Discrete and Combined Finite Discrete Element Methods for Computational Mechanics of Discontinua

Continuum mechanics has been one of the major branches of physics where theoretical developments such as theory of elasticity, theory of plasticity, fluid mechanics, and solid mechanics are mostly based on differential equations; these were developed during the second half of the nineteenth century and the first half of the twentieth century. In the second half of the twentieth century computational physics and computational mechanics of continuum were developed to such an extent that now modern science, engineering and technology cannot be imagined without computer simulations. In recent decades, a complementary approach based on discontinuum has been employed and the fields of computational physics of discontinua and computational mechanics of discontinua are mainstream analysis approaches. In this article the state-of-the-art of this modern simulation technology is summarized along with the key computational methods, i.e., molecular dynamics, discrete elements, and the combined finite-discrete element methods.