Tornetta Rockwood Adults 9781975137298 V2

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CHAPTER 1 • Biomechanics of Fractures and Fracture Fixation

zero. Since the biceps induces an upward force of 100 N and the water bottle exerts a downward force of only 10 N, an additional downward force of F = 100 N – 10 N = 90 N must be gener- ated as compression at the elbow joint to equalize forces. The fact that holding a 10 N force in the hand induces a 90 N force in the elbow joint demonstrates that internal forces tend to be far greater than external forces due to the small lever arm by which muscles act to balance external moments around joints. Fracture fixation constructs must also resist both internal and external deforming loads to maintain alignment as the frac- ture consolidates. Similar equilibrium considerations can be used to predict the type and magnitude of loading that must be counteracted by the fixation construct to retain stable fixa- tion of a fracture (Fig. 1-5C). For this purpose, the fracture site is considered a fulcrum. The fixation construct must achieve a stable equilibrium of forces and moments on both sides of the fracture site fulcrum. Internal and external forces that are offset

from the fracture site generate bending moments. The further the lever arm is offset from the fracture, the larger will be the bending moment around the fracture. The fixation construct must counterbalance these forces and moments. Short fixa- tion constructs with a small lever arm require a proportionally greater load to counterbalance the destabilizing force than con- structs with a long lever arm. Therefore, constructs with a small lever arm or working length result in high loads at the bone– implant interface and increase the risk of implant or fixation failure. Conversely, a long implant with a long working length has a greater mechanical advantage than a short plate, and will induce smaller stress risers at the implant–bone interface. This section has been limited to a basic overview of material properties, structural properties, and load transfer mechanisms pertinent to fracture care. Key parameters are summarized in Table 1-2, and will be reviewed at the end of this chapter in the context of biomechanical evaluation of fixation constructs.

TABLE 1-2. Summary of Basic Parameters and Definitions for Characterization of Material and Structural Properties

Parameter

Formula

Unit

Example

F = m [kg] × 9.81 m/s 2 ( m = mass)

[N] Newton

About 10 N force is required to lift a 1-L water bottle, weighing 1 kg

Force

M = F × d ( d = moment arm)

Moment

[Nm] Newton-meter

1–2 Nm “torque” is required to insert a 4.5-mm cortical bone screw

ε = Δ l/l (l = undeformed length)

[unitless], 0.01 = 1% Cortical bone can strain 1% before it fractures

Strain

σ = F / A (A = loading area)

[N/m 2 ; Pa], Pascal

Stress/pressure

A pressure of 1,000 Pa is required to push a keyboard key

E = σ / ε

[Pa]; 1 GPa = 1 × 10 9 Pa 100 GPa = stiffness of titanium

Young’s/E-modulus

Parameter

Definition

Deformation: elastic/ plastic

Change in size of an object in response to an external force. Elastic deformation will fully recover after the removal of the force, similar to a spring. Plastic deformation will not recover after load removal, similar to permanent bending when contouring a bone plate. Stiffness is the amount of load required to deform a sample a given amount. It is calculated as the slope of the elastic portion of a load-deformation curve. Stability is not a defined, quantitative parameter, but a subjective description of the mechanical integrity of a structure. The structural strength and resistance to bending of a uniform beam or cylinder depend on its cross-sectional shape. The second moment of inertia ( I ) is calculated based on the cross-sectional shape. Multiplying I with the E-modulus will yield the bending stiffness. The load, force, or pressure required to cause structural failure of an object. Yield strength is the load that causes the onset of permanent, plastic deformation. Ultimate strength is the load at which the object fails. For brittle material, yield and ultimate strength are almost identical. An isotropic material (steel) has the same material properties when loaded in different directions. An anisotropic material such as cortical bone has different material properties, depending on the loading direction (tension/compression, longitudinal/ transverse). Accumulation of material defects or micro-cracks during repetitive loading. The fatigue limit, fatigue strength, or endurance limit is the highest stress an object can withstand for an infinite number of cycles without failing. The fatigue limit is typically far lower than the ultimate strength of a material.

Stiffness, stability

Bending stiffness (EI), second moment of inertia

Strength: yield/ ultimate

Isotropy, anisotropy

Fatigue, fatigue limit

Viscoelasticity, creep Unlike a linear elastic material (steel), which deforms by a fixed amount in response to a constant load, a viscoelastic material continues to deform, or creep, under constant loading. The stiffness of a viscoelastic material depends on the rate or speed of loading.

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