Hierarchical multiscale simulations of crystalline β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX): Generalized interpolation material point method simulations of brittle fracture using an elastodamage model derived from molecular dynamics

Abstract

A predictive constitutive model for single-crystal β-octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (β-HMX) under simple loading conditions was developed using a hierarchical multiscale approach based on molecular dynamics and the generalized interpolation material point method. Basic mechanical behaviors, such as elastic and damage responses to external loading conditions, were predicted at the molecular level using molecular dynamics. The molecular dynamics results were used to construct a preliminary elastodamage model for the generalized interpolation material point (GIMP) simulations. Anisotropy of the β-HMX crystal, which affects the secant elastodamage stiffness tensor in the constitutive model, was taken into account. The GIMP method was used to deal with large deformation and fracture. GIMP results predicted using the hierarchically obtained elastodamage model are shown to be in close agreement with the molecular dynamics predictions. Although the evolution of local damage surfaces from GIMP is not as detailed as that from molecular dynamics, the main features of nonlinear elastodamage in the stress–strain relationship are captured by GIMP at reduced computational expense. Thus, this preliminary hierarchical multiscale procedure can be considered as useful for simulations of elastodamage behaviors in brittle materials for engineering purposes.