2.8 Material Properties determine if a tissue is good at absorbing strain energy without breaking or storing and releasing lots of elastic strain energy
Figure 2.12: Illustration of material properties. Strength is the maximum stress without failure. Deformability is the maximum strain without failure. Stiffness is the elastic modulus and is the slope of the curve. Toughness is the area in red. The input (absorbed) strain energy density is the hatched area. The output (released) strain energy density is the dotted area. The hatched area without dots is the amount of heat produced when the elastic material returns to its starting length. Resilience is the ratio of output to input strain energy density.
These material properties are
- Stiffness, aka the Modulus of Elasticity, the Elastic Modulus, or Young’s Modulus, is the slope of the stress strain curve, which is \(E = \frac{\sigma}{\epsilon}\) for a material with a linear curve. \(E\) is a measure of the resistance to deformation. I usually just refer to this measure as the material’s . The more force it takes to deform a material a certain amount, the higher the elastic modulus. Or from the view of the material, the elastic modulus is high if only a small strain creates a high stress. A material with a high elastic modulus is stiff. The opposite, a material with a low elastic modulus, is compliant. Compliant materials are easily stretched or squished.
- Strength, or breaking strength, or tensile strength (if in tension), is the maximum stress that a material can resist without , or breaking. A strong material can withstand high stress before failure. The opposite is weak.
- Deformability is the strain of the material at failure. If the material is in tension, this is extensability. All highly deformable materials are compliant but not all compliant materials are highly deformable.
- Toughness, T, is the strain energy density at failure. Materials that can absorb lots of strain energy are tough. The opposite is brittle. Stiff materials tend to be brittle. More compliant (but not too compliant!) materials tend to be tough. Bones used for support (and the wood of tree trunks) must be tough in addition to being strong.
- Resilience, R, is the percent of the total absorbed strain energy that can be used to do work and so is the ratio of the released strain energy (\(U_{out}\), the area under the unloading curve) to the total absorbed strain energy (\(U_{in}\), the area under the loading curve). This ratio is always less than one (otherwise a ball made of a material with a resilience of one could bounce forever!). The ability of a tissue to store-and-release elastic strain energy is a function of both resilience and compliance. Collagen and elastin are both very resilient but collagen is also much stiffer than elastin.