# g08 biomechanics

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• Biomechanics of FracturesGary E. Benedetti MD

• Basic BiomechanicsMaterial PropertiesElastic-PlasticYield pointBrittle-DuctileToughnessIndependent of Shape!

Structural PropertiesBending StiffnessTorsional StiffnessAxial Stiffness Depends on Shape and Material!

Material Properties: fundamental behaviors of a substance independent of its geometry.Structural Properties: the ability of an object to resist bending under torsion, axial load, or bending is a function of its shape and distribution of material around the cross section.

• Basic BiomechanicsForce, Displacement & StiffnessApplied ForceDisplacementSlope= Stiffness = Force/ Displacement

Force applied to a body causes a deformation. If one plots a graph of displacement due to the force applied to a material, the slope of the curve represent the materials stiffness.

• Basic Biomechanics

Stress=Force/ AreaStrain=Change Height (L)/ Original Height(L0)ForceAreaL

Stress: is the force applied per unit area (F/A).Strain: is the change in a materials length due to an applied stress relative to its original length = L/ L0.

• Basic BiomechanicsStress-Strain & Elastic ModulusStress=Force/AreaStrain=Change in Length/ Original Length (L/ L0)Slope=Elastic Modulus =Stress/Strain

If one graphs the resulting strain (L/ L0) due to the applied stress (F/A), the slope of the Stress-Strain curve is the Elastic Modulus.

• Basic BiomechanicsCommon Materials in OrthopaedicsElastic Modulus (GPa)

Stainless Steel 200Titanium 100Cortical Bone 7-21Bone Cement 2.5-3.5Cancellous Bone 0.7-4.9UHMW-PE 1.4-4.2

StressStrain

Review the elastic modulus of common materials encountered in orthopaedic surgery relative to each other.

• Basic BiomechanicsElastic DeformationPlastic DeformationEnergy

Energy AbsorbedForceDisplacementPlasticElastic

Elastic Deformation: In the elastic region, the relationship of displacement to the applied force in linear. In this region, the material returns to its resting state if the force is removed (elastic), like a rubber band.Stiffness: again, is the slope of the elastic portion of the force-displacement curve.Plastic Deformation: As more force is applied, the materials behavior becomes plastic, and permanent deformation occurs. The material will not return to its original state after the force is removed (like when you bend a plastic ice cream spoon to far it stays bent).Energy: The area under the curve represents energy absorbed into the material during the deformation process (work).

• Basic BiomechanicsStiffness-FlexibilityYield PointFailure PointBrittle-DuctileToughness-Weakness

ForceDisplacementPlasticElasticFailureYieldStiffness

Stiffness: The steeper the slope, the stiffer the material. A material with a flat slope is flexible.Yield Point: the point on the force-displacement curve where the material changes from elastic to plastic deformation is the yield point.Failure Point: At some point the material will break; this point due is the materials Failure Point.Brittle: a material which experiences little plastic deformation before it fails is said to be brittle (glass for example).Ductile: if a material with a large plastic deformation region before it fails is said to be ductile (copper for example).Toughness: a material which can absorb more energy prior to failure (large area under the curve) is said to be tougher.Weakness: a material which can absorb little energy prior to failure (small area under the curve) is said to be weak.

• StiffDuctile ToughStrong

StiffBrittleStrongStiffDuctileWeakStiffBrittleWeakStrainStress

• FlexibleDuctile ToughStrong

FlexibleBrittleStrongFlexibleDuctileWeakFlexibleBrittleWeakStrainStress

• Basic BiomechanicsLoad to FailureContinuous application of force until the material breaks (failure point at the ultimate load).Common mode of failure of bone and reported in the implant literature.

Fatigue FailureCyclical sub-threshold loading may result in failure due to fatigue.Common mode of failure of orthopaedic implants and fracture fixation constructs.

Compare the two types of failure: Load to Failure: Continuous application of force until the material breaks (failure point at the ultimate load). Bone usually fractures by load to failure.Fatigue Failure: Cyclical sub-threshold loading may result in failure due to fatigue.Load to failure testing often reported in the orthopaedic literature: however, clinically, failure fracture fixation constructs or implants often due to fatigue failure.

• Basic BiomechanicsAnisotropicMechanical properties dependent upon direction of loading

ViscoelasticStress-Strain character dependent upon rate of applied strain (time dependent).

Anisotropic: some materials (bone) have different mechanical properties dependent upon the type of load applied (transverse, longitudinal, shear).Viscoelastic: many biological materials to include bone reveal different stress-strain curves depending upon the speed at which the force is applied.

• Bone BiomechanicsBone is anisotropic-its modulus is dependent upon the direction of loading.Bone is weakest in shear, then tension, then compression.Ultimate Stress at Failure Cortical Bone

Compression < 212 N/m2Tension< 146 N/m2Shear< 82 N/m2

Bone is anisotropic-its modulus is dependent upon the direction of loading. Bone is weakest in shear, then tension, then compression. This can help us understand the fracture produced (failure) from various mechanisms (applied loads).Review the values of the Ultimate Stress at Failure of cortical bone based upon the different direction of loading for cortical bone.

• Bone BiomechanicsBone is viscoelastic: its force-deformation characteristics are dependent upon the rate of loading.Trabecular bone becomes stiffer in compression the faster it is loaded.

Bone is viscoelastic, the force-deformation curve will be different for different rates of loading.Trabecular bone becomes stiffer in compression the faster it is loaded. It is hypothesized that at high rates of loading the marrow elements do not have time to be push out, and act like a fluid filled shock absorber.

• Bone MechanicsBone DensitySubtle density changes greatly changes strength and elastic modulusDensity changesNormal agingDiseaseUseDisuse

Cortical BoneTrabecular BoneFigure from: Browner et al: Skeletal Trauma 2nd Ed. Saunders, 1998.

Bone, as a living material, can experience changes in its density. Subtle density changes can have great effects upon the material properties of the bone. Graph shows a marked change in the stress/strain curve of trabecular bone when its density is decreased by a factor of 3. These changes occur with normal aging, disease, use and disuse.Figure from: Browner B., Jupiter J., Levine A., Trafton P., Skeletal Trauma 2nd Edition, W.B. Saunders, 1998, figure 4-5, pg. 101

Bending Compression Torsion

These bending, torsion, tensile and compressive forces are applied to bones, and if excessive, may lead to fracture.

• Fracture Mechanics

Figure from: Browner et al: Skeletal Trauma 2nd Ed, Saunders, 1998.

The nature of the applied force is often evident by the nature of the fracture.Tension TransverseBending - Butterfly Compression - Oblique Torsion - SpiralFigure from: Browner B., Jupiter J., Levine A., Trafton P., Skeletal Trauma 2nd Edition, W.B. Saunders, 1998, figure 4-9, pg. 103.

• Fracture MechanicsBending load:Compression strength > tensile strengthFails in tension

Figure from: Tencer. Biomechanics in Orthopaedic Trauma, Lippincott, 1994.

As the bone is subjected to a bending load, one side is placed under tension, the other is placed under tension. Since the bones compressive strength is greater than its tensile strength, the bone fails first on the tension side.Figure from: Tencer A., Johnson K., Biomechanics in Orthopaedic Trauma, J.P. Lippincott, 1994, figure 3.6 (a), (b), pg. 39.

• Fracture MechanicsTorsionThe diagonal in the direction of the applied force is in tension cracks perpendicular to this tension diagonalSpiral fracture 45 to the long axis

Figures from: Tencer. Biomechanics in Orthopaedic Trauma, Lippincott, 1994.

TORSION: The diagonal in the direction of the applied force is in tension cracks perpendicular to this tension diagonalSpiral fracture 45 to the long axisFigures from: Tencer A., Johnson K., Biomechanics in Orthopaedic Trauma, J.P. Lippincott, 1994, figure 3.8 (a), pg. 41.

• Fracture MechanicsCombined bending & axial loadOblique fractureButterfly fragment

Figure from: Tencer. Biomechanics in Orthopaedic Trauma, Lippincott, 1994.

Combined bending & axial loads result in oblique fractures or those with a butterfly fragment.Figure from: Tencer A., Johnson K., Biomechanics in Orthopaedic Trauma, J.P. Lippincott, 1994, figure 3.7 (a), pg. 40.

• Moments of InertiaResistance to bending, twisting, axial compression or tension of an object is a function of its shapeRelated to distribution of mass (shape) with respect to an axis.Moment of Inertia

Figure from: Browner et al, Skeletal Trauma 2nd Ed, Saunders, 1998.

Resistance to bending, twisting, axial compression or tension of an object is a function of its cross-sectional shape with respect to a given axis. The relationship of resistance to applied forces to the distribution of mass (shape) with respect to an axis is related to t