TABLE OF CONTENTS In the preceding sections the general processes of dealing with complex, non-linear constitutive relations have been examined and some particular applications were discussed. Clearly, the subject is large and of great practical importance; however, presentation in a single chapter is not practical or possible. For different materials alternate forms of constitutive relations can be proposed and experimentally verified. Once such constitutive relations are available the processes of this chapter serve as a guide for constructing effective numerical solution strategies. Indeed, it is possible to build standard computing systems applicable to a wide variety of material properties in which new specifications of behaviour may be inserted.
What must be restated is that, in non-linear problems:
non-uniqueness of solution may arise;
convergence can never be, a priori, guaranteed;
the cost of solution is invariably much greater than it is in linear solutions.
Here, of course, the item of most serious concern is the first one, that is, that of non-uniqueness, which could lead to a physically irrelevant solution even if numerical convergence occurred and possibly large computational expense was incurred. Such non-uniqueness may be due to several reasons in elasto-plastic computations:
the existence of corners in the yield (or potential) surfaces at which the gradients are not uniquely defined;
the use of a non-associated formulation20 ,116 ,117 (to which we have already referred in Sec. 4.9.4);
the development of strain softening and localization.118 ,119
The first problem is the least...
