Definitions
Stress is force divided by cross-sectional area.
[ \text{Stress} = \frac{F}{A} ]
Strain is change in length divided by original length.
[ \text{Strain} = \frac{\Delta L}{L_0} ]
Stress has units of pressure. Strain is dimensionless.
Stress-strain curve for a ductile material
A typical sequence is:
- elastic region
- yield
- plastic deformation
- ultimate tensile strength
- necking
- fracture
Elastic region
Deformation is reversible. In the approximately linear portion, the slope is the elastic modulus.
A steeper slope means a stiffer material.
Yield point
Marks the transition to permanent deformation.
Plastic region
Removal of the load no longer returns the material to its original shape.
Ultimate tensile strength
The maximum engineering stress reached during the test.
Necking and fracture
Local reduction in cross-sectional area develops before final failure in many ductile materials.
Stiffness versus strength
These are different concepts.
- stiffness: resistance to deformation
- strength: stress required to cause failure or permanent deformation
- toughness: energy absorbed before fracture
- brittleness: failure with little plastic deformation
A material can be stiff but brittle, or flexible but strong.
Structural versus material properties
A structure's behaviour depends on both material and geometry.
For example, the stiffness of a plate or nail changes with:
- cross-sectional shape
- diameter
- wall thickness
- working length
The elastic modulus is a material property; construct stiffness is not.
Viscoelasticity
Biological soft tissues show both elastic and time-dependent viscous behaviour.
Creep
Under constant load, deformation increases with time.
Stress relaxation
Under constant deformation, the stress required to maintain that deformation falls with time.
Hysteresis
Some energy is lost during a loading-unloading cycle.
Strain-rate dependence
Many biological tissues appear stiffer when loaded more rapidly.
Biological tissues such as tendon, ligament, cartilage and disc show both elastic and time-dependent behaviour.
Creep: deformation increases with time under a constant load.
Stress relaxation: required stress falls with time when a constant deformation is maintained.
Hysteresis: some energy is lost as heat during a loading-unloading cycle.
Strain-rate dependence: the apparent stiffness and failure behaviour can change with loading speed.
Fatigue
Repeated cyclic loading below the single-load failure threshold can eventually cause fracture. Fatigue life depends on:
- stress magnitude
- number of cycles
- notches or defects
- material
- surface condition
A structure can fail under repeated submaximal loading even when each individual load is below its static failure strength. Fatigue is relevant to:
- stress fractures
- implant breakage
- stem or plate failure in the absence of union
- repeated cyclic loading of fixation constructs
If a fracture fails to unite, the implant may continue to carry load until fatigue failure occurs.
Clinical relevance
Stress-strain concepts underpin:
- implant selection
- plate and nail design
- tendon and ligament behaviour
- fracture fixation
- stress shielding
- fatigue failure
Core mechanical definitions
Stress is force divided by the area over which it acts.
Strain is change in length divided by original length.
A stress-strain curve describes material behaviour independently of specimen size. The slope of the linear elastic region is the Young modulus, a measure of material stiffness.
Stiffness of a whole structure is not the same as elastic modulus. Structural stiffness depends on geometry as well as material properties.
Elastic, plastic and failure regions
Within the elastic region, deformation is recoverable after load removal. Beyond the yield point, permanent deformation develops. Continued loading eventually causes failure.
For biological tissues, the curve may be non-linear, and the apparent stiffness can depend on loading rate and previous loading history.
Important terms:
- strength: stress at failure or another defined failure point
- toughness: energy absorbed before failure, represented by area under the stress-strain curve
- ductility: ability to undergo plastic deformation before fracture
- brittleness: failure with little plastic deformation
A material can be stiff but brittle, or relatively compliant but tough.
Bending
Bending produces tension on one side of a structure and compression on the opposite side, separated by a neutral axis. Bending stress increases with distance from the neutral axis.
The second moment of area is therefore important: moving material away from the neutral axis can markedly increase resistance to bending without proportionally increasing mass. This helps explain the mechanical efficiency of hollow long bones and tubular implant designs.
Torsion
Torsion generates shear stress. In a circular structure, shear stress increases toward the outer surface. Polar moment of inertia influences resistance to torsion.
Spiral fracture patterns are commonly associated with torsional loading because maximum tensile stresses are generated obliquely.
Stress concentration
Notches, holes, abrupt changes in cross-section and surface damage can concentrate stress. Screw holes in bone remain stress risers after plate removal. Scratches on some implant materials can reduce fatigue resistance.
FRCS synthesis
Use mechanics to explain clinical observations:
- longer working length → generally more flexible bridging construct
- larger diameter nail → much greater bending stiffness because geometry has a powerful effect
- eccentric load → bending moment
- non-union → prolonged cyclic load and fatigue risk
- stress riser → local peak stress despite modest average stress
The examiner is usually looking for application, not isolated equations.