Matter (v1): an open-source MPM solver for granular matter

Abstract. Simulating the mechanics and flow of granular media requires numerical methods that can handle extreme deformations, along with accurate constitutive models capable of capturing phenomena such as elasticity, shear banding, viscous behavior, compressibility, intergranular attractive forces and rate-dependent friction. In pursuit of this, this article introduces Matter, a Material Point Method (MPM) solver equipped with a range of models to describe dry and cohesive granular media. Rooted in a finite strain elastoplastic framework with a multiplicative decomposition of the deformation gradient, this solver features Drucker-Prager models, overstress models, critical state mechanics models as well as the μ(I)-rheology. This includes the recently proposed “critical state μ(I)-rheology model” for cohesive and compressible flows. Moreover, Matter provides a simple way of dealing with complex terrains and introduces a novel material-induced frictional boundary condition. Implemented in C++ with few required dependencies and parallelized on shared memory, it represents a lightweight yet computationally efficient option for laptops and desktops.