The influence of bone damage on press-fit mechanics

Press-fitting is used to anchor uncemented implants in bone. It relies in part on friction resistance to relative motion at the implant–bone interface to allow bone ingrowth and long-term stability. Frictional shear capacity is related to the interference fit of the implant and the roughness of its surface. It was hypothesised here that a rough implant could generate trabecular bone damage during implantation, which would reduce its stability. A device was constructed to simulate implantation by displacement of angled platens with varying surface finishes (polished, beaded and flaked) onto the surface of an embedded trabecular bone cube, to different nominal interferences. Push-in (implantation) and Pull-out forces were measured and micro-CT scans were made before and after testing to assess permanent bone deformation. Depth of permanent trabecular bone deformation (‘damage’), Pull-out force and Radial force all increased with implantation displacement and with implantation force, for all surface roughnesses. The proposed hypothesis was rejected, since primary stability did not decrease with trabecular bone damage. In fact, Pull-out force linearly increased with push-in force, independently of trabecular bone damage or implant surface. This similar behaviour for the different surfaces might be explained by the compaction of bone into the surfaces during push-in so that Pull-out resistance is governed by bone-on-bone, rather than implant surface-on-bone friction. The data suggest that maximum stability is achieved for the maximum implantation force possible (regardless of trabecular bone damage or surface roughness), but this must be limited to prevent periprosthetic cortical bone fracture, patient damage and component malpositioning.     

Surface porous fibre-reinforced composite bulk bone substitute

The aim of this study was to describe and evaluate the significance of a porous surface with bioactive glass granules (S53P4) covering an artificial bulk material based on polymethylmetacrylate (PMMA) and fibre-reinforced composite (FRC) technology. Effort was focused particularly on characters of the porous surface and biomechanical properties of the material in vitro, and test in vivo the implant in reconstruction in an experimental long bone segment defect model. The defect, 10 mm in length, created in the shaft of rabbit tibia, was reconstructed by the implant and fixed by intramedullary K-wires. The implant was incorporated within 4 weeks by new bone growth from the host bone covering particularly its posterior surface and cortex/implant junctions with bridging trabecular bone. Later, at 8 weeks, new bone was found also at the cortex/implant interface and in the medullary canal of the implant. Histometric measurements revealed direct bone/implant surface contact in 34% at the interface. Bioactive glass granules in the porous surface evoked the most direct contact with bone. The implants manufactured from PMMA only served as a control group, and showed significantly lower osteoconductive properties. Biomechanical measurements in vitro of fibre-reinforced PMMA specimens revealed values for bending strength and the flexural modulus to match them to human bone. This artificial bulk bone material based on PMMA/FRC technology seems to have proposing properties to be used as a bone substitute on load-bearing conditions. This revised version was published online in July 2006 with corrections to the Cover Date.     

Influence of the stiffness of bone defect implants on the mechanical conditions at the interface--a finite element analysis with contact

The study focused on the influence of the implant material stiffness on stress distribution and micromotion at the interface of bone defect implants. We hypothesized that a low-stiffness implant with a modulus closer to that of the surrounding trabecular bone would yield a more homogeneous stress distribution and less micromotion at the interface with the bony bed. To prove this hypothesis we generated a three-dimensional, non-linear, anisotropic finite element (FE) model. The FE model corresponded to a previously developed animal model in sheep. A prismatic implant filled a standardized defect in the load-bearing area of the trabecular bone beneath the tibial plateau. The interface was described by face-to-face contact elements, which allow press fits, friction, sliding, and gapping. We assumed a physiological load condition and calculated contact pressures, shear stresses, and shear movements at the interface for two implants of different stiffness (titanium: E=110GPa; composite: E=2.2GPa). The FE model showed that the stress distribution was more homogeneous for the low-stiffness implant. The maximum pressure for the composite implant (2.1 MPa) was lower than for the titanium implant (5.6 MPa). Contrary to our hypothesis, we found more micromotion for the composite (up to 6 microm) than for the titanium implant (up to 4.5 microm). However, for both implants peak stresses and micromotion were in a range that predicts adequate conditions for the osseointegration. This was confirmed by the histological results from the animal studies.     

The effect of tissue condition and applied load on Vickers hardness of human trabecular bone

Hardness of trabecular human bone, evaluated by microindentation testing, has generally been measured on embedded tissues. It was known that this was not ideal but it had been preferred to other conditions (e.g. wet or dehydrated) as the trabeculae could withstand the applied load and the measurements were reliable. The aim of this study was to investigate if the tissue condition of the specimen and the applied load would alter the hardness values measured by Vickers microindentation. Vickers hardness values of human trabecular bone from the femoral head, prepared in three different ways (wet, dry and embedded) and tested with two different loads (50 and 25 gf), were measured. No significant difference was found between the two different loads. However, in several cases the 50 gf indentations had to be redone because they were too large or the trabecula broke locally. Even if the outlines of the indentations on wet bone were slightly less marked than the ones done on dehydrated or embedded bone, it was possible to measure the hardness. Significant differences of Vickers hardness values were found between the three preparations: the hardness increased passing from wet to dried (10%) and from wet to embedded (35%). Whereas the variation coefficient of the three tissue conditions were comparable. In conclusion, it is recommended to test human trabecular bone in a wet condition as it better represents the in vivo condition. Furthermore the use of a 25 gf load is suggested, allowing hardness measurements on almost all trabeculae without breaking them.     

Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone

Being able to predict bone fracture or implant stability needs a proper constitutive model of trabecular bone at the macroscale in multiaxial, non-monotonic loading modes. Its macroscopic damage behaviour has been investigated experimentally in the past, mostly with the restriction of uniaxial cyclic loading experiments for different samples, which does not allow for the investigation of several load cases in the same sample as damage in one direction may affect the behaviour in other directions. Homogenised finite element models of whole bones have the potential to assess complicated scenarios and thus improve clinical predictions. The aim of this study is to use a homogenisation-based multiscale procedure to upscale the damage behaviour of bone from an assumed solid phase constitutive law and investigate its multiaxial behaviour for the first time. Twelve cubic specimens were each submitted to nine proportional strain histories by using a parallel code developed in-house. Evolution of post-elastic properties for trabecular bone was assessed for a small range of macroscopic plastic strains in these nine load cases. Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination. It is expected that the knowledge of the macroscopic behaviour of trabecular bone gained in this study will help in creating more precise continuum FE models of whole bones that improve clinical predictions.     

Effect of boundary conditions on yield properties of human femoral trabecular bone

Trabecular bone plays an important mechanical role in bone fractures and implant stability. Homogenized nonlinear finite element (FE) analysis of whole bones can deliver improved fracture risk and implant loosening assessment. Such simulations require the knowledge of mechanical properties such as an appropriate yield behavior and criterion for trabecular bone. Identification of a complete yield surface is extremely difficult experimentally but can be achieved in silico by using micro-FE analysis on cubical trabecular volume elements. Nevertheless, the influence of the boundary conditions (BCs), which are applied to such volume elements, on the obtained yield properties remains unknown. Therefore, this study compared homogenized yield properties along 17 load cases of 126 human femoral trabecular cubic specimens computed with classical kinematic uniform BCs (KUBCs) and a new set of mixed uniform BCs, namely periodicity-compatible mixed uniform BCs (PMUBCs). In stress space, PMUBCs lead to 7–72 % lower yield stresses compared to KUBCs. The yield surfaces obtained with both KUBCs and PMUBCs demonstrate a pressure-sensitive ellipsoidal shape. A volume fraction and fabric-based quadric yield function successfully fitted the yield surfaces of both BCs with a correlation coefficient \(R^{2} \ge 0.93\). As expected, yield strains show only a weak dependency on bone volume fraction and fabric. The role of the two BCs in homogenized FE analysis of whole bones will need to be investigated and validated with experimental results at the whole bone level in future studies.     

Micro-mechanical damage of trabecular bone–cement interface under selected loading conditions: a finite element study

In this study, two micro finite element models of trabecular bone–cement interface developed from high resolution computed tomography (CT) images were loaded under compression and validated using the in situ experimental data. The models were then used under tension and shear to examine the load transfer between the bone and cement and the micro damage development at the bone–cement interface. In addition, one models was further modified to investigate the effect of cement penetration on the bone–cement interfacial behaviour. The simulated results show that the load transfer at the bone–cement interface occurred mainly in the bone cement partially interdigitated region, while the fully interdigitated region seemed to contribute little to the mechanical response. Consequently, cement penetration beyond a certain value would seem to be ineffective in improving the mechanical strength of trabecular bone–cement interface. Under tension and shear loading conditions, more cement failures were found in denser bones, while the cement damage is generally low under compression.     

Simulation of bone strain by orthodontic implants using the finite element method]

Load direction of applied forces, implant geometry and other biomechanical parameters lead to varying reactions in the surrounding bone structure. Three types of endosseous implant measuring 9 mm in length and 3.3 mm in diameter with and without superperiosteal step, and a threaded surface were investigated with the aid of a finite element method using the COSMOS/M 2.5 program. The load on the implant was investigated under vertical, horizontal, and diagonal forces of between 0.01 N and 100 N. Vertical loading of simple implants caused bone deformation of more than 600 mu eps. The application of the superperiosteal step clearly reduced the deformation. The largest deformations under vertical loading were observed in the trabecular bone with all 3 implant geometries. On horizontal loading the deformation shifted from the trabecular to the cortical bone and was particularly marked at the transition between the two. The smallest deformations, less than 300 mu eps, were measured at implants with a superperiosteal step under diagonal loading. The thread did not improve loading capacity. Implants with a superperiosteal step are recommended since they contribute to more rapid healing and strengthening of the bone.     

Mechanisms of reduced implant stability in osteoporotic bone

The determining factors for the fixation of uncemented screws in bone are the bone-implant interface and the peri-implant bone. The goal of this work was to explore the role of the peri-implant bone architecture on the mechanics of the bone-implant system. In particular, the specific aims of the study were to investigate: (i) the impact of the different architectural parameters, (ii) the effects of disorder, and (iii) the deformations in the peri-implant region. A three-dimensional beam lattice model to describe trabecular bone was developed. Various microstructural features of the lattice were varied in a systematic way. Implant pull-out tests were simulated, and the stiffness and strength of the bone-implant system were computed. The results indicated that the strongest decrease in pull-out strength was obtained by trabecular thinning, whereas pull-out stiffness was mostly affected by trabecular removal. These findings could be explained by investigating the peri-implant deformation field. For small implant displacements, a large amount of trabeculae in the peri-implant region were involved in the load transfer from implant to bone. Therefore, trabecular removal in this region had a strong negative effect on pull-out stiffness. Conversely, at higher displacements, deformations mainly localized in the trabeculae in contact with the implant; hence, thinning those trabeculae produced the strongest decrease in the strength of the system. Although idealized, the current approach is helpful for a mechanical understanding of the role played by peri-implant bone.     

A nonlinear homogenized finite element analysis of the primary stability of the bone–implant interface

Stability of an implant is defined by its ability to undergo physiological loading–unloading cycles without showing excessive tissue damage and micromotions at the interface. Distinction is usually made between the immediate primary stability and the long-term, secondary stability resulting from the biological healing process. The aim of this research is to numerically investigate the effect of initial implantation press-fit, bone yielding, densification and friction at the interface on the primary stability of a simple bone–implant system subjected to loading–unloading cycles. In order to achieve this goal, human trabecular bone was modeled as a continuous, elasto-plastic tissue with damage and densification, which material constants depend on bone volume fraction and fabric. Implantation press-fit related damage in the bone was simulated by expanding the drilled hole to the outer contour of the implant. The bone–implant interface was then modeled with unilateral contact with friction. The implant was modeled as a rigid body and was subjected to increasing off-axis loading cycles. This modeling approach is able to capture the experimentally observed primary stability in terms of initial stiffness, ultimate force and progression of damage. In addition, it is able to quantify the micromotions around the implant relevant for bone healing and osseointegration. In conclusion, the computationally efficient modeling approach used in this study provides a realistic structural response of the bone–implant interface and represents a powerful tool to explore implant design, implantation press-fit and the resulting risk of implant failure under physiological loading.     

The effect of surface roughness on the stress adaptation of trabecular architecture around a cylindrical implant

The effect of implant-bone bonding and the effect of implant surface roughness on bone remodeling near the bone-implant interface were studied by using a surface remodeling theory and the boundary element method. The study has shown that implant attachment plays an important role in bone remodeling near the implant. It has been observed in animal experiments and in clinical situations that the remodeled trabecular bone architecture around a cylindrical implant could vary, on one hand, from a hub surrounding the implant with a set of external spokes to, on the other hand, a hubless situation in which a set of spokes attach directly to the implant. It is shown here that the difference in these structures may be attributed to differences in implant attachment. The results show that the bone with perfect bonding or roller boundary condition without a gap remodeled to a hubless spoke trabecular bone architecture. On the other hand, the roller boundary condition with a specified gap yielded a spoke trabecular architecture with a hub or ring surrounding the implant. These quantitative results mirror the experimental and clinical observations. It is concluded that the hub is a consequence of the gap and not a consequence of the lack of friction between the implant and the bone.     

Development of a testing methodology to quantify bone load transfer patterns for multiple stemmed implants in a single bone with an application in the distal ulna

Optimal parameters for many orthopaedic implants, such as stem length and material, are unknown. Geometry and mechanical properties of bone can vary greatly amongst cadaveric specimens, requiring a large number of specimens to test design variations. This study aimed to develop an experimental methodology to measure bone strains as a function of multiple implant stem designs in a single specimen, and evaluate its efficacy in the distal ulna. Eight fresh-frozen cadaveric ulnae were each instrumented with 12 uniaxial strain gauges on the medial and lateral surfaces of the bone. The proximal portion of each ulna was cemented in a custom-designed jig that allowed a medially directed force to be applied to the distal articular surface. An implant with a finely threaded stem was cemented into the canal by an experienced upper extremity orthopaedic surgeon. Six loads (5-30 N) were applied sequentially to the lateral surface of the prosthetic head using a materials testing machine. Testing was repeated after breaking the stem-cement bond, and after removing and reinserting the stem several times into the threaded cement mantle. Near the end of the testing period, the initial stem was reinserted and data were collected to determine if there was any change in bone properties or testing setup over time. Finally, a smooth stem was inserted for comparison to the threaded stem. Strain varied linearly with load (R(2)> or =0.99) for all testing scenarios. Bending strains were not affected by breaking the stem-cement bond (P=0.7), testing durations up to 18 h (P=0.7), nor the presence of threads when compared to a smooth stem (P>0.4). Furthermore, for all gauges, there was no interaction between the effect of the threads and level of applied load (P>0.1). This methodology should prove to be useful to compare stem designs of varying lengths and materials in the same bone, allowing for a direct comparison between implant designs for the ulna and other bones subjected primarily to bending loads. Furthermore, it will minimize the need for large numbers of specimens to test multiple implant designs. The ultimate goal of using this protocol is to optimize implant stem properties, such as length and material, with respect to load transfer.     

Precision of nanoindentation protocols for measurement of viscoelasticity in cortical and trabecular bone

Nanoindentation has recently gained attention as a characterization technique for mechanical properties of biological tissues, such as bone, on the sub-micron level. However, optimal methods to characterize viscoelastic properties of bones are yet to be established. This study aimed to compare the time-dependent viscoelastic properties of bone tissue obtained with different nanoindentation methods. Bovine cortical and trabecular bone samples (n=8) from the distal femur and proximal tibia were dehydrated, embedded and polished. The material properties determined using nanoindentation were hardness and reduced modulus, as well as time-dependent parameters based on creep, loading-rate, dissipated energy and semi-dynamic testing under load control. Each loading protocol was repeated 160 times and the reproducibility was assessed based on the coefficient of variation (CV). Additionally, three well-characterized polymers were tested and CV values were calculated for reference.The employed methods were able to characterize time-dependent viscoelastic properties of bone. However, their reproducibility varied highly (CV 9–40%). The creep constant increased with increasing dwell time. The reproducibility was best with a 30 s creep period (CV 18%). The dissipated energy was stable after three repeated load cycles, and the reproducibility improved with each cycle (CV 23%). The viscoelastic properties determined with semi-dynamic test increased with increase in frequency. These measurements were most reproducible at high frequencies (CV 9–10%). Our results indicate that several methods are feasible for the determination of viscoelastic properties of bone material. The high frequency semi-dynamic test showed the highest precision within the tested nanoindentation protocols.     

Influence of ingrowth regions on bone remodelling around a cementless hip resurfacing femoral implant

Hip resurfacing arthroplasty is an alternative to traditional hip replacement that can conserve proximal bone stock and has gained popularity but bone resorption may limit implant survival and remains a clinical concern. The goal of this study was to analyze bone remodelling patterns around an uncemented resurfacing implant and the influence of ingrowth regions on resorption. A computed tomography-derived finite element model of a proximal femur with a virtually implanted resurfacing component was simulated under peak walking loads. Bone ingrowth was simulated by six interface conditions: fully bonded; fully friction; bonded cap with friction stem; a small bonded region at the stem-cup intersection with the remaining surface friction; fully frictional, except for a bonded band along the distal end of the cap and superior half of the cap bonded with the rest frictional. Interface condition had a large influence on remodelling patterns. Bone resorption was minimized when no ingrowth occurred at the bone-implant interface. Bonding only the superior half of the cap increased bone resorption slightly but allowed for a large ingrowth region to improve secondary stability.     

The discrete nature of trabecular bone microarchitecture affects implant stability

Small endosseous implants, such as screws, are important components of modern orthopedics and dentistry. Hence they have to reliably fulfill a variety of requirements, which makes the development of such implants challenging. Finite element analysis is a widely used computational tool used to analyze and optimize implant stability in bone. For these purposes, bone is generally modeled as a continuum material. However, bone failure and bone adaptation processes are occurring at the discrete level of individual trabeculae; hence the assessment of stresses and strains at this level is relevant. Therefore, the aim of the present study was to investigate how peri-implant strain distribution and load transfer between implant and bone are affected by the continuum assumption. We performed a computational study in which cancellous screws were inserted in continuum and discrete models of trabecular bone; axial loading was simulated. We found strong differences in bone-implant stiffness between the discrete and continuum bone model. They depended on bone density and applied boundary conditions. Furthermore, load transfer from the screw to the surrounding bone differed strongly between the continuum and discrete models, especially for low-density bone. Based on our findings we conclude that continuum bone models are of limited use for finite element analysis of peri-implant mechanical loading in trabecular bone when a precise quantification of peri-implant stresses and strains is required. Therefore, for the assessment and improvement of trabecular bone implants, finite element models which accurately represent trabecular microarchitecture should be used.     

On shear properties of trabecular bone under torsional loading: effects of bone marrow and strain rate

To further improve our understanding of trabecular bone mechanical behavior in torsion, our objective was to determine the effects of strain rate, apparent density, and presence of bone marrow on trabecular bone shear material properties. Torsion tests of cylindrical trabecular bone specimens from sheep lumbar vertebrae with and without bone marrow were conducted. The bones with marrow were divided into two groups and tested at shear strain rates of 0.002 and 0.05s(-1) measured at the specimen perimeter. The bones without marrow were divided into three groups and tested at shear strain rates of 0.002, 0.015, and 0.05s(-1). Comparing the results of bones with and without marrow tested at low (0.002s(-1)) and high (0.05s(-1)) strain rates, presence of bone marrow did not have any significant effect on trabecular bone shear modulus and strength. In specimens without marrow, power relationships were used to define shear strength and modulus as dependent variables in terms of strain rate and apparent density as independent variables. The shear strength was proportional to the apparent density raised to the 1.02 power and to the strain rate raised to the 0.13 power. The shear modulus was proportional to the apparent density raised to the 1.08 power and to the strain rate raised to the 0.07 power. This study provides further insight into the mechanism of bone failure in trauma as well as failure at the interface between bone and implants as it relates to prediction of trabecular bone shear properties.     

Cortical bone viscoelasticity and fixation strength of press-fit femoral stems: finite element model

Many cementless implant designs rely upon a diaphyseal press-fit in conjunction with a porous coated implant surface to achieve primary or short term fixation, thereby constraining interface micromotion to such a level that bone ingrowth and consequent secondary or long-term fixation, i.e., osseointegration, can occur. Bone viscoelasticity, however, has been found to affect stem primary stability by reducing push-out load. In this investigation, an axisymmetric finite element model of a cylindrical stem and diaphyseal cortical bone section was created in order to parametrically evaluate the effect of bone viscoelasticity on stem push-out while controlling coefficient of friction (mu = 0.15, 0.40, and 1.00) and stem-bone diametral interference (delta = 0.01, 0.05, 0.10, and 0.50 mm). Based on results from a previous study, it was hypothesized that stem-bone interference (i.e., press-fit) would elicit a bone viscoelastic response which would reduce the initial fixation of the stem as measured by push-out load. Results indicate that for all examined combinations of mu and delta, bone viscoelastic behavior reduced the push-out load by a range of 2.6-82.6% due to stress relaxation of the bone. It was found that the push-out load increased with mu for each value of delta, but minimal increases in the push-out load (2.9-4.9%) were observed as delta was increased beyond 0.10 mm. Within the range of variables reported for this study, it was concluded that bone viscoelastic behavior, namely stress relaxation, has an asymptotic affect on stem contact pressure, which reduces stem push-out load. It was also found that higher levels of coefficient of friction are beneficial to primary fixation, and that an interference "threshold" exists beyond which no additional gains in push-out load are achieved.     

The effect of constraint on the mechanical behaviour of trabecular bone specimens

The effect of the boundary conditions between trabecular bone specimens and the test columns of the testing machine was studied together with the effect of side-constraint on the mechanical behaviour of trabecular bone during axial compression. Cylindrical specimens taken from the upper tibial epiphysis of autopsy knees were tested non-destructively by cyclic compression to 0.8% strain under different conditions. Fixation of the specimens to the test columns by a thin layer of bone cement increased the stiffness by 40% and reduced the energy dissipation to 67% of those measured under unconstrained conditions (p less than 0.001). The thin cement layer alone increased the stiffness 19% and reduced energy dissipation to 86% (n.s.). When the machine was equipped with polished steel columns coated by a film of low-viscous oil, both the stiffness and the energy dissipation were reduced to 93% of those measured under standard conditions (p less than 0.005). Trabecular bone specimens tested side-constrained by the surrounding trabecular bone (in situ) showed a 19% larger stiffness than that measured during later testing of the corresponding machined specimens (p less than 0.005) whereas the energy dissipation was not altered significantly. The same specimens showed a 22% increase of stiffness and a 68% increase of energy dissipation when they were side-constrained by a closely fitting steel cylinder (p less than 0.005).     

Microdamage assessment of bone-cement interfaces under monotonic and cyclic compression

Bone-cement interface has been investigated under selected loading conditions, utilising experimental techniques such as in situ mechanical testing and digital image correlation (DIC). However, the role of bone type in the overall load transfer and mechanical behaviour of the bone-cement construct is yet to be fully quantified. Moreover, microdamage accumulation at the interface and in the cement mantle has only been assessed on the exterior surfaces of the samples, where no volumetric information could be obtained. In this study, some typical bone-cement interfaces, representative of different fixation scenarios for both hip and knee replacements, were constructed using mainly trabecular bone, a mixture of trabecular and cortical bone and mainly cortical bone, and tested under static and cyclic compression. Axial displacement and strain fields were obtained by means of digital volume correlation (DVC) and microdamage due to static compression was assessed using DVC and finite element (FE) analysis, where yielded volumes and strains (ε_zz) were evaluated. A significantly higher load was transferred into the cement region when mainly cortical bone was used to interdigitate with the cement, compared with the other two cases. In the former, progressive damage accumulation under cyclic loading was observed within both the bone-cement interdigitated and the cement regions, as evidenced by the initiation of microcracks associated with high residual strains (ε_{zz_res}).     

Trabecular bone remodeling around smooth and porous implants in an equine patellar model

The objective of this investigation was to examine the stress-morphology relationships for trabecular bone around implants with different surface characteristics. Stainless steel spheres with either a polished surface or a sintered-bead porous coating were implanted unilaterally into equine patellae and maintained for a 6 month period. Stereological methods were used to quantify the trabecular bone morphology and finite element analyses were performed to predict the trabecular bone stresses. In general, the remodeling response around the smooth implants was greater than that around those porous implants that exhibited bone ingrowth. In accordance with these differences, the finite element models predicted greater changes in the stresses adjacent to the smooth implants due to the nonlinear boundary conditions. However, it did not appear that the trajectorial theory, in its simplest form, was applicable to the remodeling induced by the implants. A linear relationship between the change in bone areal density and the change in von Mises effective stress provides support for the hypothesis that the architecture of trabecular bone corresponds to an optimal structure. The results also demonstrated that, under certain circumstances, small changes in the stress state may result in large changes in the principal material orientation.