biomechanics

name	biomechanics
description	Biomechanics — bone mechanics, joint forces, gait analysis, muscle forces, prosthetics loads, fatigue of implants, material properties of biological tissues, FEA in biomechanics.
metadata	{"priority":7,"promptSignals":{"phrases":["biomechanics","bone","joint force","gait","implant","muscle force","prosthetics"],"minScore":3}}

Biomechanics — Complete Skill

Bone Mechanical Properties

Cortical (Compact) Bone

Tensile strength: S_t = 130-170 MPa (longitudinal) Compressive: S_c = 170-210 MPa Shear: τ = 65-75 MPa Young's modulus: E = 15-25 GPa (longitudinal), 5-12 GPa (transverse) Anisotropic: E_axial / E_transverse ≈ 2.5

Fatigue: S-N curve; endurance limit ≈ 50-70 MPa (cycle: 10⁶-10⁷ for cortical) Stress fracture: cyclic loading during running at σ > ~60 MPa

Trabecular (Cancellous) Bone

Porous foam-like structure; apparent density ρ* = 0.1-0.9 g/cm³ E = C × (ρ*)^n (Gibson-Ashby: n ≈ 2, C ≈ 12,000 MPa/(g/cm³)²) Compressive strength: σ_c = 0.1-40 MPa (highly variable with density) Energy absorption: progressive crushing; good for impact loads

Joint Forces (Static Analysis)

Hip Joint (Single-Leg Stance)

Free-body diagram: hip abductor muscle M_abd balances W_body moment M_abd × d_abd = W_body × d_body (moment about hip joint) F_hip = W_body + M_abd (vector sum) Hip force ≈ 3-5 × body weight during walking; up to 8× during running

Knee Joint

Tibio-femoral contact force: depends on flexion angle and muscle activity Quad force: F_Q = M_knee / d_Q (d_Q = patellar tendon moment arm ≈ 40-50 mm) Joint force ≈ 2-3× body weight walking; 5-7× during squatting

Gait Analysis

Ground Reaction Forces

Normal GRF pattern (sagittal, vertical): double-humped, ~1.2 BW peak First peak (heel strike): 1.1-1.2 BW Valley (midstance): ~0.8 BW Second peak (push-off): 1.1-1.3 BW Horizontal: ±0.2 BW (braking at heel, propulsive at toe-off)

Gait phases: Stance: ~60% gait cycle (heel strike to toe-off) Swing: ~40% (toe-off to next heel strike)

Implant Design Loads

Total Hip Replacement (THR)

ISO 7206 standard test loads: Axial: 2300 N (static); Cyclic: 3000 N × 10⁷ cycles fatigue test Bending: 230 N·m (hip angle 10°, abduction 10°) Material: Ti-6Al-4V (stem, S_y = 800-900 MPa), CoCrMo (head), UHMWPE/ceramic (cup)

Total Knee Replacement (TKR)

ISO 14243 loads: ~2600 N axial, ±1000 N AP shear Wear testing: 10⁶ cycles simulated walking cycle Contact stress (bearing surface): 10-25 MPa typical

Fatigue of Implants

Titanium (Ti-6Al-4V) endurance limit: ~500 MPa (R = -1) After machining: reduce by 10-20% (surface defects) In vivo: further reduced by corrosion-fatigue in body fluid

Stress concentration at porous surfaces: K_t = 3-8 (porous coating) Modified endurance: σ_e,modified = σ_e / (K_f × K_s × K_r)

Cartilage and Soft Tissue

Articular cartilage: E = 0.5-5 MPa (fluid-saturated, biphasic behavior) Biphasic model: fluid + solid phases; viscoelastic creep Ligament: nonlinear J-curve stress-strain; E_toe = 50-200 MPa; E_linear = 200-800 MPa Meniscus: circumferential tensile stiffness (hoop stress from compression)

FEA in Biomechanics

Material assignment: bone density from CT Hounsfield units → E = f(HU) E [MPa] = a × HU^b (a ≈ 0.001-0.003, b ≈ 2.5-3.0, varies by study) CT-based FEA: automatic material mapping from scan Validation: compare strain gauge measurements or DXA with simulation

Output

Provide: joint force [BW and N], muscle force [N], implant stress σ_max [MPa] vs. endurance limit, fatigue safety factor, bone density-modulus mapping, gait cycle phase identification, ISO test load compliance check.