6.5 Residual Stress
273
1997). Experimentally, these investigators found that residual stress evolves in
response to changes in blood pressure and suggested that these changes are caused
by differential growth (Fung and Liu 1989; Liu and Fung 1989; Fung 1991; Fung
and Liu 1991).
These studies show that the generation of residual stress is a dynamic process that
may play multiple roles. Its biological effects likely depend on the specific function
of a tissue or organ.
6.5.2 Determining Residual Stress in Soft Tissues
In general, experimentally determining stress in soft tissues is a formidable task,
regardless of whether the stress is caused by external loads or internal loads
generated by growth and contraction. To measure stress directly, investigators have
developed microscopic transducers that measure forces in individual structural
proteins (Sugimura et al. 2016), but it is not always clear how to convert these
measurements into a stress tensor at the tissue level.
Indirect stress estimates provide a useful alternative. One way to determine
residual stress in both man-made and biological materials is to physically cut the
material and measure the resulting deformation caused by relieving the stress.
Strains caused by the cut can be estimated from measured changes in tissue
geometry or displacements of tissue markers, e.g., beads or stained cell nuclei. Then,
if the material properties are known, this information can be used to compute the
stress relieved by the cut. If the cut eliminates all stress, which is not always easy
to know (see below), the computed stress represents the full extent of the residual
stress in the intact tissue.
Cutting has been and remains a popular method used to probe residual stress in
soft tissues. Various types of mechanical dissection have been employed at the tissue
level (Nelson 2013), while laser ablation is a popular method used at the cell and
subcellular levels (Sugimura et al. 2016). A judicious choice of cutting method can
make the job of determining residual stress easier.
For illustration, suppose we are presented with the tri-layered bar of Example 6.4.
We observe that the ends of the bar bulge outward (see Fig. 6.4d), suggesting that
either the middle layer has grown longer or the outer layers have shortened by
atrophy or contraction. On the other hand, it is also possible that the bar was just
created with this shape. If we cut the bar in half, we would see that the new ends
also bulge outward, indicating the intact bar contained residual stress, but additional
experiments would be needed to determine the biological process that created this
stress. 4
4 In some cases, the effects of growth and contraction can be separated using biochemical inhibitors
of cell proliferation and actomyosin activity, respectively. However, drugs generally affect more
than one process. For example, inhibiting contraction also can inhibit cell division, which generally
273
1997). Experimentally, these investigators found that residual stress evolves in
response to changes in blood pressure and suggested that these changes are caused
by differential growth (Fung and Liu 1989; Liu and Fung 1989; Fung 1991; Fung
and Liu 1991).
These studies show that the generation of residual stress is a dynamic process that
may play multiple roles. Its biological effects likely depend on the specific function
of a tissue or organ.
6.5.2 Determining Residual Stress in Soft Tissues
In general, experimentally determining stress in soft tissues is a formidable task,
regardless of whether the stress is caused by external loads or internal loads
generated by growth and contraction. To measure stress directly, investigators have
developed microscopic transducers that measure forces in individual structural
proteins (Sugimura et al. 2016), but it is not always clear how to convert these
measurements into a stress tensor at the tissue level.
Indirect stress estimates provide a useful alternative. One way to determine
residual stress in both man-made and biological materials is to physically cut the
material and measure the resulting deformation caused by relieving the stress.
Strains caused by the cut can be estimated from measured changes in tissue
geometry or displacements of tissue markers, e.g., beads or stained cell nuclei. Then,
if the material properties are known, this information can be used to compute the
stress relieved by the cut. If the cut eliminates all stress, which is not always easy
to know (see below), the computed stress represents the full extent of the residual
stress in the intact tissue.
Cutting has been and remains a popular method used to probe residual stress in
soft tissues. Various types of mechanical dissection have been employed at the tissue
level (Nelson 2013), while laser ablation is a popular method used at the cell and
subcellular levels (Sugimura et al. 2016). A judicious choice of cutting method can
make the job of determining residual stress easier.
For illustration, suppose we are presented with the tri-layered bar of Example 6.4.
We observe that the ends of the bar bulge outward (see Fig. 6.4d), suggesting that
either the middle layer has grown longer or the outer layers have shortened by
atrophy or contraction. On the other hand, it is also possible that the bar was just
created with this shape. If we cut the bar in half, we would see that the new ends
also bulge outward, indicating the intact bar contained residual stress, but additional
experiments would be needed to determine the biological process that created this
stress. 4
4 In some cases, the effects of growth and contraction can be separated using biochemical inhibitors
of cell proliferation and actomyosin activity, respectively. However, drugs generally affect more
than one process. For example, inhibiting contraction also can inhibit cell division, which generally