Four-dimensional lattice spring method using a level set approach for contact problems in geomechanics

Abstract

Lattice Spring Methods (LSM) have gained increasing attention in recent years due to their effectiveness in handling fracturing and nonlinear problems. However, their ability to address general contact issues in geomechanics remains limited. Directly handling contact using discrete geometry often results in local locking, a common challenge in particle-based methods like DEM and LSM. This work introduces a level set approach to overcome this limitation. Block and granular geometries are represented by a level set function, which is also employed to manage contact interactions between blocks and granules. A specialized contact algorithm is developed for the lattice model using a signed distance function (SDF) that accounts for lattice discretization. The new LS-4D-LSM demonstrates its capability to solve complex contact problems through various numerical examples, including both deformation and fracturing of blocks. Given that contact plays a key role in many geomechanics tests, incorporating realistic contact behavior into these analyses leads to a more accurate fit with experimentally observed data. This suggests that the digital twin concept could be a powerful tool for analyzing experimental data in geomechanics. The proposed method is also applicable to other numerical approaches, such as DEM, enhancing their ability to handle deformable and fragmentable blocks or granules.