Von Mises Strain Research Articles

Reassessment of temperature increase and equivalent strain calculation during high-pressure torsion

The problems of temperature increase during high-pressure straining and equivalent strain calculation are reassessed on the basis of general considerations and experimental evidence. Temperature evolution is measured for some pure fcc and hcp metals (Cu, Al, Ni, Ti and Zr) and different regimes of HPT (pressure, strain accumulated and strain rate). The results obtained are compared with modelling and theoretical estimates. A simple model taking into account microstructure evolution during HPT is applied in order to explain the consequent "straining-hardening-softening". The heat release of plastic work is calculated on the basis of both the von Mises and Hencky equivalent strains giving some assessment on the applicability of these equations.

Problems associated with use of the logarithmic equivalent strain in high pressure torsion

The logarithmic "equivalent" strain is frequently recommended for description of the experimental flow curves determined in high pressure torsion (HPT) tests. Some experimental results determined at -196 and 190 °C on a 2024 aluminum alloy are plotted using both the von Mises and logarithmic equivalent strains. Three types of problems associated with use of the latter are described. The first involves the lack of work conjugacy between the logarithmic and shear stress/shear strain curves, a topic that has been discussed earlier. The second concerns the problems associated with testing at constant logarithmic strain rate, a feature of particular importance when the material is rate sensitive. The third type of problem involves the "history dependence" of this measure in that the incremental logarithmic strain depends on whether the prior strain accumulated in the sample is known or not. This is a difficulty that does not affect use of the von Mises equivalent strain. For these reasons, it is concluded that the qualifier "equivalent" should not be used when the logarithmic strain is employed to describe HPT results.

Real-time displacement and strain mappings of lithium-ion batteries using three-dimensional digital image correlation

This work presents the first application of three-dimensional digital image correlation for real-time displacement and strain analysis of a pouch type lithium-ion battery. During the electrochemical charge–discharge processes, displacements in the x-, y- and z-directions vary at different states-of-charge (SOCs) attributed to the expansion and the contraction of the interior structure. The z-displacement is observed to develop and concentrate at the vicinity of the openings of the jelly-roll structure. By resolving the displacement components, the progression and distribution of the surface strains, including principal and von-Mises strains, are computed in the charge–discharge processes. It is shown that the dominant strains are up to 0.12% in the rolling direction of the jelly-roll structure and distribute uniformly on the x–y plane over the surface.

Finite element analysis of copper–Nb3Sn contact performance under transverse compression

It turns out from recent researches on Nb3Sn conductor that contact strain is important for Nb3Sn conductor, as it could cause the degradation of the conductor itself. Few experimental results describing the behavior of Nb3Sn sub cables under transverse load are available. Numerical modeling is one method to investigate the contact strain inside the cable. In this paper, finite element method was used to analyze the two- and three strand contact strains under two pressing configurations: flat and concave plates. From the finite element analysis, it is found that the average von-Mises strain of bottom Nb3Sn in Nb3Sn–Nb3Sn–Nb3Sn contact model and copper–Nb3Sn–Nb3Sn contact model is the same under flat or concave plates; the average von-Mises strain of bottom Nb3Sn in two strand contact model is also the same. It is also verified that the shape of the top copper press has no more influence on the strain distribution in Nb3Sn strand under the transverse compression.

Optimization of spinal implant screw for lower vertebra through finite element studies.

The increasing older population is suffering from an increase in age-related spinal degeneration that causes tremendous pain. Spine injury is mostly indicated at the lumbar spine (L3-L5) and corresponding intervertebral disks. Finite element analysis (FEA) is now one of the most efficient and accepted tools used to simulate these pathological conditions in computer-assisted design (CAD) models. In this study, L3-L5 spines were modeled, and FEA was performed to formulate optimal remedial measures. Three different loads (420, 490.5, and 588.6 N) based on three body weights (70, 90, and 120 kg) were applied at the top surface of the L3 vertebra, while the lower surface of the L5 vertebra remained fixed. Models of implants using stainless steel and titanium alloy (Ti6Al4V) pedicle screws and rods with three different diameters (4, 5, and 6 mm) were inserted into the spine models. The relative strengths of bone (very weak, weak, standard, strong, and very strong) were considered to determine the patient-specific effect. A total of 90 models were simulated, and von Mises stress and strain, shear stress, and strain intensity contour at the bone-implant interface were analyzed. Results of these analyses indicate that the 6-mm pedicle screw diameter is optimal for most cases. Experimental and clinical validation are needed to confirm these theoretical results.

Finite element analysis of the femur during stance phase of gait based on musculoskeletal model simulation.

In this study, the accuracy of the inputs required for finite element analysis, which is mainly used for the biomechanical analysis of bones, was improved. To ensure a muscle force and joint contact force similar to the actual values, a musculoskeletal model that was based on the actual gait experiment was used. Gait data were obtained from a healthy male adult aged 29 who had no history of musculoskeletal disease and walked normally (171 cm height and 72 kg weight), and were used as inputs for the musculoskeletal model simulation to determine the muscle force and joint contact force. Among the phases of gait, which is the most common activity in daily life, the stance phase is the most affected by the load. The results data were extracted from five events in the stance phase: heel contact (ST1), loading response (ST2), early mid-stance (ST2), late mid-stance (ST4), and terminal stance (ST5). The results were used as the inputs for the finite element model that was formed using 1.5mm intervals computed tomography (CT) images and the maximum Von-Mises stress and the maximum Von-Mises strain of the right femur were examined. The maximum stress and strain were lowest at the ST4. The maximum values for the femur occurred in the medial part and then in the lateral part after the mid-stance. In this study, the results of the musculoskeletal model simulation using the inverse-dynamic analysis were utilized to improve the accuracy of the inputs, which affected the finite element analysis results, and the possibility of the bone-specific analysis according to the lapse of time was examined.

Noninvasive assessment of osteoarthritis severity in human explants by multicontrast MRI

Medical imaging has the potential to noninvasively diagnose early disease onset and monitor the success of repair therapies. Unfortunately, few reliable imaging biomarkers exist to detect cartilage diseases before advanced degeneration in the tissue. In this study, we quantified the ability to detect osteoarthritis (OA) severity in human cartilage explants using a multicontrast magnetic resonance imaging (MRI) approach, inclusive of novel displacements under applied loading by MRI, relaxivity measures, and standard MRI. Displacements under applied loading by MRI measures, which characterized the spatial micromechanical environment by 2D finite and Von Mises strains, were strong predictors of histologically assessed OA severity, both before and after controlling for factors, e.g., patient, joint region, and morphology. Relaxivity measures, sensitive to local macromolecular weight and composition, including T1ρ, but not T1 or T2, were predictors of OA severity. A combined multicontrast approach that exploited spatial variations in tissue biomechanics and extracellular matrix structure yielded the strongest relationships to OA severity. Our results indicate that combining multiple MRI-based biomarkers has high potential for the noninvasive measurement of OA severity and the evaluation of potential therapeutic agents used in the treatment of early OA in animal and human trials.

Bending behavior and design model of bolted flange-plate connection

This paper focuses on the bending behavior of flange-plate connections under pure-bending and aims for putting forward a practical design model. Four basic types of bolted flange-plate connections are tested and related finite element analysis is implemented. The finite element model is verified by experimental results and proved to be precise and reliable. Based on the finite element analysis, the distribution of von-Mises strain and contact pressure at end plates of the connections is revealed. The valuable information can be directly used in the theoretical model to present a relatively clear yield line mechanism and definite pressure center. The bending capacity determined by flange-plates is derived with the virtual work principle. It is proved that the theoretical model can give a good prediction for the yield bending capacity of the connections. Meanwhile, traditional T-stub analogy is introduced to obtain the bending capacity determined by bolts. Combining with the two different design models and assuming that the end plates should fail before high strength bolts, a practical design procedure is put forward. The connections designed according to this procedure will meet the demand of safety and economy. Furthermore, the design model herein can provide useful reference for practical design of other kinds of bolted flange-plate connections.

Nonlinear characterization of breast cancer using multi-compression 3D ultrasound elastography in vivo

The main objective of this article is to introduce a new nonlinear elastography based classification method for human breast masses. Multi-compression elastography imaging is elucidated in this study to differentiate malignant from benign lesions, based on their nonlinear mechanical behavior under compression. Three classification parameters were used and compared in this work: a new nonlinear parameter based on a power-law behavior of the strain difference between breast masses and healthy tissues, mass-soft tissue strain ratio and the mass relative volume between B-mode and elastography imaging. Using 3D elastography, these parameters were tested in vivo. A pilot study on 10 patients was performed, and results were compared with biopsy diagnosis as a gold standard. Initial elastography results showed a good agreement with biopsy outcomes. The new estimated nonlinear parameter had an average value of 0.163±0.063 and 1.642±0.261 for benign and malignant masses, respectively. Strain ratio values for the benign and malignant masses had an average value of 2.135±0.707 and 4.21±2.108, respectively. Relative mass volume was 0.848±0.237 and 2.18±0.522 for benign and malignant masses. In addition to the traditional normal axial strain, new strain types were used for elastography and constructed in 3D, including the first principal, maximum shear and Von Mises strains. The new strains provided an enhanced distinction of the stiff lesion from the soft tissue. In summary, the proposed elastographic techniques can be used as a noninvasive quantitative characterization tool for breast cancer, with the capability of visualizing and separating the masses in a three dimensional space. This may reduce the number of unnecessary painful breast biopsies.

Prediction of Matrix Failure in Fibre Reinforced Polymer Composites

Recent development has enabled fibre and matrix failure in a fibre reinforced composite material to be predicted separately. Matrix yield/failure prediction is based on a Von Mises strain and first strain invariant criteria. Alternative matrix failure criteria for enhanced prediction accuracy are discussed in this paper. The proposed failure envelope formed with basic failure criteria intersects with uniaxial compression, pure shear and uniaxial tensile test data points smoothly. For failure of typical neat resin, significant improvement of prediction accuracy compared with measured material data is demonstrated. For a unit cell with a fibre and surrounding matrix with typical material properties, a FEM analysis indicates a significant improvement in prediction accuracy in the pure shear load case and a marginal improvement in the biaxial tensile load case. This paper also provided a preliminary discussion about the issues when material nonlinearity of the matrix material is involved.

Noninvasive dualMRI-based strains vary by depth and region in human osteoarthritic articular cartilage

To noninvasively assay the mechanical and structural characteristics of articular cartilage from patients with osteoarthritis (OA) by magnetic resonance imaging (MRI), and to further relate spatial patterns of MRI-based mechanical strain to joint (depth-wise, regional) locations and disease severity. Cylindrical osteochondral explants harvested from human tissue obtained during total knee replacement surgery were loaded in unconfined compression and 2D deformation data was acquired at 14.1 T using a displacements under applied loading by MRI (dualMRI) approach. After imaging, samples were histologically assessed for OA severity. Strains were determined by depth, and statistically analyzed for dependence on region in the joint and OA severity. Von Mises, axial, and transverse strains were highly depth-dependent. After accounting for other factors, Von Mises, axial, and shear strains varied significantly by region, with largest strain magnitudes observed in explants harvested from the tibial plateau and anterior condyle near exposed bone. Additionally, in all cases, strains in late-stage OA were significantly greater than either early- or mid-stage OA. Transverse strain in mid-stage OA explants, measured near the articular surface, was significantly higher than early-stage OA explants. dualMRI was demonstrated in human OA tissue to quantify the effects of depth, joint region, and OA severity, on strains resulting from mechanical compression. These data suggest dualMRI may possess a wide range of utility, such as validating computational models of soft tissue deformation, assaying changes in cartilage function over time, and perhaps, once implemented for cartilage imaging in vivo, as a new paradigm for diagnosis of early- to mid-stage OA.

Comment on “A comparison of the von Mises and Hencky equivalent strains for use in simple shear experiments”

Onaka has shown (2010) that the Hencky equivalent strain is the appropriate quantity to represent the degree of severe plastic deformation based on simple-shear deformation. In a recent paper, Shrivastava et al. have criticized (2011) the Onaka paper and stated that the Hencky formulation does not apply to large simple-shear deformation. In this response, it is shown that this claim of Shrivastava et al. is not consistent with recent accepted knowledge on the Hencky strain.

A comparison of the von Mises and Hencky equivalent strains for use in simple shear experiments

The von Mises equivalent strain increment is derived for the case of large strain simple shear (torsion testing). This is used, in conjunction with the von Mises yield surface, to define the von Mises equivalent stress as well as the incremental work per unit volume. Integration of the equivalent strain increment leads to the definition of the von Mises equivalent strain for torsion. The Hencky equivalent strain increment is derived from the Hencky strain defined as the logarithm of the semi major and minor axes of the strain ellipse. This is then used, via the incremental work, to derive the ‘Hencky equivalent stress’. In the Onaka approach, the numerical values of the principal strain increments were integrated without taking into account the continuous rotation of the strain ellipse. This invalid operation leads to an expression for the equivalent strain increment that cannot be applied to the large strains considered by Onaka. Using the correct increments of the Hencky strain, it is shown that the shear strain increments turn negative and consequently, the incremental work becomes negative when the shear is large.

Three‐Dimensional Image Correlation Analyses for Strains Generated by Cement and Screw‐Retained Implant Prostheses

This study aimed to measure and compare strains generated by splinted implant crowns retained by cement or screws for two implants with applied load. A stereolithic resin model was printed using computed tomography data from a patient missing all mandibular molar teeth. Two 4 × 6 mm implants were consecutively placed in the left side. One set of splinted cement and screw-retained crowns were made to fit the two implants. Image correlation technique was used for full-field measurement of strains using an image correlation software and two synchronized high-resolution digital cameras. A random dot pattern was applied to the model surface. Cameras recorded changes in random dot patterns as prostheses were loaded up to 400 N in vertical and oblique directions using a universal testing machine. Testing was repeated three times for cement and screw-retained prostheses. An image correlation algorithm used the dot pattern to define correlation areas or virtual strain gauge boxes. Three-dimensional coordinates of gauge box centers were determined for each recorded photograph and used to calculate strains. Strain distribution data were compared for major, minor, and von Mises strains for each loading condition, as well as peak and average strains for the field of view using an analysis of variance (α = 0.05). Patterns and magnitudes of strain for cement- and screw-retained splinted crowns were similar under vertical loading. Neither peak nor mean strains were significantly different for the two retention methods. For oblique loading, peak strains were lower for the screw-retained crowns; however, there were no statistically significant differences between the two groups when strains were averaged throughout the entire field of view. Cement retention did not improve the magnitude of transferred strains for splinted implant crowns using either loading condition.

Theoretical–experimental study of shock wave-assisted metal forming process using a diaphragmless shock tube

The use of high-velocity sheet-forming techniques where the strain rates are in excess of 102/s can help us solve many problems that are difficult to overcome with traditional metal-forming techniques. In this investigation, thin metallic plates/foils were subjected to shock wave loading in the newly developed diaphragmless shock tube. The conventional shock tube used in the aerodynamic applications uses a metal diaphragm for generating shock waves. This method of operation has its own disadvantages including the problems associated with repeatable and reliable generation of shock waves. Moreover, in industrial scenario, changing metal diaphragms after every shot is not desirable. Hence, a diaphragmless shock tube is calibrated and used in this study. Shock Mach numbers up to 3 can be generated with a high degree of repeatability (±4 per cent) for the pressure jumps across the primary shock wave. The shock Mach number scatter is within ±1.5 per cent. Copper, brass, and aluminium plates of diameter 60 mm and thickness varying from 0.1 to 1 mm are used. The plate peak over-pressures ranging from 1 to 10 bar are used. The midpoint deflection, circumferential, radial, and thickness strains are measured and using these, the Von Mises strain is also calculated. The experimental results are compared with the numerical values obtained using finite element analysis. The experimental results match well with the numerical values. The plastic hinge effect was also observed in the finite element simulations. Analysis of the failed specimens shows that aluminium plates had mode I failure, whereas copper plates had mode II failure.

Microstructure Evolution and Analysis of a Single Crystal Nickel-Based Superalloy during Tensile Creep

By means of the finite element method (FEM) for calculating the von Mises stress and strain energy density in the cubic γ/γ′ phases, the regularity of γ′ phase directional growth is investigated. Results show that the change of the strain energy density in the different planes of the cubical γ′ phase occurs during tensile creep of alloy, the cubical γ′ phase is directionally grown, along the crystal plane with bigger strain energy, to transform into the mesh-like rafted structure along the direction perpendicular to the applied stress axis. The change of the atomic potential energy, interfacial energy and lattice misfit stress is thought to be the driving force for promoting the elements diffusion and directional growth of γ′ phase.

The effects of modeling simplifications on craniofacial finite element models: The alveoli (tooth sockets) and periodontal ligaments

Several finite element models of a primate cranium were used to investigate the biomechanical effects of the tooth sockets and the material behavior of the periodontal ligament (PDL) on stress and strain patterns associated with feeding. For examining the effect of tooth sockets, the unloaded sockets were modeled as devoid of teeth and PDL, filled with teeth and PDLs, or simply filled with cortical bone. The third premolar on the left side of the cranium was loaded and the PDL was treated as an isotropic, linear elastic material using published values for Young's modulus and Poisson's ratio. The remaining models, along with one of the socket models, were used to determine the effect of the PDL's material behavior on stress and strain distributions under static premolar biting and dynamic tooth loading conditions. Two models (one static and the other dynamic) treated the PDL as cortical bone. The other two models treated it as a ligament with isotropic, linear elastic material properties. Two models treated the PDL as a ligament with hyperelastic properties, and the other two as a ligament with viscoelastic properties. Both behaviors were defined using published stress–strain data obtained from in vitro experiments on porcine ligament specimens. Von Mises stress and strain contour plots indicate that the effects of the sockets and PDL material behavior are local. Results from this study suggest that modeling the sockets and the PDL in finite element analyses of skulls is project dependent and can be ignored if values of stress and strain within the alveolar region are not required.

Biomechanical evaluation of a spherical lumbar interbody device at varying levels of subsidence

BackgroundUlf Fernström implanted stainless steel ball bearings following discectomy, or for painful disc disease, and termed this procedure disc arthroplasty. Today, spherical interbody spacers are clinically available, but there is a paucity of associated biomechanical testing. The primary objective of the current study was to evaluate the biomechanics of a spherical interbody implant. It was hypothesized that implantation of a spherical interbody implant, with combined subsidence into the vertebral bodies, would result in similar ranges of motion (RoM) and facet contact forces (FCFs) when compared with an intact condition. A secondary objective of this study was to determine the effect of using a polyetheretherketone (PEEK) versus a cobalt chrome (CoCr) implant on vertebral body strains. We hypothesized that the material selection would have a negligible effect on vertebral body strains since both materials have elastic moduli substantially greater than the annulus.MethodsA finite element model of L3-L4 was created and validated by use of ROM, disc pressure, and bony strain from previously published data. Virtual implantation of a spherical interbody device was performed with 0, 2, and 4 mm of subsidence. The model was exercised in compression, flexion, extension, axial rotation, and lateral bending. The ROM, vertebral body effective (von Mises) strain, and FCFs were reported.ResultsImplantation of a PEEK implant resulted in slightly lower strain maxima when compared with a CoCr implant. For both materials, the peak strain experienced by the underlying bone was reduced with increasing subsidence. All levels of subsidence resulted in ROM and FCFs similar to the intact model.ConclusionsThe results suggest that a simple spherical implant design is able to maintain segmental ROM and provide minimal differences in FCFs. Large areas of von Mises strain maxima were generated in the bone adjacent to the implant regardless of whether the implant was PEEK or CoCr.

Fatigue Life Prediction Strategies for High-Heat-Load Components

High-heat-load components such as photon shutters and masks made of Glidcop Al-15 are subjected to intense thermal cycles from the X-ray beams at the third generation light sources. This paper presents thermal fatigue life prediction results of high-heat-load components at the beam line front end of Shanghai Synchrotron Radiation Facility (SSRF) under different power conditions. Used in this analysis are four typical multiaxial fatigue life prediction models, i.e. the maximum principal strain model, equivalent vonMises strain model, maximum shear strain model and critical plane approach. Detailed comparisons among them were implemented from various aspects including applicable conditions, physical meanings and resultant veracities. Critical plane approach was finally determined to be more appropriate method for dealing with multiaxial fatigue of high-heat-load components. To obtain the multiaxial stress-strain fields, nonlinear finite element analysis (FEA) was performed with commercial software ANSYS.

Finite element analysis of implant-embedded maxilla model from CT data: Comparison with the conventional model

There are no entire maxillary finite element analysis models available, as a base of reference for the dimensions of conventional segment finite element analysis models. The objectives of this study were: (1) to construct a maxillary model derived from a human skull and to investigate the strain distribution around a posterior implant embedded in it; (2) to investigate the usability of conventional segment maxillary models. CT DICOM data of a human dried skull maxilla was imported into the Mesh Generation Tools (ANSYS AI environment) and a computer-generated implant-abutment unit was bicortically embedded into it. In this Large model, Von Mises strains under axial and buccolingual loads were then calculated by a finite element program. Moreover, two simplified maxillary segments (Simplified models) were computer-generated and their Von Mises strains were similarly calculated. Although absolute values differed markedly, strain distribution patterns in the cortical bone were similar to those in the Simplified models: high Von Mises strains in the cortical bone concentrated in the sinus floor around the implant apex under axial load, and in the alveolar crest around the implant neck under buccolingual load. The simplified and segmented three-dimensional finite element models of the human maxilla showed the same locations of the highest equivalent strains as the full maxilla model created from CT DICOM data. If absolute strain values are not of interest, the Simplified models could be used in strain analyses of simulated posterior maxilla for diagnostic suggestions in implant placement.