32.8 The Application of Kröner’s Method to the Brazilian Test
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32.8 The Application of Kröner’s Method to the Brazilian
Test
In order to demonstrate the algorithm for solving inelastic problems described in
the previous section, we consider the plane deformation of a circular disk, to which
uniform normal pressure q is applied along two equal arcs symmetrically relative to
its center (Fig. 32.15).
32.8.1 Zero Approximation
We will use the solution of the problem of elastic deformation of the indicated disk
given in Sect. 9.6. The functions of Muskhelishvili [13] ) and (ζ ) for this task
are represented by formulas (9.41). They can also be written as
) = −
q
2πi
ln
(σ 2 − ζ )(σ 4 − ζ )
(σ 1 − ζ )(σ 3 − ζ )
− 2iθ 0
,
(ζ ) = −
q
2πiζ
1
σ 4 − ζ
+
1
σ 2 − ζ
−
1
σ 1 − ζ
−
1
σ 3 − ζ
(32.50)
with the appropriate choice of the branch of the logarithm in the first of the
formulas (32.50).
Fig. 32.15 For the inelastic
problem of testing brittle
materials using the Brazilian
method