• resistance of a structure to applied load (force) depends on: material properties and structural properties

Structural Terms – depends on amount and distribution of material (i.e. size, shape, organization, etc)

• Load = applied force (F)
• Deformation = change in length (D L)
• Stiffness = resistance to deformation = F/D L
• Failure load = amount of force applied to cause a structure to fail
• Moment of Inertia (I): contributes to resistance to bending and torsion; depends on amount and distribution of material
• higher I Þ higher resistance to loading
• rule of thumb: to increase I, put material further away from the center
• e.g., cylinder: I µ r⁴ Þ small increase in radius = large increase in moment
• biological examples:
• bones are hollow Þ same amount of material, larger radius = better mechanical efficiency
• callus of a healing bone grows on the outside of the bone
• aging bone loses mass from the center and gains on the outside (less mass, but still able to support weight)

Materials – intrinsic properties of the material (i.e. strength, toughness) independent of structure

• Stress = s = force/area
• consequence: smaller area (i.e. cross section of bone) Þ more stress on the material for a given load
• Strain = e = D L/L₀ = deformation/original length
• consequence: for the same deformation (change in length) a shorter structure (i.e. tendon) will have more stress
• Modulus = E = stress/strain
• consequence: higher modulus materials have a higher resistance to deformation
• Strength = stress at failure (amount of stress a material can take before failing)

Loading modes – how is the force applied?

• all loading modes can be described in terms of:
• tension: pulling/ stretching
• compression: pushing
• shear: sliding (bones are weak in shear; compression often results in shear forces causing failure)
• other loading mode terms:
• axial: load applied to an axis (i.e. center of a cylinder)
• eccentric: load applied off-axis
• bending: load applied eccentrically or laterally (bending involves tension on the larger curve of the bend and compression on the lesser curve)
• torsion: twisting a material; creates a shear force Þ bones are weak under torsion

• elastic behavior: material returns to original state after load is removed
• plastic behavior: material is permanently changed after load is removed
• viscoelastic behavior: material behavior depends on time or rate of loading
• i.e. bone is stiffer when the load is applied rapidly

• creep: load applied with continually increasing magnitude
• fatigue: load applied cyclically (repeated loading and unloading of material)
• monotonic: constant load over time; material responds by increased deformation over time until failure
• relaxation: constant deformation over time; material responds by decreasing the load required to hold the deformation

• brittle: catastrophic failure involving little energy; generally little plastic deformation before failure
• brittle materials can still be very stiff and strong (but when they go, they go in a big way - e.g., ceramics)
• tough or ductile: complex failure involving high energy; generally much plastic deformation before failure (e.g., bending a paperclip to break)

• homogeneous: uniform distribution of properties - do not depend on position (i.e. steel)
• inhomogeneous: non-uniform distribution of properties - material properties depend on position (i.e. bone, tendon)
• isotropic: material properties do not depend on direction (i.e. steel)
• anisotropic: material properties depend on direction (i.e. bone, tendon, muscle)
• composites: materials composed of more than one component (i.e. bone = collagen, water, minerals, etc)