A New Contact Algorithm for the Total-Lagrangian Material Point Method

The Total Lagrangian Material Point Method (TLMPM) is a relatively new variant of the now popular MPM, a method to solve partial differential equations appearing in solid and fluid mechanics problems. In TLMPM, each solid has its own grid, and all calculations are carried out in a configuration of reference, often the original configuration. Because of this, TLMPM is free of numerical fracture, cell crossing instability and is efficient. An unfortunate result of having individual grids is that TLMPM does not have a built-in contact algorithm. Recently, a contact algorithm based on particle-to-particle contact was published for TLMPM. However, it scales quadratically with the number of particles and is therefore slow for a large number of particles. This paper introduces a new contact algorithm for TLMPM using a flexible contact grid. The advantages of this algorithm are: (1) all the advantages of TLMPM are kept, such as the absence of numerical fracture and good convergence rates; (2) the core principle of using a background grid in the material point method for contacts is preserved; (3) different basis functions can be used for each grid, and (4) boundary conditions can be enforced with more flexibility. The performance of the new algorithm is demonstrated through several two and three-dimensional numerical examples exhibiting large elastic and plastic deformation.