bone-mechanics

name	bone-mechanics
description	Bone mechanics — cortical/cancellous properties, anisotropy, fracture toughness, Wolff's law, bone remodeling, implant fixation, stress shielding, ASTM F1185, biocompatibility.
metadata	{"priority":7,"promptSignals":{"phrases":["bone mechanics","cortical bone","cancellous bone","bone stiffness","Wolff's law","bone remodeling","bone implant"],"minScore":3}}

Bone Mechanics — Complete Skill

Bone Structure and Types

Cortical (compact) bone: Dense outer shell; highly organized osteon structure; load-bearing Haversian system: concentric lamellae around Haversian canal (blood vessel) Porosity: 5–10%

Cancellous (trabecular/spongy) bone: Porous network of trabeculae; located at bone ends (epiphysis), vertebrae Porosity: 50–95%; apparent density 0.1–1.0 g/cm³ Trabecular architecture aligns with principal stress directions (Wolff's law)

Mechanical Properties

Cortical Bone

Elastic modulus: Longitudinal (along bone axis): E_L = 17–27 GPa (femur, tibia) Transverse: E_T = 6–12 GPa Shear: G = 3–5 GPa Orthotropic → full compliance matrix needed for precise analysis

Strength: Compressive: σ_c = 130–200 MPa (longitudinal); 100–150 MPa (transverse) Tensile: σ_t = 110–170 MPa (longitudinal); 50–65 MPa (transverse) Shear: τ = 50–70 MPa Cortical bone is stronger in compression than tension (anisotropy)

Fracture toughness: K_IC = 2–5 MPa√m (lower than metals; brittle in single crack propagation) Energy to fracture: 1–3 kJ/m² (crack deflects through osteons → toughening)

Yield strain: ε_yield ≈ 0.7–0.9% (longitudinal); near linear to yield Post-yield: microcracking; quasi-ductile behavior; damage accumulation

Cancellous Bone

Gibson-Ashby scaling (cellular solid): E_cancel = E_solid × C₁ × (ρ_app/ρ_solid)² [C₁ ≈ 0.03–0.15; n = 2 for open-cell foam behavior] σ_cancel = σ_solid × C₂ × (ρ_app/ρ_solid)^1.5 [strength scaling]

Apparent density ρ_app and stiffness: ρ_app = 0.1 g/cm³ (very porous): E ≈ 1 MPa ρ_app = 0.5 g/cm³ (dense): E ≈ 500–1000 MPa ρ_app = 1.0 g/cm³ (dense; near cortical): E ≈ 5–15 GPa

Relationship to BMD (bone mineral density): E [MPa] = 33.9 × (ρ_app [g/cm³])^2.2 [Kopperdahl-Keaveny; vertebral bone] σ_c [MPa] = 37.8 × (ρ_app)^2.0 [similar power law]

Age and Disease Effects

Osteoporosis: Loss of cancellous architecture; reduced BMD; ρ_app decreases 30–50% from peak E and σ reduce by more than proportional (structure loss, not just density) Fracture risk: hip, vertebral, wrist

Aging (cortical): E changes little with age; strength and K_IC decrease ~0.5–1% per year after age 35 Increased mineralization → more brittle; reduced ductility

Wolff's Law and Bone Remodeling

Wolff's law (1892): bone adapts its structure to mechanical loading Trabeculae align with principal stress directions Loading stimulates new bone formation (modeling + remodeling)

Mechanobiology: Osteocytes sense mechanical strain → signal osteoblasts (formation) and osteoclasts (resorption) Threshold strain for remodeling stimulus: 1000–2500 μstrain (0.1–0.25%) [daily loading] Below 200 μstrain → disuse atrophy; above 10,000 μstrain → pathological fracture risk

Stress shielding (implants): Metal implant (E = 110 GPa Ti; 200 GPa steel) shields bone from load → bone resorption → implant loosening Mitigation: use low-modulus implant (Ti alloy E = 100 GPa → still high); HA coating; porous surface for osseointegration; composite implant

Remodeling equation (Huiskes strain energy): ΔV/V = k × (S - S_ref)^n [bone volume change rate; S = strain energy density; S_ref = reference SED; k, n = material constants]

Bone-Implant Mechanics

Osseointegration: direct bone-implant bonding without fibrous tissue; required for long-term fixation Implant surface requirements:

• Porous surface (coating or AM lattice): pore size 100–500 μm for bone ingrowth
• Surface roughness Ra = 0.5–2 μm for optimal protein adsorption
• HA (hydroxyapatite) coating: promotes faster bone bonding

Primary stability (initial fixation): Micro-motion limit for osseointegration: < 50–150 μm relative motion at bone-implant interface Above → fibrous tissue forms → implant failure

Implant stress shielding (hip stem): Stress in bone = σ_bone = P_total × E_bone / (E_bone + E_implant × A_implant / A_bone) [simplified composite] Minimize E_implant or A_implant for better load sharing

ASTM Standards for Bone/Implant Testing

Standard	Scope
ASTM F1185	Composition of HA (hydroxyapatite) for implants
ASTM F2996	Hip prosthesis; torsion/bending test
ASTM F384	Metallic bone screws — axial pullout
ASTM F543	Metallic bone screws — torque and pullout
ISO 7206	Implant for surgery; hip joint prostheses
ASTM E8/E466	Tensile/fatigue testing (applies to bone-analog materials)

Biocompatibility

Acceptable implant materials (ISO 10993): Ti-6Al-4V (medical grade; ASTM F136): E = 114 GPa; biocompatible 316L SS (ASTM F138): E = 193 GPa; less preferred (Ni release concern) CoCrMo (ASTM F75): E = 220 GPa; wear-resistant; for articulating surfaces PEEK (polymer): E = 3.6 GPa → much lower stress shielding; radiolucent for imaging

Cytotoxicity (ISO 10993-5): elution test; no toxic ion release acceptable

Output

Provide: bone type (cortical/cancellous), elastic modulus E [GPa], compressive and tensile strength [MPa], fracture toughness K_IC [MPa√m] (if fracture risk), apparent density ρ_app [g/cm³] (cancellous), stress shielding ratio E_implant/E_bone, implant material and modulus, surface preparation for osseointegration (HA coating/porosity/Ra [μm]), micro-motion limit [μm], remodeling stimulus (strain energy density target), applicable standard (ISO 7206, ASTM F136/F138/F75), and biocompatibility reference (ISO 10993).