Spheropolygons: A new method to simulate conservative and dissipative interactions between 2D complex-shaped rigid bodies

I present a method to simulate complex-shaped interacting bodies, a problem which appears in many areas, including molecular dynamics, material science, virtual reality, geo- and astrophysics. The particle shape is represented by the classical concept of a Minkowski sum, which permits the representation of complex shapes without the need to define the object as a composite of spherical or convex particles. A well-defined conservative and frictional interaction between these bodies is derived. The model (particles+interactions) is much more efficient, accurate and easier to implement than other models. Simulations with conservative interactions comply with the statistical mechanical principles for conservative systems. Simulations with frictional forces show that particle shape strongly affects the jamming phenomena in granular flow.