Section 12: Mechanics of Materials Stress / Strain 12-1 Basic - - PowerPoint PPT Presentation

Section 12: Mechanics of Materials – Stress / Strain

12-1

Basic Biomechanics Basic Biomechanics

Force Force

Area ΔL

Stress = Force/Area Strain =

Change Height (ΔL) /

12-2 From: Le

Force/Area

g g ( ) Original Height(L0)

Stress Stress

• Stress (σ): internal

Stress (σ): internal resistance to an external load

Axial – Axial (compressive or tensile) σ=F/A Sh F/A ( ll l – Shear τ = F/A (parallel

• r tangential forces)
• Units Pascal (Pa) =

Shear

Units Pascal (Pa) 1Nm2

Shear

12-3 From: Noffal

12-4 From: Grimm and Atkinson

12-5 From: Seeley

Definition of Stress Definition of Stress

F

• A

F = σ

F

• This is the definition of engineering stress.
• F is the force in Newton (N)

A0 ( )

• A0 is the initial area of the specimen in m2.
• The unit of stress is therefore N/m2.
• 1 N/m2=1 Pascal or 1 Pa.
• 1 KPa=103 Pa; 1 MPa=106 Pa; 1 GPa=109 Pa

F

• 1 KPa=103 Pa; 1 MPa=106 Pa; 1 GPa=109 Pa.
• Strengths of metals are usually in MPa; elastic modulus of

metals usually in GPa. F

12-6 From: Wei

Basic Biomechanics

Force, Displacement & Stiffness Force

Slope = Stiffness =

• ce

Slope Stiffness Force/Displacement

12-7 From: Le

Displacement

Basic Biomechanics

Stress-Strain & Elastic Modulus Stress = Stress Force/Area Slope = Elastic Modulus = Stress/Strain

Strain =

Ch i L th/O i i l L th (ΔL/ L )

12-8 From: Le

Change in Length/Original Length (ΔL/ L0)

12-9 From: Grimm and Atkinson

Basic Biomechanics

Common Materials in Orthopaedics

• Elastic Modulus

(GPa)

• Stainless Steel

200

• Titanium

100

• Cortical Bone

7-21

• Bone Cement

2.5-3.5

• Cancellous Bone 0.7-

4.9

Stress

• UHMW-PE

1.4-4.2

Strain

12-10 From: Le

Strain

12-11 From: Seeley

12-12 From: Seeley