Use of quasi-Newton methods for large strain elastic-plastic finite element computations

In this paper, quasi-Newton methods are used to solve large strain elastic-plastic problems. The governing nonlinear equations are derived from the principle of virtual work written in an updated Lagrangian manner. The constitutive equations result directly from the definition of free energy and plastic potential that involve a convex functional form. A mixed algorithm is proposed that combines the Newton-Raphson method and modified Newton-;Raphson method with symmetric quasi-Newton update. The efficiency of the algorithm, measured in terms of rate of convergence and computation time is studied on numerical tests. The procedure has a very wide field of application in nonlinear elastic-plastic analysis.