Materials with no significant frictional strength (cases 4 and 7 in Table 12.1) range from ductile metals to overconsolidated clay.

**Purely Cohesive Materials (**ϕ=0**)**

Materials with no
significant frictional strength (cases 4 and 7 in Table 12.1) range from
ductile metals to overconsolidated clay. They are the elastic, perfectlyplastic
solids (EPS) of classical elasticity and plasticity (at least in compression).

the slip planes are at
45 o to the principal orientation. Equation (12.14c) can be integrated directly
to give the normal stress

where *K* is the constant of integration.

The pair of slip lines
at a point are at right angles. Let us consider the slip surface to have the
counterclockwise angle α from the *x* axis
so that the normal to it (the other slip line) is at the clockwise angle ρ* _{z}*
in Figure 12.7. Then from Mohr’s Circle

While mathematically
trivial, this solution is physically profound. We know it is correct in regions
where τ* _{zx}*
= const and therefore the orientation of the principal stresses do not change.

A general solution can be obtained by assuming

where *a*, *b*, and *c* are
constants.

Thus, for a material with ϕ=0, the failure surface in Cartesian coordinates must be *made up of
straight lines and/or circles* combined in some way to satisfy the stress
boundary conditions.

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Civil : Principles of Solid Mechanics : Slip Line Analysis : Purely Cohesive Materials (ϕ=0) |

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