Principal Surface Strains Research Articles

P8. Correlations between sagittal plane disc dimensions and principal surface strains across the L3-4 intact IVD during in vitro multidirectional loading

<h3>BACKGROUND CONTEXT</h3> Understanding the biomechanical behavior of the intact intervertebral disc (IVD) is of great importance when studying disc disease. Experimental data describing the relationship between disc size and sub-regional principal strains of the intact lumbar intervertebral disc during multi-directional loading are lacking. <h3>PURPOSE</h3> The purpose of this study was to investigate possible relationships between lateral view disc dimensions and principal surface strains across different regions of an intact L3-4 disc assessed using digital image correlation (DIC) during multi-directional loading. <h3>STUDY DESIGN/SETTING</h3> Correlation analysis of dimensional data obtained from lateral X-rays of intact L3-4 lumbar discs at rest and principal surface strains of the same discs obtained from digital image correlation analysis during in vitro loading. <h3>PATIENT SAMPLE</h3> There were 14 cadaveric spine segments including 6F/8M, mean(±SD) age: 45±13years; BMD: 0.916±0.120 g/cm2. <h3>OUTCOME MEASURES</h3> Correlation coefficients (and p-values) between disc dimensions (sagittal view disc height and area) and principal surface strains during multi-directional loading, in sub-regions of intact L3-4 IVD. <h3>METHODS</h3> The mean height and depth of the L3-4 IVD of 14 seemingly healthy human spine segments at rest were determined using lateral view X-rays and ImageJ. The IVDs were part of L3-S1 spine segments that were tested using non-destructive loading (7.5 Nm) in flexion (FL), extension (EX), right lateral bending (RLB) right/left axial rotation (RAR/LAR), followed by compression (Comp, 400 N). Mean principal strains (Pmax and Pmin) in four similarly sized quarters of the L3-4 IVD were assessed using 3D DIC (Vic-3D) during loading with cameras positioned directly lateral on the specimen's left side. Relationships between sagittal view disc dimensions at rest and mean principal strains per lateral view disc quarter [Q1(ant)-Q4(post)] during loading were studied using Pearson Correlation analysis (SigmaPlot v14 with p<0.05). <h3>RESULTS</h3> Disc height correlated significantly and positively with Pmax (tensile/stretching strain) mid-anteriorly (Q2) during Comp (R=0.545, p=0.044). There were no other significant correlations between disc height and principal strains in any other region of the disc during any direction of loading (p>0.05). In the mid-posterior disc region (Q3), Pmax correlated significantly and negatively with sagittal plane disc area during FL (R=-0.538, p=0.047) and RLB (R=-0.592, p=0.033, Fig.), showing that a larger disc (taller and deeper) bulges/stretches less during flexion and right lateral bending than a smaller disc (narrow disc height combined with shorter vertebral depth, anterior-posteriorly), mid-posteriorly. Pmin (compressive strain) correlated significantly and positively with sagittal plane disc area in the mid-posterior disc region during Comp (Q3: R=0.650, p=0.012; and Q4: R=0.619, p=0.018), indicating that a larger disc (taller and deeper) shrinks less vertically than a small disc posteriorly during compression. <h3>CONCLUSIONS</h3> Significant relationships were found between disc dimensions and mean principal strains in sagittal view sub-regions of the L3-4 intervertebral disc, during different directions of loading. These relationships aid in understanding intact disc biomechanical behavior during loading and will help improve the quality of finite element models of lumbar spine segments. <h3>FDA DEVICE/DRUG STATUS</h3> This abstract does not discuss or include any applicable devices or drugs.

Effects of varying degrees of surface strain anisotropies on endothelial cells

Event Abstract Back to Event Effects of varying degrees of surface strain anisotropies on endothelial cells Ravi Sinha1*, Severine Le Gac2*, Nico Verdonschot1*, Albert Van Den Berg2*, Bart Koopman1* and Jeroen Rouwkema1* 1 University of Twente, Department of Biomechanical Engineering, Netherlands 2 University of Twente, BIOS, Lab on a chip group, Netherlands Introduction: Cyclic strain is well known to affect cell behavior. It is also known that isotropic and anisotropic strain can affect cells differently[1]. While in-vivo cells experience varying degrees of anisotropy (d.o.a.), in-vitro anisotropic strain studies have mostly focused on uniaxial strains. In order to create a better understanding of cellular behaviour under physiological strain conditions, the response of cells to strains with varying d.o.a. should be investigated. In this study, we determined the effects of varying d.o.a. on human umbilical vein endothelial cells (HUVECs) using a newly developed device. Studies like this can be used to determine and optimize the mechanical stimulation needed to elicit physiological cellular responses, and are beneficial for applications such as tissue engineering and organs-on-chip systems. Materials and Methods: The device, which is a modified version of our previously developed device to apply surface strains in combination with flow induced shear stresses to cells[2], has 100 units producing various anisotropic strains (1a). This is achieved by stretching a polydimethylsiloxane (PDMS) membrane over circular pillars into surrounding ellipse trenches. The dimensions of the ellipse determine the d.o.a., which is defined as the ratio of maximum to minimum principal surface strains. Each condition contains four replicates. The presence of fluid flow channels allows for the determination of combined effects of anisotropic strains and flow induced shear stresses, which is currently under investigation. Computational models were used to aid in the device design (1b) and the strains were empirically characterized by tracking beads embedded in the membrane (1c). HUVECs were seeded on the device, allowed to attach for 18 hours and then stained with CellTracker Green CMFDA. The cells were mechanically stimulated (maximum principal strain up to 10% at 1 Hz, sine strain profile) and imaged after 0, 6 and 19 hours of stimulation. The cells were then fixed and stained with Alexa 488 Phalloidin (actin stain) and DAPI (nuclear stain) and imaged again. Images were analyzed using CellProfiler to detect the effects of the mechanical stimuli on the cells. Results: The models and empirical measurements showed that strains with varying d.o.a. could be generated on the device. Maximum principal strains up to ~20% could be achieved. HUVECs were found to become elongated and align along the minimum principal strain direction. Alignment was visible after 6 hours of stimulation and increased with longer stimulation times. Apart from that, an increase in d.o.a. resulted in increased cell alignment (2a-c). Conclusions: HUVECs respond to various d.o.a. With an increasing d.o.a., the cells show an increasing alignment response. The variations in response of cells highlight the need to study the effects of strains of varying d.o.a. on cells. Our device permits such experiments with an increased throughput, which makes it an important tool to better understand these mechanobiological principles. This work was financially supported by a VENI grant by the Dutch Technology Foundation STW. J.R. was supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 622294.

Full-field strain measurement and fracture analysis of rat femora in compression test

There is a growing interest in studying the fracture behavior of bones, primarily due to the increasing societal burden of osteoporotic fractures. In addition, bone is one of the most important biological materials whose fracture behavior is not yet well understood. This is partly due to the fact that bone is a complex hierarchical material, and exhibits heterogeneous, anisotropic, and viscoelastic mechanical behavior. Understanding the fracture behavior of such a complex material requires application of a full-field strain measurement technique. Digital image correlation (DIC) is a relatively new full-field strain measurement technique that can be used for measurement of 3D surface strains during mechanical testing of different types of bones. In this study, we use the DIC technique to measure the surface strains during compression testing of two groups of rat femora. The first group of femora was harvested from young animals (12 weeks), while the second group was harvested from more mature animals (26 weeks). The surface strains are measured both in the linear range and close to the fracture. Using the measured data, we assess two strain-based fracture prediction criteria, namely equivalent strain fracture criterion and fracture limit diagram, to determine whether they can consistently predict the onset of fracture. The maximum load is measured to be 296±22N (mean±SD) for young animals and 670±123N for mature animals. It is shown that fracture in the vast majority of cases occurs in the area of maximum tensile strain. The equivalent strain fracture criterion predicts that the fracture occurs when the equivalent strain reaches 1.04±0.02% (average±SD) for young animals and 1.39±0.24% for mature animals. The fracture limit diagram predicts that the fracture occurs once the sum of major and minor principal surface strains reaches 0.63±0.23% for young animals and −0.63±0.30% for mature animals. Based on these numbers and consistency of the criteria with the strain values recorded at the fracture locations, it is concluded that the equivalent strain fracture criterion tends to be more consistent among the tested specimens.

Changes in hoof surface strain distribution in response to moderate exercise in Standardbreds

To quantify changes in hoof wall strain distribution associated with exercise and time in Standardbreds. 18 young adult Standardbreds. 9 horses were exercised 4 d/wk for 30 to 45 minutes at a medium trot for 4 months; 9 nonexercised horses served as the control group. Rosette strain gauges were used to measure the principal surface strains at the toe, lateral quarter of the hoof wall (LQ), and medial quarter of the hoof wall (MQ) of the right forefoot at the beginning and end of the experiment. Midstance maximal (msϵ1) and minimal (msϵ2) principal and peak minimal principal (pkϵ2) surface strains were measured; SDs of each of those variables were also calculated. Results were compared through ANOVA of time and exercise effects between and within the groups. Both the exercised and nonexercised groups had changes in strain distribution in their hooves over time. The msϵ1 did not change significantly with exercise; however, it changed significantly in both groups at both hoof quarters over time. At the beginning of the study, mean msϵ2 and pkϵ2 values were significantly higher in the exercised group than in the control group at the MQ and LQ but not at the toe. At the end of the study, these values were significantly higher in the control group than in the exercised group at the toe but not at the MQ or LQ. Detected changes in hoof wall surface strain may indicate the ability of hoof capsule material to respond to exercise. A better understanding of hoof adaptation to applied forces may allow implementation of proper trimming and shoeing techniques to promote adaptation to exercise loads in horses.

Prediction of sheet forming limits with Marciniak and Kuczynski analysis using combined isotropic–nonlinear kinematic hardening

The forming limit curve (FLC), a plot of the limiting principal surface strains that can be sustained by sheet metals prior to the onset of localized necking, is useful for characterizing the formability of sheet metal and assessing the forming severity of a drawing or stamping process. Both experimental and theoretical work reported in the literature has shown that the FLC is significantly strain-path dependent. In this paper, a modified Marciniak and Kuczynski (MK) approach was used to compute the FLC in conjunction with two different work-hardening models: an isotropic hardening model and a mixed isotropic–nonlinear kinematic hardening model, which is capable of describing the Bauschinger effect. Predictions of the FLC using the MK analysis have been shown to be dependent on the shape of the initial yield locus and on its evolution during work hardening; therefore the hardening model has an influence on the predicted FLC. In this investigation, published experimental FLCs of AISI-1012 low carbon steel and 2008-T4 aluminum alloy sheets that were subjected to various nonlinear loading paths were compared to predictions using both hardening models. The predicted FLCs were found to correlate quite well with experimental data and the effects of strain path changes and of the hardening model on predicted FLCs are discussed.

Validation of a finite element model of the human metacarpal

Implant loosening and mechanical failure of components are frequently reported following metacarpophalangeal (MCP) joint replacement. Studies of the mechanical environment of the MCP implant-bone construct are rare. The objective of this study was to evaluate the predictive ability of a finite element model of the intact second human metacarpal to provide a validated baseline for further mechanical studies. A right index human metacarpal was subjected to torsion and combined axial/bending loading using strain gauge (SG) and 3D finite element (FE) analysis. Four different representations of bone material properties were considered. Regression analyses were performed comparing maximum and minimum principal surface strains taken from the SG and FE models. Regression slopes close to unity and high correlation coefficients were found when the diaphyseal cortical shell was modelled as anisotropic and cancellous bone properties were derived from quantitative computed tomography. The inclusion of anisotropy for cortical bone was strongly influential in producing high model validity whereas variation in methods of assigning stiffness to cancellous bone had only a minor influence. The validated FE model provides a tool for future investigations of current and novel MCP joint prostheses.

Stress-state dependence of cavitation and flow behavior in superplastic aluminum alloys

A detailed and quantitative investigation of the stress-state dependence of superplastic cavitation in fine-grained aluminum alloys has been carried out to develop clear evidentiary support to build future models. Several stress states, such as uniaxial tension, plane-strain tension, plane-strain compression, shear, and equibiaxial tension have been examined. Tests were carried out to large strain in an interrupted manner under a constant effective strain rate (\(\dot \varepsilon \)e) in the range of 10−4 to 10−2 s−1. Measurements of volume fraction, population density, and size distribution of cavities, made by image analysis via optical microscopy, show continuous emergence of new cavities as well as growth of cavities during superplastic straining. The total cavity volume fraction (V) increases exponentially with strain. The cavity growth rate, represented by η (equal to d ln V/dee), as well as the cavity population evolution rate with strain (dNc/dee, where Nc is the cavity number/unit area) are found to increase with normalized mean hydrostatic tensile stress (σm/ σe). An empirical equation for the biaxial forming limit in terms of the principal surface strains (e1 and e2) has been defined for a fixed cavity volume, as given by e1=a Vb − α e2, where a and b are constants determined from e1 values for plane strain (e2=0). The value of b is found to be 0.2 to 0.3, and α is 0.4 to 1.0.

A theoretical and experimental investigation of limit strains in sheet metal forming

The paper deals with an analytical technique for predicting FLDs based on linear, bilinear and trilinear straining paths—although any general curvilinear strain path can be handled by the method. The analytical procedure was based on the work of Marciniak and Kuczynski (known as the M-K model). The influence of material properties, such as anisotropy, strain hardening and strain rate sensitivity, as well as the effect of strain path, on the shape and level of the FLD were investigated. Material property data were determined from tests on Interstitial Free (IF) steel sheet. An experimental FLD was constructed for the IF steel sheet in the as-received condition. Additional FLDs were also produced following pre-straining of the as-received sheet. Comparison between the experimentally determined FLDs and those predicted from the theoretical model was favourable. Conventional FLDs are constructed in strain space with the principal surface strains as coordinate axes. However, they can be plotted in principal stress space, and some investigators have claimed this is a better representation. By knowing the strain path the stress state at the limit strain can be determined, and these limit stresses were plotted in principal stress space in order to construct a Forming Limit Stress Diagram (FLSD). It turned out that regardless of the shape of the FLD and the type of pre-strain imposed, all the FLSDs were almost identical. In contrast when plotted in strain space the FLD was very sensitive to the type of straining path.

On strength, stiffness and dent resistance of car body panels

There are cases in which practitioners wish to be able to predict the properties of a panel, should they replace one material by another. In this study, the yield strength, stiffness and dent resistance of double-curvature car body panels are treated both theoretically and experimentally. The results of the investigation show that the above-mentioned properties of a pressed panel can be predicted provided that the magnitude of the principal surface strains and the magnitude of the panel radii at the panel centre are known.

Biaxial Flexing of a Fiber Reinforced Aluminum Composite

Disks of silicon carbide continuous fiber reinforced ([0°/90°]4s) aluminum were supported circumferentially on one side and loaded at the center of the other side with a pin. Maxima principal tensile surface strains were determined during flexing with strain gages. Failure under monotonic loading initiated on the convex side of the disks with the for mation of multiple breaks in the first layer of fibers. With further flexing cracking extended to inner fiber layers. Finally, fracture extended through the convex surface layer of the alu minum matrix. On cyclic flexing, fiber cracking was found to be the failure mechanism whenever the cyclic principal surface strain range was 0.0035 or greater. For cyclic strain ranges less than 0.0035, slip bands and cracks were formed in the matrix in addition to the cracks formed in the fibers. The cyclic strain range limit for 10 6 cycles of life was found to approach 0.0015. The latter limit corresponded to a maximum cyclic fiber strain of 0.00132, which is only 15 % of the fiber strain to failure under monotonic uniaxial compos ite loading.

Three-Beam Interferometric Technique For Determination Of Strain Of Curved Surfaces

By using three noncoplanar coherent laser beams intersecting one another at angles larger than 30°, three sets of interferometric gratings are generated. By placing a specimen coated with a photosensitive material inside this grating field and exposing it before and after load, one can obtain three distinctive moire fringe patterns, from which principal surface strains can be calculated by using the strain rosette formula.

Forming limit curves: Out-of-plane and in-plane stretching

The study of deformation and failure of biaxially stretched sheets is of considerable practical interest in the area of sheet metal press forming. During biaxial stretching of sheet metal, the uniform plastic straining regime is often followed by a localised plastic straining regime which finally leads to fracture. The technique of analysing failures in sheet metal pressing through the use of circle grids and “forming limit curves” has gained considerable popularity. The forming limit curve describes the combination of the two principal surface strains of a biaxially stretched sheet metal at which a localised xone of thinning or necking is bound to occur. Forming limit curves thus provide excellent guidelines for adjusting material, tooling and lubrication conditions in the plant. In spite of their usefulness, however, in an actual forming operation, material parameters interact with the pressing process variables in a complex manner and comparison of different forming limit curves becomes difficult. Forming limit curves are strongly dependent on material parameters, such as the sheet thickness, the straining path and the strain gradients, and also on the geometry of the tooling. The type of stretching process can also influence the forming limit curve. In the present work, forming limit curves have been determined experimentally for annealed aluminium alloy sheets by two methods: out-of-plane stretching, where the sheet is bulged by lateral hydrostatic pressure, and in-plane stretching by tensile forces lying in the plane of the sheet. It is found that the former method produces higher limit strains than the latter under identical degrees of strain biaxiality and initial sheet thickness. A study of the various parameters present in each method which may influence the strain localisation process indicates that the overall strain gradient across the bulged testpiece is responsible for the higher strain limits.

Failure in thin sheets stretched over rigid punches

Criteria for diffuse and local necking in sheet metals stretched over a hemispherical punch have been developed. During stretching, a peak develops in the distribution of strain across the dome. This peak is a ring of thinned material around the pole which moves outward radially with continued deformation. The present approach essentially focuses on the loading rate of the region bounded by this ring of maximum thinning referred to here as thecrown. While diffuse instability is identified with a vanishing rate of crown loading, local necking is associated with the onset of a rapid rate of thinning under falling crown load. The principal surface strains were measured from incremental stretching of several different materials and time dependent constitutive relations were used to predict the instability strains. Such predictions agree with experimentally observed forming limits defined by the onset of visible necking and provide an understanding of the failure of biaxially stretched sheets deformed by a rigid punch. Since no satisfactory plasticity analyses have been developed to predict the strain distribution during punch stretching, the empirical input to the present instability criterion is required.

An Aid to Practical Sheet Metal Forming

Until recently, no analytical technique was available for the study of failure in complex sheet metal pressing. However, if the maximum ( e1) and minimum ( e2) principal surface strains at failure on sheet metal pressing are measured, a plot of e1 against e2 results in a so-called forming limit diagram. FLD can be constructed in the laboratory and used as an aid to die try-out, production failures and metal specification.