TABLE OF CONTENTS The finite element discretization technique in plasticity problems follows precisely the same procedures as those of corresponding elasticity problems. Any of the elements already discussed can be used for problems in plane stress; however, for plane strain, axisymmetry, and three-dimensional problems it is usually necessary to use elements which perform well in constrained situations such as encountered for near incompressibility. For this latter class of problems use of mixed elements is generally recommended, although elements and constitutive forms that permit use of reduced integration may also be used.
The use of mixed elements is especially important in metal plasticity as the Hubervon Mises flow rule does not permit any volume changes. As the extent of plasticity spreads at the collapse load the deformation becomes nearly incompressible, and with conventional (fully integrated) displacement elements the system locks and a true collapse load cannot be obtained.71 ,72
Finally, we should remark that the possibility of solving plastic problems is not limited to a displacement and mixed formulation alone. Equilibrium fields form a suitable vehicle,73 ,75 but owing to their convenient and easy interpretation displacement and mixed forms are most commonly used.
Figure 4.11 shows the configuration and the division into simple triangular and quadrilateral elements. In this example plane stress conditions are assumed and solution is obtained for both ideal plasticity and strain hardening. This problem was studied experimentally by Theocaris and Marketos76 and was...
