Section 12: Mechanics of Materials – Stress / Strain 12-1
Basic Biomechanics Basic Biomechanics Force Force Area Δ L Strain = Stress = Change Height ( Δ L) / g g ( ) Force/Area Force/Area Original Height(L 0 ) 12-2 From: Le
Stress Stress • Stress ( σ ): internal Stress ( σ ): internal resistance to an Axial external load – Axial (compressive or tensile) σ =F/A – Shear τ = F/A (parallel Sh F/A ( ll l or tangential forces) • Units Pascal (Pa) = Units Pascal (Pa) Shear Shear 1Nm 2 12-3 From: Noffal
From: Grimm and Atkinson 12-4
From: Seeley 12-5
Definition of Stress Definition of Stress F F σ = F A o o •This is the definition of engineering stress. A 0 •F is the force in Newton (N) ( ) •A 0 is the initial area of the specimen in m 2 . •The unit of stress is therefore N/m 2 . •1 N/m 2 =1 Pascal or 1 Pa. •1 KPa=10 3 Pa; 1 MPa=10 6 Pa; 1 GPa=10 9 Pa •1 KPa=10 3 Pa; 1 MPa=10 6 Pa; 1 GPa=10 9 Pa. F F •Strengths of metals are usually in MPa; elastic modulus of metals usually in GPa. 12-6 From: Wei
Basic Biomechanics Force, Displacement & Stiffness Force o ce Slope = Stiffness = Slope Stiffness Force/Displacement Displacement 12-7 From: Le
Basic Biomechanics Stress-Strain & Elastic Modulus Stress = Stress Slope = Force/Area Elastic Modulus = Stress/Strain Strain = Change in Length/Original Length ( Δ L/ L 0 ) th ( Δ L/ L ) Ch i L th/O i i l L 12-8 From: Le
From: Grimm and Atkinson 12-9
Basic Biomechanics Common Materials in Orthopaedics • Elastic Modulus • Stainless Steel 200 (GPa) • Titanium 100 • Cortical Bone 7-21 • Bone Cement 2.5-3.5 • Cancellous Bone 0.7- Stress 4.9 • UHMW-PE 1.4-4.2 Strain Strain 12-10 From: Le
From: Seeley 12-11
From: Seeley 12-12
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