In contrast to the classical linear theory of elasticity the solution of the initial boundary-value problem of elastic-plastic bodies genuinely depends on the history of loading. Incremental methods take this fact into account, in general, by replacing the highly non-linear problem by a sequence of linear problems. This change of the mathematical model may lead to mispredictions of the behaviour of the considered body like the missing out of bifurcations and drifting of the solution. Moreover, minimum properties of incremental variational principles have only reduced value because the basic assumption of the exact knowledge of the reference state holds exclusively for the natural state.
|Title of host publication||Integral Methods in Science and Engineering|
|Number of pages||5|
|Publication status||Published - 2002|
- boundary value
- linear mathematics
- fluid dyanmics