Physical Chemistry of Foods

where thePoisson ratiomis given by

m¼

1

2

ð 1 

dlnv

de

Þð 17 : 2 Þ

The second term between parentheses is a measure of the change in volumev
upon application of a tensile stress on the material. The relative volume
change is quite small for most solid foods, implying that the Poisson ratio is
close to 0.5, leading toEu¼ 3 G, etc. Foods of a spongy nature, like bread
crumb, may havemclose to zero.
It should further be understood that the deformation will often be of
an intermediate type, although elongational components tend to be
dominant. Pure biaxial elongation occurs around a gas bubble that expands
in a semisolid food. Also the flow of material between two approaching
particles is largely biaxial elongation. For undefined flow types, we will use
Efor modulus andefor strain.
Prediction of the magnitude of the modulusfrom the properties of the
structural elements, and the geometry of the network that they form, is
desirable but quite difficult to achieve. Consider a simple system, consisting
of a network of identical structural elements. An external forceFexis applied
in thexdirection, leading to deformation. The cross section of the specimen
perpendicular to the direction of force equalsA. The deformation causes a
reaction force, and the condition of force balance leads to

Fex¼
AN

dFin

dh

Dx ð 17 : 3 Þ

whereNis the number of connections between structural elements per unit

FIGURE17.1 Various modes of deformation. Cross sections through test pieces;
—?—?—indicates an axis of revolution. Arrows indicate forces. In (d) the broken
line depicts a compressed test piece.