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Mechanical properties of

Cortical and Cancellous Bone

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

Anisotropy of boneExample: 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 mineraldensity variation, which are constituted, according to Wolff s law, by the internal stress fields.From Kosmahl. 1c

Ultimate stress for human adult cortical bone specimens. Shaded area indicates ultimate stress for trabecular bone.From Nordin & Frankel. 1d

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

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Two types of bending tests can be taken: A. Three-point bending and B. Four-point bending.From Nordin & Frankel. 2b

Maximal stress at the surface of bone for bending or torsion can be estimated for bone with circular shape using the following relations. 2c

Loading modes for bone specimens

2dFrom Nordin & Frankel.

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Behavior of bone in uniaxial tension compared to other common materials

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

4From Nordin & Frankel.

Illustration of the different types of loading that can be imposed 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

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

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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 σσ 1 and n2 cycles of the lower stress σσ 2. 9

Viscoelasticity of bone: strain-rate dependency.

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Creep and recovery.

Stress σσ and strain εε vs. time t. From Lakes. 11

Stress relaxation in a viscoelastic material

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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.

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Stress vs. strain for linearly viscoelastic material under oscillatory load history. From Lakes. 16

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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

MOTOR

Torque-meter

Str

ain

Time

|G*|= dynamic shear modulus

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

G = storage modulus

G = loss modulus

δ=tan-1(G /G )

Or, phase between sinusoidal load and measured moment17

BONE VISCOELASTICITY

From Lakes., J. Biomech. Eng.

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

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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. 19

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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 δδ versus the loading frequency. From Lakes.

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22From Lakes., J. Biomech. Eng.

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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).

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

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24From Lakes., J. Biomech. Eng.

25From Lakes., J. Biomech. Eng.

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From Lakes., J. Biomech. Eng. 26

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 fivemicrostructures 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 75-85).

From Cowin.

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