Modelling the deformation and failure processes occurring in polymer bonded explosives (PBX) and other energetic materials is of great importance for processing methods and lifetime storage purposes. Crystal debonding is undesirable since this can lead to contamination and a reduction in mechanical properties. An insensitive high explosive (PBX-1) was the focus of the study. This binary particulate composite consists of (TATB) filler particles encapsulated in a polymeric binder (KELF800). The particle/matrix interface was characterised with a bi-linear cohesive law, the filler was treated as elastic and the matrix as visco-hyperelastic. Material parameters were determined experimentally for the binder and the cohesive parameters were obtained previously from Williamson et al. (2014) and Gee et al. (2007) for the interface. Once calibrated, the material laws were implemented in a finite element model to allow the macroscopic response of the composite to be simulated. A finite element mesh was generated using a SEM image to identify the filler particles which are represented as a set of 2D polygons. Simulated microstructures were also generated with the same size distribution and volume fraction only with the idealised assumption that the particles are a set of circles in 2D and spheres in 3D. The various model results were compared and a number of other variables were examined for their influence on the global deformation behaviour such as strain rate, cohesive parameters and contrast between filler and matrix modulus. The overwhelming outcome is that the geometry of the particles plays a crucial role in determining the onset of failure and the severity of fracture in relation to whether it is a purely local or global failure. The model was validated against a set of uniaxial tensile tests on PBX-1 and it was found that it predicted the initial modulus and failure stress and strain well.

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We review the concept of stochasticity—i.e., unpredictable or uncontrolled fluctuations in structure, chemistry, or kinetic processes—in materials. We first define six broad classes of stochasticity: equilibrium (thermodynamic) fluctuations; structural/compositional fluctuations; kinetic fluctuations; frustration and degeneracy; imprecision in measurements; and stochasticity in modeling and simulation. In this review, we focus on the first four classes that are inherent to materials phenomena. We next develop a mathematical framework for describing materials stochasticity and then show how it can be broadly applied to these four materials-related stochastic classes. In subsequent sections, we describe structural and compositional fluctuations at small length scales that modify material properties and behavior at larger length scales; systems with engineered fluctuations, concentrating primarily on composite materials; systems in which stochasticity is developed through nucleation and kinetic phenomena; and configurations in which constraints in a given system prevent it from attaining its ground state and cause it to attain several, equally likely (degenerate) states. We next describe how stochasticity in these processes results in variations in physical properties and how these variations are then accentuated by—or amplify—stochasticity in processing and manufacturing procedures. In summary, the origins of materials stochasticity, the degree to which it can be predicted and/or controlled, and the possibility of using stochastic descriptions of materials structure, properties, and processing as a new degree of freedom in materials design are described.

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