On the use of a modified Newton method for nonlinear finite element analysis

In this paper, the usefulness of modified Newton methods for solving certain minimization problems arising in nonlinear finite element analysis is investigated. The application considered is nonlinear elasticity, in particular geometrically nonlinear shells. On a test problem, it is demonstrated that a particular implementation of a modified Newton method using both descent directions and directions of negative curvature is able to identify a minimizer, whereas an unmodified Newton method and modified Newton methods using only descent directions fail to converge to the minimizer. The use of modified Newton methods is suggested as a useful complement to the present continuation methods used for nonlinear finite element analysis.