Efficiency of high-order elements in large-deformation problems of geomechanics

This paper investigates the application of high-order elements within the framework of the arbitrary Lagrangian-Eulerian method for the analysis of elastoplastic problems involving large deformations. The governing equations of the method as well as its important aspects such as the nodal stress recovery and the remapping of state variables are discussed. The efficiency and accuracy of 6-, 10-, 15-, and 21-noded triangular elements are compared for the analysis of two geotechnical engineering problems, namely, the behavior of an undrained layer of soil under a strip footing subjected to large deformations and the soil behavior in a biaxial test. The use of high-order elements is shown to increase the accuracy of the numerical results and to significantly decrease the computational time required to achieve a specific level of accuracy. For problems considered in this study, the 21-noded elements outperform other triangular elements.