A Matrix‐Free, Scalable, and Robust Implicit Material Point Method

An implicit material point method is presented using a new dynamic relaxation solver, allowing for a simple and efficient quasi‐static formulation that may be readily implemented in existing explicit‐dynamic codes. The use of dynamic relaxation and aggregation is shown to produce an extremely robust material point method scheme, with good convergence characteristics across a range of challenging problems. A new simple fictitious mass matrix formulation based on estimated wave‐speed is derived and presented, allowing for the trivial restructuring of explicit dynamic codes to implicit to solve quasi‐static problems. Finally, a range of large deformation quasi‐static problems, both elastic and elasto‐plastic, are used to demonstrate the convergence characteristics of the method.