A semi-implicit integration scheme for a combined viscoelastic-damage model of plastic bonded explosives

Abstract

SUMMARYThis paper presents a new implementation of a constitutive model commonly used to represent plastic bonded explosives in finite element simulations of thermomechanical response. The constitutive model, viscoSCRAM, combines linear viscoelasticity with isotropic damage evolution. The original implementation was focused on short duration transient events; thus, an explicit update scheme was used. For longer duration simulations that employ significantly larger time step sizes, the explicit update scheme is inadequate. This work presents a new semi‐implicit update scheme suitable for simulations using relatively large time steps. The algorithm solves a nonlinear system of equations to ensure that the stress, damaged state, and internal stresses are in agreement with implicit update equations at the end of each increment. The crack growth is advanced in time using a sub‐incremental explicit scheme; thus, the entire implementation is semi‐implicit. The theory is briefly discussed along with previous explicit integration schemes. The new integration algorithm and its implementation into the finite element code, Abaqus, are detailed. Finally, the new and old algorithms are compared via simulations of uniaxial compression and beam bending. The semi‐implicit scheme has been demonstrated to provide higher accuracy for a given allocated computational time for the quasistatic cases considered here. Published 2014. This article is a US Government work and is in the public domain in the USA.

Quasistatic mechanical behavior of HMX- and TATB-based plastic-bonded explosives

“…Some models consider damage as inducing additional strain (SCRAM, VS, VS-VP, VE-VP) while for others (VE-P, E-VP, and VDT-P), damage affects the (visco)elastic stiffness. However, by comparing the final equations of these models (equations 10,13,19,24), it is clear that these two modelling choices are the same. The damage is purely deviatoric in VS and VS-VP while it is also volumetric in VE-P and VE-VP.…”

Using Neutron Diffraction to Investigate Texture Evolution During Consolidation of Deuterated Triaminotrinitrobenzene (d-TATB) Explosive Powder

“…If the initial powder has no texture in the reference state, i.e., M 0 (θ 0 , φ 0 ) = 1, then the maximum of Equation (3) occurs at an orientation n = v which maximizes Equation (2). By inspection, it is clear that this orientation is obtained by solving the eigenvalue problem:…”

“…Macroscale models of the thermomechanical response of PBXs used to simulate material response under such scenarios are often based on phenomenology including viscoelasticity of binder [1], intergranular and transgranular fracture, and viscoplasticity [2]. In order to capture detailed physical processes associated with the deformation of PBX materials, it is becoming widely recognized that new models must connect critical aspects of the material microstructure with an improved understanding of deformation mechanisms at that scale to build up realistic macroscale constitutive models.…”

A finite-deformation constitutive model of particle-binder composites incorporating yield-surface-free plasticity

“…The model was developed to predict the nonlinear stress-strain response of the material, as well as the strain-softening and nonlinearity observed due to extensive cracking at larger deformations. The model has since been extensively implemented in finite element analyses and used to predict the thermo-mechanical behavior of PBX and study hotspot generation (Rangaswamy et al, 2010;Buechler & Luscher, 2014). In the context of PBX undergoing low-frequency vibrational loading, nonlinear viscoelastic models for a mass-material system undergoing base excitation were proposed by Paripovic & Davies (2013.…”