Stress and strain

Stress

  • Definition: Force applied per unit area.
  • Formula: σ=F/A (Force/Area)
  • Unit: N/m² or Pascals (Pa)
    Example: 1 Pascal is equivalent to the force of an apple on a 1m² coffee table.

Strain

  • Definition: The measure of deformation, representing the change in length relative to the original length.
  • Formula: Strain=ΔL/L0​
  • Unit: Unit less
    It is expressed as a ratio or percentage.

Material Properties

A material’s properties depend on the forces applied to it:

Isotropic Materials

  • Definition: Mechanical properties remain the same regardless of the type of force applied.
  • Examples: Woven bone, polymers, and many metals.

Anisotropic Materials

  • Definition: Mechanical properties vary with the type of force applied.
  • Examples: Most living tissues, such as cortical bone, tendons, and ligaments.

Stress-Strain Curve

  • Purpose: Used to analyze material properties.

  • Young’s Modulus: The gradient of the stress-strain curve. It measures the stiffness of a material.

    • High Young’s Modulus: Stiffer material.
    • Formula: ( E = ) (Stress/Strain)

Young’s Modulus of Various Orthopaedic Materials:

Material Young’s Modulus (GPa)
Ceramic 250
Cobalt Chrome (CoCr) 225
Stainless Steel 200
Titanium 100
Cortical Bone 20
PMMA 2
Polyethylene 1.5
Cancellous Bone 1
Tendon 0.1
Cartilage 0.02

Regions of the Stress-Strain Curve

1. Elastic Region

  • Behavior: Stress and strain are proportional.
  • Law: Follows Hooke’s Law.
  • Key Property: If stress is removed, the material returns to its original shape.

2. Toe Region (Tendons/Ligaments only)

  • Behavior: Non-linear increase in stress and strain due to the uncrimping of fibers.

3. Plastic Region

  • Proportional Limit: Stress is no longer proportional to strain, but deformation is still recoverable.
  • Elastic Limit: The end of recoverable deformation.
  • Yield Point: The material begins to deform plastically and will not return to its original shape after stress is removed.

Material Toughness and Ductility

  • Toughness: The area under the entire stress-strain curve. It represents the total energy absorbed before the material fractures.

  • Ductile Materials: Exhibit a large plastic region before fracturing (e.g., metals).

  • Brittle Materials: Show almost no plastic behavior; the yield point is very close to the fracture point (e.g., ceramics).

Ultimate Tensile Strength (UTS)

  • Definition: The maximum stress a material can withstand before breaking.
  • Application: Stainless steel plates have a high UTS and are more suitable for non-union fractures compared to titanium plates.

Other Key Material Properties

Fatigue Failure

  • Definition: Failure due to repetitive stress below the ultimate tensile strength.
  • S-N Curve: Represents the relationship between stress and the number of cycles to failure.
Component Endurance Limit
Hip Replacements Above endurance limit
Knee Replacements Below or at endurance limit

Additional Properties

  • Stiffness vs. Rigidity: Stiffness is a material property, while rigidity refers to a structure’s ability to resist deformation.

  • Notch Sensitivity: A material’s resistance to fracture when notched or irregular.

    • Low Notch Sensitivity: Ceramics.
    • High Notch Sensitivity: Ductile materials like steel and polyethylene.

Visco-Elastic Behavior

Many living tissues exhibit visco-elastic behavior, meaning they have both elastic and viscous properties. This behavior is time-dependent:

Types of Visco-Elastic Behavior

  1. Creep: Time-dependent deformation under a constant load (e.g., Ponsetti treatment).
  2. Stress Relaxation: Time-dependent reduction in the stress required to maintain deformation (e.g., ACL graft cycling).
  3. Hysteresis: The difference in the stress-strain curve during loading and unloading due to energy loss (heat).
Back to top