TRACING THE EQUILIBRIUM PATH BY DYNAMIC RELAXATION IN MATERIALLY NONLINEAR PROBLEMS

Material non-linearity in non-associated high friction materials exhib iting post-peak softening such as granular materials poses a great pro blem in solving the non-linear differential equations. In this regard, a dynamic relaxation (DR) family of solutions provides a very strong tool to solve. In this paper, the DR method is evaluated from the view point of its ability to trace the whole equilibrium curve in the load- displacement (stress-strain) space. In the case of material non-linear ity, usually there is a snap-through. This problem has been handled in three ways: (1) load control with a real time dynamic solution at pos t-peak, (2) direct displacement control and (3) are-length control. Th ese three methods of non-linear equilibrium path tracing are criticall y evaluated with respect to their speed of convergence, accuracy of th e solution and states of unequilibrium. Finally, the results of multi- element FEM simulations of a bearing capacity test of a strip footing on sand carried out to validate the DR methods are presented.