Models for the Mechanics of Joining Dissimilar Materials - Structural Interfaces and Attachments in Biology - page 50

a

b

Fig. 3.6 ( a ) All linear, isotropic material mismatches can be represented by the two Dundurs
parameters, which range over the shaded region. The lighter regions represent pairs of a and b for
which an elastic singularity occurs at the free edge of the interface of a butt joint (inset) between
the two materials. Tendon and bone lie within the hatched region. ( b ) Most engineering material
pairs congregate in a narrow region of the parameter space, and a few pairs do not result in an
elastic singularity for a butt joint and are non-singular. The figure is anti-symmetric about a ¼ 0,
so data are plotted only for a > 0. ( b ) Is based upon data plotted in [ 23 ]

and the displacement field has the form:

u i ¼ Hr l G i ðy; lÞ (3.14)

where m ¼ {1,2} represents the material number and simple but lengthy expressions
for F ij and G i can be found in [ 20 ]. The free edge intensity factor, H , depends upon y 1
and y 2 and also upon the material properties of the tendon and bone. The parameter