A nonlocal Eulerian-based finite-element approach for strain-softening materials

The dependency of finite element (FE) results on mesh size is a major concern for the numerical analysis of strain -softening materials. The local methods of strain regularization rely on the shear strains of a solitary point. However, the nonlocal methods incorporate strain-softening, including the strain in surrounding soil elements, which show less mesh dependency. Previously, nonlocal methods were mostly implemented in Lagrangian-based FE programs and simulated the response for small to moderate strain levels. However, many geotechnical problems, such as large-scale landslides in sensitive clays, involve extremely large deformation. This study presents the implementation of the original and two modified nonlocal methods in a Eulerian-based large deformation FE program using a relatively simplified approach where simple soil models, such as von-Mises criteria for undrained behaviours, can be used. Two biaxial compression tests are simulated by using the nonlocal Eulerian-based FE program, and the results are compared with a nonlocal Lagrangian-based FE analysis and a nonlocal Material Point Method (MPM) of simulation, respectively. Among the three, the modified nonlocal methods, especially the over-nonlocal method, show a better performance in mesh convergence anal-ysis. Several approaches have been proposed to minimize the computational costs, as nonlocal modelling is generally computationally expensive.

Automated summary

This study implements original and modified nonlocal methods in a Eulerian-based large deformation FE program, using a simplified approach to simulate two biaxial compression tests. The results are compared with nonlocal Lagrangian-based FE analysis and nonlocal Material Point Method (MPM) of simulation. The modified nonlocal methods, especially the over-nonlocal method, show better performance in mesh convergence analysis. Several approaches have been proposed to minimize the computational costs of nonlocal modelling.