MECH 547 L1-6

What’s the difference between Biological materials & Biomaterials?

Biological materials: Materials produced by natural organisms. Describes resources and where they come from.
Biomaterials: Materials used for biomedical use (designed to repair/supplement human organs)

Biological materials

Materials produced by natural organisms. Describes resources & where they come from

Biomaterials

Materials used for biomedical use

Bio-inspired materials

Use biomaterial GEOMETRY with other materials. Materials whose design and/or synthesis was inspired by a natural material.

When did biological materials become intensely studied by engineers?

starting in 1990

What are the 3 areas of the natural materials paradigm?

Mechanical Function, Composition & Structure, Mechanical Properties

How many orders of magnitude do the mechanical properties of biological materials span?

5-6 orders of magnitude!

Nature produces things in-situ and from _____ (top down or bottom up)

Bottom up

What’s the impact of hierarchy in natural materials?

At each scale specific structures control specific mechanisms & behavior at microscale is the “sum” of contribution of the mechanisms at each scale

Functions in mechanical engineering design…

Are identified first and then the material with adequate properties is selected

Materials in nature… (to do with functions)

Are optimized for one or several specific functions. Function and properties are closely connected

What is stress?

internal forces generated from external forces exerted on a component

What is strain?

When a component deforms internally due to external loading
Measure of elongation, compression, and shear deformations.

What connects stresses & strains?

A constitutive law (T tensor & E tensor)

What does the simple tension tensor look like? (F in x direction)

Only normal stress

What does the pure bending stress tensor look like?

Where are the bending stresses highest on the femur?

Edges! There is denser bone there. Bone architecture follows directions of principal stresses

What is the small strains approx?

When strains are small (~5%) the 2nd order terms can be neglected.

What are the 3 types of strain and their formulas?

1. Engineering strain (e) = elongation / length in ref state = (l-L)/L

2. Natural strain (∂ɛ) = ∂l/l

3. Lagrangian strain (ɳ) = 1/2*((l/L)²-1

Formula for stretch (ʎ)

ʎ = l/L

What is the strain energy function?

A scalar energy density that quantifies how much elastic energy is stored in a material due to deformation

What is the strain energy function in terms of the stress strain relation?

s = dW/dλ or σ = dW/dɛ

What are 2 types of stress?

1. True stress (σ) = force / area in current state

2. Nominal stress (engineering stress) s = force / area in reference state

What are the 4 parts of the strain energy density function for a neo-Hookean material?

On what material does the Neo-Hookean model work well?

Rubbery materials like rubbers & hydrogels

What is the formula for the Mooney-Rivlin model?

When should you use the Neo-Hookean model?

simple elastic materials moderate strains

When should you use the Mooney Rivlin model?

Rubbers & elastomers. moderate stretches

When should you use the Ogden model?

Large strains, biological tissues, complex stiffening

When should you use the arruda-boyce model?

Polymers & elastomers. Finite extensibility

When should you use the Yeoh model?

Isotropic materials. Large deformations

When should you use the gent model?

Strain-stiffening materials. Approaching stretch limits

What is hardness?

A measure of how a material resists plastic deformation

How do you measure the following from a stress-strain curve? (stiffness/elastic mod, strength, extensibility/strain @ failure, stretchability, energy absorption, spring capacity)

1. Initial slope of stress-strain curve

2. Typically max stress on stress-strain curve

3. Strain at failure

4. Stretch ratio @ failure

5. Area under stress-strain curve

6. Area under stress-strain curve in elastic region

What are important considerations when doing a unidirectional tensile test on a biological material?

1. Specimen prep

2. Small specimens

3. Clamping

4. Hydration

5. Anisotropy

6. Age / gender difference

What complications can occur during compression testing?

1. Contact with platens

2. Friction at platens

3. Spurious stresses

What is nano/micro indentation?

Highly localized measurements of mechanical properties (including elastic mod, hardness, fracture toughness, viscoelasticity)

What are the pros of nano/micro indentation?

• High spatial resolution

• Small sample requirements

• Minimally destructive testing

• high throughput & automation

What is AFM indentation?

Atomic force microscope => detects deflection

How do you analyze data from nanoindentation?

Look @ load-displacement curve

What are the main material properties (used to pick materials for a certain use case)

• Density

• Stiffness

• Strength

• Strain @ failure

• Work at failure

• Hardness

• Work of fracture

• Toughness

• Viscosity

• Spring capability

What are the two fracture criteria?

1. Strength criterion

2. Fracture mechanics criteria

What is the strength criterion? (in fracture mechanics)

Fracture happens when the max local tensile stress reaches the material’s intrinsic strength

What is the fracture mechanics criteria?

• Stress intensity reaches fracture toughness (K_I >= K_IC)

• Griffith energy criterion: energy release rate reaches fracture energy (G >= G_c)

What is fracture energy (G_IC)?

G_IC = (K_IC²)/E

Energy consumed per unit area of crack in ruptured materials

Is fracture energy a material property?

YES

How do you determine fracture energy?

1. Look it up in a material data sheet (steel > alu > polymers > ceramics > glass)

2. Measure it experimentally through a fracture test

3. Numerical simulation

What is the process zone in fracture mechanics

Irwin proposed thing where there are small bubbles on edges of a crack where:

• Plastic deformation

• Viscoelasticity

• Phase transformation

• Breaking bonds

What is the stress concentration factor? (K_T)

σ_max / σ_0

What is the stress intensity factor? (K_I)

K_I = beta*σ*sqrt(pi*a)
A function of geometry, mechanical loads, shape/size of crack

Why do you want to make a large crack in the test specimen for a fracture toughness test?

1. Dominate any other natural crack/defect

2. Be measured

Why is smaller stronger?

Tensile strength = toughness / sqrt(pi*size). So if size is super small, then tensile strength is huge

What are 4 of the main elements used in nature?

C, H, O, N