Ductile structural components subjected to explosive loadings exhibit a large range of behaviors. The response of beams, walls, and blast doors is estimated using two methods. The engineering level approaches are highly simplified and neglect much of the relevant physics while the use of finite element or shock-code simulation is expensive and not suited to rapid problem solving and parameter studies. In this dissertation, a medium fidelity reduced order modeling approach has been derived to capture the most relevant physics governing rupture of ductile bodies dynamically deforming in tension.
Solution of the inertially stretching jet is used to reveal the deformation arrest mechanics with large plastic strains and high strain-rates. This phenomenon is exemplified by applying a moving boundary technique to a rigid-plastic interface associated with tensile flow-stress release (Mott-Lee wave). A system of differential-algebraic-equations for the axisymmetric jet is formulated for mass, momentum, and energy balances as well as constraints for kinematic compatibility. Dimensional analysis uncovers distinctive dimensionless numbers and the relationship to the plastic velocity increment found in the stability analysis for plastic jet particulation. The closed form solution process reveals underlying mechanics not realized prior. Predictive theoretical rupture conditions, plastic zone size, mass and velocity of the detached particle if rupture occurs, the time for motion to cease as well as the rupture strain are obtained. The numerical solution is in excellent agreement with both shock-code and finite-element simulations. The solution also illustrates the velocity pullback phenomena observed in prior experiments and parametric representation results for the body shape at any instant during deformation.
It is shown that isotropic homogeneous constitutive equations for plastic flow-stress can be included in the governing system of equations for deformation arrest. This is exemplified using the Johnson-Cook viscoplastic relation with the addition of a plastic work to temperature rise equation. The influence of thermal softening, strain-rate stiffening, and work hardening is discussed on the behavior of the inertially stretching jet.
External and coupling loads are applied to the mathematical treatment proposed. Closed form solution is obtained to the application of a tensile step loading on the jet tip. Analysis results in the rectangular-hyperbolic relationship between loading and its impulse on the rupture threshold. The asymptote for minimum impulse at maximum loading is found to be dependent on both the jet slender ratio and kinetic energy density to yield strength ratio. The asymptote for the minimum pressure at maximum loading is found to only depend on the kinetic energy density to yield strength ratio. Drag resistance has been applied to the jet tip with little influence on jet motion unless the density of the surrounding fluid is comparable to the jet material. Coupling the deformation arrest process for linearly stretching ductile material to a single-mode beam undergoing late-time motion with angular deflection has been accomplished. Solution results show complicated features including rupture and full arrest.
Dynamic Plasticity, Plastic Fracture, Continuum Mechanics, Solid Mechanics, Viscoplasticity, Beam Rupture
Level of Degree
First Committee Member (Chair)
Second Committee Member
Third Committee Member
Fourth Committee Member
Sandia National Laboratory
Kullback, Brendan A.. "The Mathematical Theory of Deformation Arrest in Large-Strain Dynamic Plasticity." (2017). https://digitalrepository.unm.edu/me_etds/129