A continuum consistent discrete particle method for continuum–discontinuum transitions and complex fracture problems

In numerical simulations where complex fracture behavior plays a prominent role in the material’s mechanical behavior, particle methods are an attractive computational tool since they adequately accommodate arbitrary discontinuities. However, existing either limited their constitutive flexibility, like Discrete Element Method (DEM), or prone to instabilities, Smoothed Particle Hydrodynamics (SPH) and Peridynamics. this paper we present alternative formulation, referred as Continuum Bond (CBM). The method has same flexibility conventional continuum Finite (FEM), while still being able incorporate discontinuities DEM, SPH CBM, body is divided into series of material points each point carries fraction body’s mass. A triangulation procedure establishes bonds between particles that interact with other. deformation gradient tensor determined via volume weighted averaging over volumes spanned by pairs nearest neighboring particles. obtained approximation field on allows for straightforward implementation laws. To assess property simulation outcomes elastic nonlinear plastic tensile bar compared FEM results. While stress–strain curves FEM, CBM coincide quite accurately, it found local strains much closer reference solution than ability account demonstrated dynamic simulations. It shown that, without need additional crack tracking routines, can instability phenomena branches. conclusion, suitable maintaining advantageous discontinuous properties methods. • Particle-based directly compatible Suitable integration codes, e.g. LAMMPS. Local response independent cut-off radius penalty correction. Comparable level accuracy state. Crack branching events simulated criteria.