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

In this paper we present a globally convergent modification of Newton's method for integrating constitutive equations in elasto-plasticity of geomaterials. Newton's method is known to be q-quadratically convergent when the current solution approximation is adequate. Unfortunately, it is not unusual to expend significant computational time in order to achieve satisfactory results. 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 the traditional concept of backtracking along the Newton direction if a full if Newton step provides unsatisfactory results. The method is also known as line search technique. The technique is applied to the fully implicit Newton algorithm for a hardening or softening general isotropic geomaterials at the constitutive level. Various solution details and visualizations are presented, which emerge from the realistic modelling of highly non-linear constitutive behaviour observed in the analysis of cohesionless granular materials.