• "The study of the laws of nature" Planck
• "All of science is physics or it is merely stamp collecting" Planck (Theoretical or Experimental Physics)
• Scientific Method
• Theory Boundaries

• Length, Time, Mass, Temperature, Electric Current, Amount, Luminosity, meter (m), second (s), Kilogram (kg), Kelvin (K), ampere (A), mole (mol), Candela (cd)

Laws of Motion- Newton 1687

"The Principia"

• 1^st Law Inertia
• Tendency to resist change
• Mass is a measure of inertia
• 2^nd Law
• F=ma
• 3^rd Law
• When 2 objects interact the force exerted on one object is equal in size and opposite in direction to the force exerted on the other object

Centripetal Force

F=(mv²)/r

• A quantity such as mass, time, or length completely defined by a number and an appropriate unit
• Follow standard addition & subtraction rules

• A quantity such as force that is completely defined by a number, an appropriate unit, and a direction
• Does not follow standard addition and subtraction rules

• compression, tension, shear
• Forces- tendency is to bend or break
• Structures- tendency is to be malleable or brittle

Structural Properties of Bone

Hydroxyapatite CaPO₄(H₂O) 70%

Structural Properties of Bone

Collagen- a structural protein with approx. 1,000 amino acids

the amount of deformation

Within limits, stress and strain are proportional (Hooke's Law)

S_m= Shear Stress/ Shear Strain

• Force per x-sectional area/change in angle of deformation (measured in radians relative to original angle)

B= Uniform Stress/ Uniform Strain

• Force per unit area/ change in volume (relative to original volume). Internal pressure can increase or decrease.

For most solids, B>E>S_m

Strength of tubes versus rods. Optimum wall thickness for a given load?

S= pie²(EI/ L²)

Where S= force of failure; E=Young's Modulus; I= second moment of x-sectional area; and L is length

I= pie r³t 

Where r= radius and t= thickness

Therefore,

S=pie²(E* pie* r³* t/ L²)

Study of complex x-sectional shapes requires analysis relative to multiple axes. 

Biological constraints often require compromises

ability to resist static compression or tension

energy built up in material being stressed (i.e rubber bands)

SE= 1/2(stress²/E)

SE measured in J/m³

amount of energy that can be stored without damaging the material

Materials with a low Young's Modulus store more energy for a given stress

Energy absorption is also enhanced by low E values

assumed to be reached when the atoms are pulled by 20% 

Σ= F/A= (Δh/h)E

Critical Crack Length

How large does a crack have to be for material to fail?

Critical Crack Length

Griffith point L_g

measured to direction of load

decreases as the crack extends by a factor l²

for breaking bonds, creating new surfaces, and generating heat. 

Fracture energy scales with crack length

due to the motion of the crack.

KE scales with l² v²

• Stresses are concentrated at the tips of cracks
• Sharper the tip, greater the stress
• Stress proportional to l/r, where r is the radius of curvature at the tip
• Example: Shark Tooth
• L_g= -1/B (dU/da)