Bones: Why are they hollow? Bending of a Long, Solid, Bone: Tension Compression Stress Free in the middle
Bones: Why are they hollow? Eliminate the inside to save weight but keep strength: Tension Compression
Bone: An Old, High Tech Material Human Skull: Porous Center with Solid Sides. Resists Denting Composite Honeycomb Sandwich Panel B. Kosoff, Bones
Bone: A Living, Responsive, Material Unloaded Control Loaded for 12 weeks Univ. of Michigan Load Micro-CT scan of 1cm bone cylinder: FEA
Joints: How does cartilage work? Bone Cartilage: 80% water in a “tight sponge” of solid matrix. Water does not squeeze out: takes most of load Water can’t fail; little stress on solid (living) portion Also: self-lubricating (u=0.005), ~self-repairing Cartilage Bone Cartilage
Spine: Lower Back Pain LBP costs $20-$50B/yr Affects 80% of population Hand load creates reactions in spine and back muscles Back Muscle Force Spinal Column Force 50lbs.
Spine: Lower Back Pain Lever Model 50 lb Hand Load F spine F muscle 2” 20” F muscle =(20/2)*50lbs = 500lbs. F spine =F m +50lbs = 550lbs. Forces up to 1000lbs Fulcrum
Spine: Lower Back Pain Computer models predict muscle and spine forces for any posture and loads. Design safer work environments Univ. of Michigan
Knee: Chondromalacia Bottom View Resultant Force Outside Excessive Pressure
Tissue Engineering: Grow Your Own Carnegie-Mellon U. Stem cells seeded onto a biodegradable scaffold/matrix Local gene therapy instructs cells to regenerate bone, ligament, cartilage, skin, nerves, organs… Body’s cells join in Bone cartilage forms, scaffold is absorbed
Nature: The Cube-Square Law Why can fleas jump 100x their own height? Why can’t elephants even jump ¼ x their own height? Cube-Square Law: “Size”: “average dimension” of the animal Muscle Force ~ Cross-Sectional-Area ~ Size 2 Mass ~ Volume ~ Size 3
Cube-Square Law Acceleration Capacity of Animals: F = m*a a = F/m a ~ (Size 2 ) / (Size 3 ) = Size -1 Smaller animals can accelerate faster: - Hard to catch a fly - Football kick-returners - Soccer players
The Cube-Square Law Jumping Height of Animals (1st order model): Mass ~ Size 3 Force ~ Size 2 Work = Increase in Potential Energy F * Distance = M * g * Height change Size 2 * Size ~ Size 3 * Height change Size cancels on both sides: Height change of CG is not a function of Size
Shoulder Experiment Doctors believe the capsule is stretched after the first dislocation, allowing further dislocations, but it has not been shown. Surgical shortening of the capsule improves stability. Shortening can restricts range of motion. Aim of my experiment: Measure the strain field in the capsule due to a dislocation
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