Numerical simulations of arbitrary evolving cracks in geotechnical structures using the nonlinear augmented finite element method (N-AFEM)

This paper presents an integrated numerical algorithm based on the nonlinear augmented finite element method (N-AFEM) to accurately simulate the arbitrary evolving strong discontinuities (cracks/slip lines) and failure behaviors in geotechnical structures. A novel nonlinear elemental augmentation and condensation scheme was first proposed within the N-AFEM framework, which allows the consideration of nonlinear coupled intra-element cracks without the need of additional nodes or nodal DoFs. Then a modified exponential cohesive zone model (CZM) that considers the coupling effects between tension/compression and shear at the fracture surface was proposed to describe the fracture process of geomaterials. Besides, a nonlinear yielding function based on the Mohr-Coulomb strength theory was introduced into the framework and serves as the fracture initiation criteria for geomaterials. Finally, several benchmark examples were simulated and the predicted results were compared with existing numerical or experimental data to demonstrate the validity of the proposed method.

Automated summary

This paper presents an integrated numerical algorithm based on the nonlinear augmented finite element method (N-AFEM) to accurately simulate the arbitrary evolving strong discontinuities and failure behaviors in geotechnical structures. By introducing novel nonlinear elemental augmentation and condensation scheme, a modified exponential cohesive zone model, and a nonlinear yielding function based on the Mohr-Coulomb strength theory, the method successfully describes the fracture process of geomaterials. Several benchmark examples were simulated to validate the proposed method by comparing predicted results with existing numerical or experimental data.