NEWTON-LIKE METHODS WITH LIMITED STORAGE, FOR THE SOLUTION OF ELASTOVISCOPLASTICITY PROBLEMS

Quasi-Newton and Secant-Newton methods have been successful in solving problems of elasto-plasticity. In this paper these methods are applied to elasto-viscoplastic analyses, in an algorithm coupling the global solution for displacement increments with local Newton-Raphson stress iteration at each sampling point. The familiar rank-two DFP and BFGS methods are generalized to the Broyden family of algorithms, and this generalization is also used to produce a Secant-Newton algorithm corresponding to Hoshino's method. Consideration is given to the most effective strategy when only a limited number of Quasi-Newton iterates may be stored; overwriting, re-start or continuation in Secant-Newton form. Results are presented for a tunnelling problem using both plane strain and axisymmetric formulations.