patterns induced by high pressure torsion and their impact on hardness evolution
Acta Materialia, 2011Co-Authors: Y B Wang, Roberto B Figueiredo, W L Zheng, Megumi Kawasaki, Li Chang, Simon P. Ringer, X Z Liao, Terence G LangdonAbstract:The Shear Strain imposed on austenite/ferrite duplex stainless steel discs at different stages of high-pressure torsion (HPT) processing was imaged in plan-view and cross-section using optical microscopy and scanning electron microscopy. The effect of the Shear Strain was correlated to the hardness evolution of the discs. The Shear-Strain patterns are complex and are different on the top and bottom surfaces of the discs. A double-swirl pattern emerged on the top surface in the early stages of HPT. These two centres of the swirl moved towards the centre of the disc as the numbers of HPT revolutions was increased and ultimately the double-swirl evolved into a single-swirl. Less regular Shear-Strain patterns were observed on the bottom surfaces of the discs. Multiple ring-like patterns with mirror symmetry over the central axes of the discs were visible from cross-sectional observations. Nanoindentation testing on the two surfaces and a cross-section of HPT discs showed that the hardness is insensitive to specific Shear-Strain patterns, but is closely related to the widths of the austenite and ferrite phase domains. Late in the deformation process, the hardness in the interior of an HPT disc may be higher than at either of the disc surfaces because of the development of finer microstructural phase distributions.
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a visualization of Shear Strain in processing by high pressure torsion
Journal of Materials Science, 2010Co-Authors: Y B Wang, Saleh N Alhajeri, W L Zheng, Simon P. Ringer, X Z Liao, Terence G LangdonAbstract:Optical microscopy was used to examine the Shear Strain imposed in duplex stainless steel disks during processing by high-pressure torsion (HPT). The results show a double-swirl pattern emerges in the early stages of HPT and the two centres of the swirl move towards the centre of the disk with increasing revolutions. Local Shear vortices also develop with increasing numbers of revolutions. At 20 revolutions, there is a uniform Shear Strain pattern throughout the disk and no local Shear vortices.
