EXISTENCE AND UNIQUENESS OF SOLUTIONS IN NONASSOCIATED MOHR-COULOMB ELASTOPLASTICITY

In 1902 Jacques Hadamard [1] formulated three conditions that mathematical models of physical phenomena should satisfy, namely that: (a) A solution exists (b) The solution is unique (c) The solution depends continuously on the problem data Problems involving models that satisfy all of these conditions are termed well-posed. Otherwise, if one or more conditions are violated, the problem is said to be ill-posed. The meaning of condition (a) is quite clear. Conditions (b) and (c) are often intimately linked and can for many practical purposes be coalesced into a single condition. In finite element analysis “non-unique ” solutions are often generated by altering the problem data slightly, for example through introduction of random imperfections. It is relatively well known (though not always appreciated to its full extent) that standard elastoplastic constitutive models may violate conditions (b) and (c) if the flow rule is not associated. Indeed, since the pioneering work of Rice [2], the ensuing ill