BIOL 325 - Material Properties

Compression (def & what does it act on?)

Stress generated when inward force is applied to a material, perpendicular to it. Can act on gases, liquids, & solids

Tension (def, what does it act on?)

Stress generated when an outward force is applied to a material, perpendicular to it. Can a act on liquids & solids. 

Shear (def & what can it act on?)

• Stress generated when a force is applied to a material, parallel to the surface.

• Can only act on solids

• Denoted by tau - τ

Simple solid (based on composition)

made of only one material

Composite solid (base on composition)

combination of 2 or more materials

isotropic solid (based on direction)

mechanical properties are not dependent on direction

Anisotropic solid (based on direction)

mechanical properties ARE dependent on direction (resistant to certain directions of force)

Tensile vs Pliant vs Rigid

Tensile - can stretch

Pliant - can bend easily

Rigid - unable to force out of shape

Hookean Material

a material in which the displacement is directly proportional to the applied load

Stress (denoted by sigma - σ)

Force/ CS area measure in Pascals like pressure

Strain (denoted by epsilon - ε)

change in L/ initial un-stretched L, no units

Properties given by Stress(y-axis)/ Strain (x-axis) plots & shape

Modulus or stiffness, strength, extensibility, toughness, resilience; curves tend to be J shaped.

Young’s modulus of elasticity (E) (4 points)

• Stiffness or elastic modulus of a material.

• Give by slope of the Stress/ Strain curve. Steeper slope = stiffer material

• Units in Pascals like stress or pressure.

• Change in Stress (sigma)/ change in Strain (epsilon)

Tensile Strength 

• Stress at the failure point (breaking stress) 

• Units in Pascals

Extensibility 

• Strain at failure point (breaking strain)

• No units as it is a ratio

Toughness (def, units, & calculate)

• Work required to stretch a unit volume of the material to failure

• Units = J/m³

• Calculated by integrating the area under the stress-strain curve

Resilience (def, units, formula, < or > 1)

• Measure of energy recovered from elastic storage. 

• No units, expressed in % of energy recovered

• = work of contraction/ work of extension 

• always less than 1

shear strain

• Denoted by gamma - γ

• change in length/ height = tan θ

shear modulus

shear stress/ shear strain = τ/γ

Response to shear stress (solids vs fluids)

• Solid responds by deforming 

• Fluid responds by moving 

Velocity gradient = Shear strain rate (γ^. - dot in the middle on top of gamma)

• Rate at which a fluid moves in response to shear stress

• change in velocity/ distance between the bottom of the fluid and the top (Δv/d)

• units in s^-1

Dynamic viscosity (μ) ( 5 points - formula, def, units, graph)

• shear stress/ shear strain rate [τ/(Δv/d)]

• units of Pa.s

• slope of the line in shear stress vs shear strain rate graph 

• related to a fluid’s resistance to flow 

• a measure of the internal friction of a fluid’s molecule as they flow past each other. 

High viscosity fluid vs Newtonian fluid vs Low viscosity fluid

• HV Fluid - a high shear stress results in low shear strain rate

• Newtonian fluids have a linear relationship between shear stress and shear strain; double the shear stress, double the shear strain rate

• LV Fluids - a low shear stress results in a high shear strain rate 

shear thickening 

a fluid that becomes more viscous with increase in shear strain

shear thinning

a fluid that becomes less viscous with increase in shear strain

Bingham plastic

a material which flows once stress exceeds yield stress eg: toothpaste

Viscoelastic materials (4 points - properties, constant stress, constant strain, effective stiffness)

• Display both viscous properties; can flow like a fluid and elastic properties like a solid 

• when stress is constant, the strain increases with time; material will flow/stretch 

• when strain is constant, the stress decreases with time (relaxes)

• effective stiffness depends on rate of application of stress

Viscous materials (under stress)

• apply stress, it will strain (stretch)

• continues to stretch till stress is applied.

• stop applying stress, the strain remains

• eg: dashpot/ syringe

elastic materials (under stress)

• apply stress, strain increases in direct proportion

• remove stress, strain decreases

• eg: spring 

relaxation of viscoelastic material

strain held constant, stress diminishes with time

creep in viscoelastic material

stress held constant, strain increases with time

Elastic Materials Harmonic Analysis

• Stress & strain in phase 

• Materials acts as a Hookean Solid, described by Young’s Modulus 

• Lissajous curve - a straight line

Viscous materials Harmonic Analysis

• Stress & strain 90^o out of phase 

• Material acts like a Newtonian Fluid, described by viscosity 

• Lissajous Curve - a circle 

• Highest stress occurs at highest rate of strain 

Viscoelastic material Harmonic Analysis 

• Stress & strain are somewhere between in phase (0^o) and 90^o out of phase

• Materials act as a viscoelastic substance 

• Lissajous Curve is a tilted ellipse 

viscometer

• a device that measures the force required to shear a fluid between a rotating inner cup and a stationary outer wall

• fluids in contact with the wall doesn’t slip

• when a motor makes the inner cup rotate, a shear stress is applied to the fluid across the inner cup surface