Mechanical properties of Cortical and Cancellous Bone

Schematic drawing showing microstructure of cortical and cancellous bone. From Nordin & Frankel. 1a

Anisotropy of bone Example: the femoral shaft (From Nordin & Frankel)

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Anisotropy of bone specimens is determined by local variations in trabecular shape, density and orientation, as well as by mineral density variation, which are constituted, according to Wolff s law, by the internal stress fields. From Kosmahl.

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Ultimate stress for human adult cortical bone specimens. Shaded area indicates ultimate stress for trabecular bone. From Nordin & Frankel.

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Illustration of a bone test specimen and a stress-strain curve resulting from a tensile test 2a

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Two types of bending tests can be taken: A. Three-point bending and B. Four-point bending. From Nordin & Frankel.

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Maximal stress at the surface of bone for bending or torsion can be estimated for bone with circular shape using the following relations.

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Loading modes for bone specimens

From Nordin & Frankel. 2d

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Behavior of bone in uniaxial tension compared to other common materials 3

Illustration of the strain-rate sensitivity of cortical bone (from a canine tibia). As the strain-rate increases, the stiffness and ultimate stress increases. From Nordin & Frankel. 4

Illustration of the different types of loading that can be impos ed on bone. Bones can be subjected to axial compression, axial tension, torsion, shear, bending, or any combination of these. 5

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Because bones can resist more compression than tension, they typically fail in tension. For this reason, we theorize that osteoporotic fractures of the femoral neck happen by virtue failure at the superior aspect of the femoral neck (where tension develops as a result of weight-bearing during locomotion). From Kosmahl.

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Illustration of the effect that muscle forces can have on bone stresses

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Effect of Aging: Vertebral cross-sections from autopsy specimens of young (A) and old (B) bone show a marked reduction in trabecular bone in the later. Bone reduction with aging (C) is schematically depicted 7

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Effect of Aging: Stress-strain curves for samples of adult human tibia of two widely differing ages tested in tension 8

Illustration of an Injury Threshold dependent on the magnitude of the load and the number of times the load is applied. The curve indicates that the bone can withstand

n1 cycles of stress σ 1 and n 2 cycles of the lower stress σ 2.

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Viscoelasticity of bone: strain-rate dependency.

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Creep and recovery. Stress σ and strain ε vs. time t. From Lakes.

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Stress relaxation in a viscoelastic material 12

This animation shows creep of a rod (60 cm long, 3 mm diameter) of polymethyl methacrylate (PMMA) in cantilever bending at room temperature, ~20 deg. C.

Images of the free rod end were captured after ~1, 10, 100, 1,000, 104, 105 seconds, 106 seconds (about 11 days), 107 seconds (almost four months).

From Lakes.

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Regions of creep behavior. Strain e vs. time t, for different load levels. 14

Stress and strain vs. time t (in arbitrary units) in dynamic loading of a viscoelastic material. From Lakes. 15

Stress vs. strain for linearly viscoelastic material under oscillatory load history. From Lakes.

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MOTOR

BONE VISCOELASTICITY Torsion of a bone specimen: -Specimen with circular cross-section -Loaded with cyclic sinusoidal torsion -Shear developing due to torsion -Constant compression for fixing the specimen

|G*|= dynamic shear modulus Torque-meter

|G*|2 =(G ) 2 +(G ) 2

Strain

G = storage modulus G = loss modulus Time

δ=tan-1 (G / G )

Or, phase between sinusoidal load and measured moment 17

Setup for torsion experiments to determine the viscoelasticity of a bone specimen

From Lakes., J. Biomech. Eng.

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Viscoelastic behavior of bone under torsion: Shear modulus vs. time and the loss angle δδ vs. the loading frequency. From

Lakes.

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Viscoelastic behavior of bone: stiffness versus damping for bone and synthetic materials. From Lakes.

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Viscoelastic behavior of bone: loss angle δ versus the loading frequency. From Lakes. 21

From Lakes., J. Biomech. Eng.

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Motion of cement lines between osteons as a cause for viscoelastic behavior of bone:

Cement lines are compliant (Katz, 1980). Viscous-like cement line motion gives rise to a portion of the viscoelasticity in bone, particularly at long times (Lakes and Saha, 1979). 23

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From Lakes., J. Biomech. Eng.

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From Lakes., J. Biomech. Eng.

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From Lakes., J. Biomech. Eng.

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From Lakes., J. Biomech. Eng.

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Nanoindentation technique for bone tissue elastic modulus measurements. From Cowin.

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Microtesting techniques for measuring mechanical properties of cancellous bone tissue. From Cowin.

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Modulus results for different cortical specimen preparation and testing conditions using nanoindentation. The subscripts a,b, and c denote the initial, immediate repeat, and delayed repeat indentation at 500 nm. The error bars show standard deviations. The moduli of dry specimens are significantly greater than the wet, and wet and embedded specimens. From Cowin.

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Elastic moduli measured by the nanoindentation technique in five microstructures in eight individual femurs (Dia Ost: Diaphyseal Osteons; Dia Int: Diaphyseal Interstitial; Neck Ost: Neck Osteons; Neck Int: Neck Interstitial; Neck Tra: Neck Trabeculae). The error bars indicate the standard deviation. From Cowin.

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Estimation of elastic modulus of cancellous bone tissue using large scale micro-imaging based finite element methods From Cowin.

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Tissue modulus measured from 4-point-bending microtesting for cancellous (A) and cortical (B) bone specimens from human vertebral bodies of various age groups. Cortical tissue (2.44 GPa) is 14% stiffer than cancellous tissue (2.11 GPa). In addition, the tissue from the younger age group (20-40) is stiffer than the older age groups (55-65 and 7585). From Cowin.

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