Line search techniques for elasto-plastic finite element computations in geomechanics

In this paper we present a globally convergent modification of Newton's met hod for integrating constitutive equations in elasto-plasticity of geomater ials. Newton's method is known to be q-quadratically convergent when the cu rrent solution approximation is adequate. Unfortunately, it is not unusual to expend significant computational time in order to achieve satisfactory r esults. We will present a technique which can be used when the Newton step is unsatisfactory. This scheme can be considered as a modified version of t he traditional concept of backtracking along the Newton direction if a full Newton step provides unsatisfactory results. The method is also known as l ine search technique. The technique is applied to the fully implicit Newton algorithm for a hardening or softening general isotropic geomaterials at t he constitutive level. Various solution details and visualizations are pres ented, which emerge from the realistic modelling of highly non-linear const itutive behaviour observed in the analysis of cohesionless granular materia ls. Copyright (C) 2001 John Wiley & Sons, Ltd.