A nonlinear threshold model applied to spallation analysis

Abstract

Spallation in heterogeneous media is a complex, dynamic process. Generally speaking, the spallation process is relevant to multiple scales and the diversity and coupling of physics at different scales present two fundamental difficulties for spallation modeling and simulation. More importantly, these difficulties can be greatly enhanced by the disordered heterogeneity on multi-scales. In this paper, a driven nonlinear threshold model for damage evolution in heterogeneous materials is presented and a trans-scale formulation of damage evolution is obtained. The damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that some dimensionless numbers govern the whole process of deformation and damage evolution. The effects of heterogeneity in terms of Weibull modulus on damage evolution in spallation process are also investigated.

Failure Process Analysis of Cement under Explosive Loading with a Generalized Driven Nonlinear Threshold Model

“…Similar to [5], in order to establish a closed, complete formulation, Eq. (8) should be associated with traditional, macroscopic equations of continuum, momentum, and energy, constitutive relationship and Eq.(4).…”

“…Where f is the dynamic function of damage (DFD), the agent linking mesoscopic microdamage relaxation and macroscopic damage evolution. Similar to [5], in order to establish a closed, complete formulation, Eq. ( 8) should be associated with traditional, macroscopic equations of continuum, momentum, and energy, constitutive relationship and Eq.…”

“…On the other hand, larger m value represents a homogeneous material in which the stress threshold is almost constant. There are various ways to determine the characteristic relaxation time of damage τ [5] . For simplicity, we may assume that if…”