The relation between stress and strain is in principle as given in frame (d). It
shows a sharp buckling point, beyond which the apparent modulus is greatly
decreased. For most practical, i.e., far less regular, systems the transition
will be more gradual. It is also seen that the stress starts to increase strongly
at high strain values. Compression then causesdensification, i.e., an increase
of the relative density of the system, and eventually the rheological
properties become equal to those of the matrix material.
If the matrix consists of aplasticmaterial, implying that it has a yield
stress, yielding will occur, e.g., as illustrated in Figure 17.29c and e. Some
stress overshoot then is common. After yielding, the stress does not greatly
increase until appreciable densification occurs. Also for a yielding material,
the overall yield stress will not be so sharply defined for a less even cellular
structure. What often happens is that a layer of one or a few cells in
thickness suddenly yields, to be followed by other layers at a higher overall
strain: the layer mostly is about perpendicular to the direction of the stress.
Such phenomena also occur when a shear stress is applied, but then the
orientation of the layer tends to be at 45 degrees to the direction of shear.
If the matrix material isbrittle, large deformation will lead to fracture,
but then we are outside the realm of soft solids.
The variablesaffecting the results discussed so far are j, open or
closed cells, and rheological properties of the matrix material. Other aspects
are
Theproperties of the materialare often unknown, because the material
may strongly change during formation or growth of the cellular
structure. The walls and beams may well be markedly anisotropic.
Thegeometry of the matrixcan vary considerably. This concerns cell
size and especially shape; the distribution of matrix material over
beams and walls; and the overall structure. The latter often is
uneven: it may vary from place to place (e.g., from the outside to the
inside of a specimen), it may be anisotropic, and it may have weak
spots or regions.
At large strains, themode of deformation, such as uniaxial compres-
sion, uniaxial extension, shear, or bending, may considerably affect
the shape of the stress–strain curve.All of these variables affect the mechanical properties of the system, but few
general rules can be given.
Bread and Comparable Baked Products. These are made by
baking a leavened dough. The high temperature causes considerable
expansion of the gas cells and (after some time) rupture of the lamellae
between cells. Upon cooling, a soft solid sponge is obtained.