A non-classical continuum approach to study the fragmentation of brittle solids

Abstract

In this thesis, a non-local continuum approach coupled with the phase-field theory and Jones-Wilkins-Lee (JWL) equation of state (EOS) is proposed to model and simulate blast-induced fracture in brittle materials. Also, we study the evolution of field variables in the underground explosion of steel fiber reinforced concrete (SFRC). For numerical implementation, we have used a non-ordinary state-based peridynamic theory coupled with a diffusive phase-field damage approach. Moreover, JWL EOS from the family of isentropes has been formed, and finally, the constitutive relations have been arrived with the help of the JWL EOS. As the conventional equation of motion cannot capture the discontinuities in the damaged portion of the material, derivative-free integro-differential equations of motion have been used in line with the peridynamics approach to overcome the limitation of the conventional equation of motion. The motivation for using non-ordinary state-based (NOSB) peridynamics (PD) over the bond-stretch-based (BSB) or bond-energy-based (BEB) models comes from the fact that the applicability of BSB and BEB models are only limited to materials with Poisson's ratio 1/4. We have introduced a dynamic failure mechanism due to blast-induced stress wave propagation in rock media, generated due to the pressure of a high-velocity gaseous detonator. Furthermore, an expansion of stress wave in the SFRC mass due to the underground explosion of highly pressurized detonators (Iregel 1175U) has been studied in this thesis. A program-burn algorithm inside the JWL EOS has been implemented to model rock fragmentation. A predictor-corrector explicit time integration scheme has been used to update the field variables at every time step. The phase-field damage can capture well the explosive-induced fracture in rock media and damage in the SFRC medium for the underground explosion. The current numerical approach suggests a versatile physics-oriented future model for this class of problems. The formulation proposed in the thesis has been validated against two numerical benchmark tests and has shown good predictive quality.