Biomedical Engineering Reference
In-Depth Information
Fig. 3.5 Idealized stress-
strain response of different
materials
3.2.2.1 Stress-Strain Behaviour
In Fig.
3.5
, idealized stress-strain curves of some important materials are quali-
tatively (not to scale) depicted, where arrows represent loading and unloading path
directions. Numbering corresponds to the curve numbers in Fig.
3.5
.
1. Rigid Material. Materials show practically no deformation under arbitrary
loading. This assumption is extremely idealized and is valid only for mate-
rials that exhibit negligible small deformation. The loading and unloading
path corresponds to a vertical line.
• Elastic material behaviour is characterized by identical loading and unloading
paths. The loaded component recovers its original configuration. This process is
reversible and such materials are said to have no memory. The following cases
can be distinguished:
2. Linear-Elastic Materials. The stress-strain response is linear up to the
proportionality limit (i.e. up to point A which, strictly speaking, is situated
below the point of yield) where the strains are assumed to be very small (but
finite). Such materials are also termed strictly linear.
3. Non-Linear Elastic Materials. The stress-strain response is non-linear and
strain may become very large. Such material behaviour can be observed in
biological structures (e.g. human soft tissue, etc.) and in elastomeric mate-
rials (e.g. rubber, foam). In addition, such materials most often exhibit
hysteresis. When hysteresis effects are eliminated (split of elastic and
inelastic properties), the elastic parts (equilibrium elasticity) correspond with
• Plastic material behaviour is characterized such that after reaching a stress
limit (yield stress r
y
), the loading and unloading paths no longer coincide, and
after unloading an existing strain e
p
remains. Such processes are not reversible,
and these materials are said to exhibit a permanent memory. The following cases
can be distinguished:
