Fractures in the Horse. Группа авторов

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Fractures in the Horse - Группа авторов


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load and displacement are recorded as stress and strain. In other words, for the bone organ as a whole, the deformation is a function of the load applied. Within the bone material, the strain is a function of the stress induced [42]. The International Organization for Standardization (ISO) and the American Society of Testing and Materials (ASTM) develop and maintain standards for testing materials and structures in different industries.

      Structural Properties and the Load–Deformation Curve

      The initial curved portion is known as the toe region, where low load invokes relatively large deformation, which reflects the uncrimping of collagen fibres in highly collagenous tissues. The linear portion of the curve is called the elastic region, where the object maintains the capacity to return to its original shape once the load is removed. If loading continues through the elastic region to the yield point, then the structure incurs damage. The plastic region of the curve follows the yield point, wherein the material is no longer capable of returning to its original configuration when the load is removed. In the plastic region, the structure deforms to a greater extent for a given load than in the elastic region. If the load continues to increase, the structure will eventually fail. In a clinical setting, the failure point for bone is the load at which it fractures, but in an experimental setting the failure point for a specific biomechanical test may be defined by the investigator. The ultimate load prior to failure is referred to as the ultimate strength of the material. The failure point of bone typically coincides with peak load, as bones have limited ability to deform plastically. The stiffness of the structure is indicated by the slope of the elastic region of the load–displacement curve. The yield, ultimate and failure strengths of a structure correspond to the yield, ultimate and failure load points on the load–deformation curve. The ultimate and failure strength are usually similar in bone but may be different in other materials. Work to fracture (energy absorbed to failure) of a structure is analogous to the material property of toughness and is represented by the area under the load–displacement curve.

Schematic illustration of representative load–deformation curve for a whole bone.

      Material Properties and the Stress–Strain Curve

      Material properties are determined using a standardized bone specimen and the results of tests are represented graphically on a stress–strain curve. The stress–strain curve is analogous to a load–deformation curve for bone structural properties, with the distinction of being normalized to load distribution and specimen geometry.

      Strain (ε) is a change in dimension that develops within a material in response to stress, divided by the original dimension (Figure 3.10b). Strain may be normal (i.e. a change in length or width) or shear (i.e. a change in shape). Normal strain refers to the length (or width) of a structure divided by its original length (or width) and is therefore dimensionless but commonly measured in units of microstrain (με), so that a strain of 0.01 (1%) would be 10 000 microstrain. For reference, maximum strains in the third metacarpal bones of Thoroughbred racehorses galloping at racing speeds of 16 m/s have been measured in the range of 3250–5670 με (0.3–0.6%) [69]. Shear strain is the amount of angular deformation from a right angle lying in the plane of interest in a sample (Figure 3.10c). Shear strain is expressed in radians ( γ ) or degrees (1 rad = 57.3°).

Schematic illustration of diagrammatic representations of stresses and strains.

      Source: Modified from Morgan and Bouxsein [36].

      Change in one dimension is accompanied by a change in a perpendicular dimension. The relative amount of change in perpendicular dimensions is represented by Poisson’s ratio. For example, in a tensile test, lengthening of a structure is accompanied by a narrowing of the width. The quotient of strains in longitudinal and transverse directions is called Poisson’s ratio ( ν ), defined as ν = −(ΔW/W)/(ΔL/L). It is a measure of how loading in the longitudinal direction (axially) affects the structure transversely (laterally). Typically, axial tension results in transverse contraction, while axial compression results in transverse bulging. Poisson’s ratio for bone typically has values between 0.2 and 0.5 (average: 0.3) [70].

      The Role of Geometry

      Bone geometry markedly influences structural mechanical properties. Axial stiffness, which is the resistance of bone to deformation during loading in tension or compression, is proportional to the cross‐sectional area, while bending and torsional stiffness depend on how the bone material is distributed around the axis of bending or torque.


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