Application of the Tsai–Wu Quadratic Multiaxial Failure Criterion to Bovine Trabecular Bone

1999 ◽  
Vol 121 (1) ◽  
pp. 99-107 ◽  
Author(s):  
T. M. Keaveny ◽  
E. F. Wachtel ◽  
S. P. Zadesky ◽  
Y. P. Arramon
Keyword(s):  
Trabecular Bone ◽  
Apparent Density ◽  
Failure Criterion ◽  
Radial Pressure ◽  
Nonlinear Dependence ◽  
Triaxial Tests ◽  
Failure Behavior ◽  
Transverse Loading ◽  
Trabecular Network ◽  
Stress States

As a first step toward development of a multiaxial failure criterion for human trabecular bone, the Tsai–Wu quadratic failure criterion was modified as a function of apparent density and applied to bovine tibial trabecular bone. Previous data from uniaxial compressive, tensile, and torsion tests (n = 139 total) were combined with those from new triaxial tests (n = 17) to calibrate and then verify the criterion. Combinations of axial compression and radial pressure were used to produce the triaxial compressive stress states. All tests were performed with minimal end artifacts in the principal material coordinate system of the trabecular network. Results indicated that the stress interaction term F12 exhibited a strong nonlinear dependence on apparent density (r2 > 0.99), ranging from −0.126 MPa−2 at low densities (0.29 g/cm3) to 0.005 MPa−2 at high densities (0.63 g/cm3). After calibration and when used to predict behavior of new specimens without any curve-fitting, the Tsai–Wu criterion had a mean (± SD) error of −32.6 ± 10.6 percent. Except for the highest density triaxial specimens, most (15/17 specimens) failed at axial stresses close to their predicted uniaxial values, and some reinforcement for transverse loading was observed. We conclude that the Tsai–Wu quadratic criterion, as formulated here, is at best only a reasonable predictor of the multiaxial failure behavior of trabecular bone, and further work is required before it can be confidently applied to human bone.

Axial-Shear Failure Behavior of Human Femoral Trabecular Bone

1999 ◽  
Author(s):  
Yves P. Arramon ◽  
Oscar C. Yeh ◽  
Elise F. Morgan ◽  
Tony M. Keaveny
Keyword(s):  
Mechanical Behavior ◽  
Trabecular Bone ◽  
Failure Criterion ◽  
Shear Failure ◽  
Computer Models ◽  
Failure Behavior ◽  
Multiaxial Loading ◽  
Bone Implant ◽  
Computer Aided ◽  
Stress States

Abstract An understanding of the failure of trabecular bone subjected to multiaxial loading has relevance in the mechanics of trauma and bone implant interfaces. The development of computer aided tomography-based computer models allow predictions of the mechanical behavior of whole bones when subjected to stress states too complex to be described analytically (Ford et al., 1996; Keyak et al., 1998; Oden et al., 1998). However, these models cannot confidently predict the failure of the trabecular bone without an experimentally validated multiaxial failure criterion.

Biaxial Failure Behavior of Bovine Tibial Trabecular Bone

2002 ◽  
Vol 124 (6) ◽  
pp. 699-705 ◽  
Author(s):  
Glen L. Niebur ◽  
Michael J. Feldstein ◽  
Tony M. Keaveny
Keyword(s):  
Trabecular Bone ◽  
Volume Fraction ◽  
Yield Criterion ◽  
Failure Mechanisms ◽  
Tissue Level ◽  
Failure Behavior ◽  
Transverse Loading ◽  
Wide Range ◽  
Plain Strain ◽  
Apparent Level

Multiaxial failure properties of trabecular bone are important for modeling of whole bone fracture and can provide insight into structure-function relationships. There is currently no consensus on the most appropriate form of multiaxial yield criterion for trabecular bone. Using experimentally validated, high-resolution, non-linear finite element models, biaxial plain strain boundary conditions were applied to seven bovine tibial specimens. The dependence of multiaxial yield properties on volume fraction was investigated to quantify the interspecimen heterogeneity in yield stresses and strains. Two specimens were further analyzed to determine the yield properties for a wide range of biaxial strain loading conditions. The locations and quantities of tissue level yielding were compared for on-axis, transverse, and biaxial apparent level yielding to elucidate the micromechanical failure mechanisms. As reported for uniaxial loading of trabecular bone, the yield strains in multiaxial loading did not depend on volume fraction, whereas the yield stresses did. Micromechanical analysis indicated that the failure mechanisms in the on-axis and transverse loading directions were mostly independent. Consistent with this, the biaxial yield properties were best described by independent curves for on-axis and transverse loading. These findings establish that the multiaxial failure of trabecular bone is predominantly governed by the strain along the loading direction, requiring separate analytical expressions for each orthotropic axis to capture the apparent level yield behavior.

scholarly journals Mesoscale Modelling of Concretes Subjected to Triaxial Loadings: Mechanical Properties and Fracture Behaviour

Materials ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1099
Author(s):  
Qingqing Chen ◽  
Yuhang Zhang ◽  
Tingting Zhao ◽  
Zhiyong Wang ◽  
Zhihua Wang
Keyword(s):  
Mechanical Properties ◽  
Tensile Stress ◽  
Failure Criterion ◽  
Mesoscale Model ◽  
Fracture Behaviour ◽  
Descent Method ◽  
Triaxial Stress ◽  
Gradient Descent Method ◽  
Stress States ◽  
Shear Failures

The mechanical properties and fracture behaviour of concretes under different triaxial stress states were investigated based on a 3D mesoscale model. The quasistatic triaxial loadings, namely, compression–compression–compression (C–C–C), compression–tension–tension (C–T–T) and compression–compression–tension (C–C–T), were simulated using an implicit solver. The mesoscopic modelling with good robustness gave reliable and detailed damage evolution processes under different triaxial stress states. The lateral tensile stress significantly influenced the multiaxial mechanical behaviour of the concretes, accelerating the concrete failure. With low lateral pressures or tensile stress, axial cleavage was the main failure mode of the specimens. Furthermore, the concretes presented shear failures under medium lateral pressures. The concretes experienced a transition from brittle fracture to plastic failure under high lateral pressures. The Ottosen parameters were modified by the gradient descent method and then the failure criterion of the concretes in the principal stress space was given. The failure criterion could describe the strength characteristics of concrete materials well by being fitted with experimental data under different triaxial stress states.

scholarly journals LSSVM-Based Rock Failure Criterion and Its Application in Numerical Simulation

2015 ◽  
Vol 2015 ◽  
pp. 1-13 ◽  
Author(s):  
Changxing Zhu ◽  
Hongbo Zhao ◽  
Zhongliang Ru
Keyword(s):  
Rock Mass ◽  
Failure Criterion ◽  
Nonlinear Problems ◽  
Failure Criteria ◽  
Rock Failure ◽  
Support Vector ◽  
Failure Behavior ◽  
Circular Tunnel ◽  
Vector Machines

A rock failure criterion is very important for the prediction of the failure of rocks or rock masses in rock mechanics and engineering. Least squares support vector machines (LSSVM) are a powerful tool for addressing complex nonlinear problems. This paper describes a LSSVM-based rock failure criterion for analyzing the deformation of a circular tunnel under differentin situstresses without assuming a function form. First, LSSVM was used to represent the nonlinear relationship between the mechanical properties of rock and the failure behavior of the rock in order to construct a rock failure criterion based on experimental data. Then, this was used in a hypothetical numerical analysis of a circular tunnel to analyze the mechanical behavior of the rock mass surrounding the tunnel. The Mohr-Coulomb and Hoek-Brown failure criteria were also used to analyze the same case, and the results were compared; these clearly indicate that LSSVM can be used to establish a rock failure criterion and to predict the failure of a rock mass during excavation of a circular tunnel.

Comparative study of coral sand and silica sand in creep under general stress states

2017 ◽  
Vol 54 (11) ◽  
pp. 1601-1611 ◽  
Author(s):  
Yaru Lv ◽  
Feng Li ◽  
Yawen Liu ◽  
Pengxian Fan ◽  
Mingyang Wang
Keyword(s):  
Grain Size ◽  
Creep Behavior ◽  
Confining Pressure ◽  
Silica Sand ◽  
Triaxial Tests ◽  
Particle Crushing ◽  
Particle Rotation ◽  
General Stress ◽  
Coral Sand ◽  
Stress States

Coral sand has individual characteristics that differ from silica sand, such as creep behavior that is always attributed to particle crushing under high stress states. To understand the creep behavior of coral sand under general stress levels, three series of comparative triaxial tests relevant to the deviator stress, confining pressure, and relative density were performed on coral sand and silica sand creeping for more than 5 days. The volumetric, axial, and shear creeps of coral sand are considerably larger than those of silica sand, particularly under a relatively high confining pressure. The volumetric creep strain of coral sand was found to be contractive, but that of silica sand appeared dilative according to the creep time. This difference is not mainly governed by particle crushing in coral sand because the grain-size distribution prior to and after creep is similar. The grain skeletons were observed using a scanning electron microscope, finding that, independent of the grain size and shape, the coral grains include large amounts of cavities. The creep of coral sand under general stress conditions is mainly caused by particle interlocking, i.e., the angular regions of some particles interlock into the cavities of other particles due to particle rotation. This structuration is induced by breakage of asperities and voids during creep such as the local instability near cavities.

Uniqueness of steady state and liquefaction potential

1994 ◽  
Vol 31 (1) ◽  
pp. 132-139 ◽  
Author(s):  
D. Negussey ◽  
M.S. Islam
Keyword(s):  
Steady State ◽  
Bedding Plane ◽  
Triaxial Tests ◽  
Initial State ◽  
Liquefaction Potential ◽  
Initial Anisotropy ◽  
Anisotropic Consolidation ◽  
Stress States ◽  
Undrained Loading ◽  
Loading Form

A given sand is presumed to have a unique steady-state line. The proximity of an initial state to the steady-state line is considered to be a measure of liquefaction potential. This line of reasoning and application in practice is based on data obtained predominantly from triaxial tests in compression-mode loading. In such tests, relative orientations of bedding plane and principal stress directions remain fixed while stress states along actual failure surfaces may range from active to passive. This study examines the uniqueness of the steady state relative to the mode of loading, form of consolidation, and initial anisotropy as induced by bedding orientation. A sample-preparation method was developed to form triaxial samples with different bedding orientations. Steady states of a uniform sand reached under compressional and extensional modes of triaxial undrained loading of samples with different bedding orientation are compared. Effects of isotropic and anisotropic consolidation are examined. The results indicate the steady-state line obtained for compression-mode loading is different from and does not apply for extension-mode loading. Use of a compression side steady-state line for extension-mode failure states would result in overestimation of steady-state strengths and unconservative stability evaluations. Key words : anisotropy, compression, extension, liquefaction, sand, steady state, triaxial.

Unbound Aggregate Rutting Models for Stress Rotations and Effects of Moving Wheel Loads

2005 ◽  
Vol 1913 (1) ◽  
pp. 41-49 ◽  
Author(s):  
In Tai Kim ◽  
Erol Tutumluer
Keyword(s):  
Test Data ◽  
Permanent Deformation ◽  
Confining Pressure ◽  
Stress Path ◽  
In Situ Stress ◽  
Triaxial Tests ◽  
Wheel Loading ◽  
Stress States ◽  
Granular Layers ◽  
Unbound Aggregate

The latest research findings on stress rotations caused by moving wheel loads and their effects on permanent deformation or rut accumulation in pavement granular layers are presented. Realistic pavement stresses induced by moving wheel loads were examined in the unbound aggregate base and subbase layers, and the significant effects of rotation of principal stress axes were indicated for a proper characterization of the permanent deformation behavior. To account for the rutting performances of especially thick granular layers, a comprehensive set of repeated load triaxial tests was conducted in the laboratory. Triaxial test data were obtained and analyzed from testing aggregates under various realistic in situ stress paths caused by moving wheel loading. Permanent deformation characterization models were then developed on the basis of the experimental test data to include the static and dynamic stress states and the slope of stress path loading. The models that also considered the stress path slope variations predicted the stress path dependency of permanent deformation accumulation best. In addition, multiple stress path tests conducted to simulate the extension–compression–extension type of rotating stress states under a wheel pass gave much higher permanent strains than those of the compression-only single path tests. The findings indicated actual traffic loading simulated by the multiple path tests could cause greater permanent deformations or rutting damage, especially in the loose base or subbase, when compared with deformations measured from a dynamic plate loading or a constant confining pressure type laboratory test.

A Structurally Based Stress-Stretch Relationship for Tendon and Ligament

1997 ◽  
Vol 119 (4) ◽  
pp. 392-399 ◽  
Author(s):  
C. Hurschler ◽  
B. Loitz-Ramage ◽  
R. Vanderby
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Failure Criterion ◽  
Probability Distribution Function ◽  
Mechanical Response ◽  
Elastic Fiber ◽  
Tissue Level ◽  
Constitutive Law ◽  
Failure Behavior ◽  
Simplified Form

We propose a mechanical model for tendon or ligament stress–stretch behavior that includes both microstructural and tissue level aspects of the structural hierarchy in its formulation. At the microstructural scale, a constitutive law for collagen fibers is derived based on a strain-energy formulation. The three-dimensional orientation and deformation of the collagen fibrils that aggregate to form fibers are taken into consideration. Fibril orientation is represented by a probability distribution function that is axisymmetric with respect to the fiber. Fiber deformation is assumed to be incompressible and axisymmetric. The matrix is assumed to contribute to stress only through a constant hydrostatic pressure term. At the tissue level, an average stress versus stretch relation is computed by assuming a statistical distribution for fiber straightening during tissue loading. Fiber straightening stretch is assumed to be distributed according to a Weibull probability distribution function. The resulting comprehensive stress–stretch law includes seven parameters, which represent structural and microstructural organization, fibril elasticity, as well as a failure criterion. The failure criterion is stretch based. It is applied at the fibril level for disorganized tissues but can be applied more simply at a fiber level for well-organized tissues with effectively parallel fibrils. The influence of these seven parameters on tissue stress–stretch response is discussed and a simplified form of the model is shown to characterize the nonlinear experimentally determined response of healing medial collateral ligaments. In addition, microstructural fibril organizational data (Frank et al., 1991, 1992) are used to demonstrate how fibril organization affects material stiffness according to the formulation. A simplified form, assuming a linearly elastic fiber stress versus stretch relationship, is shown to be useful for quantifying experimentally determined nonlinear toe-in and failure behavior of tendons and ligaments. We believe this ligament and tendon stress–stretch law can be useful in the elucidation of the complex relationships between collagen structure, fibril elasticity, and mechanical response.

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