Numerical models and homogenization to study the sensitivity of energetic materials: effect of damage and microstructure

Shock sensitivity is often studied in order to improve the safety of energetic materials (i.e., explosives). Numerous studies have shown that the former is sensitive to microstructural characteristics. However, the exact mechanisms responsible for the interplay between mechanical damage, microstructure heterogeneities (grains shape, intra or extra-granular effects) during initiation have not been fully understood.

The French-German research institute “Institut Saint-Louis” (ISL) and the French Atomic Energy Commission  CEA-Gramat have started a collaboration on this topic in 2015, followed by MINES ParisTech in 2017, through Élodie Kaeshammer’s PhD. Formulations of “RDX” and wax have been produced and experimentally characterized at ISL whereas CEA has conducted microtomography analysis. Experimental studies carried out at ISL have shown that shock sensitivity is reduced when the density of intra-granular defects decreases, and that morphology is an important parameter. This underlines the effect of the mechanical behavior in these explosives. The Centre for Mathematical Morphology (CMM) of MINES ParisTech develops numerical models of random structures representative of complex microstructures and homogenization tools that are used to predict the mechanical response of heterogeneous media.

The segmentation of 3D microtomography images with various morphologies has been carried out by Élodie Kaeshammer (see image 1). Fourier-based methods are being used to compute the full-field thermoelastic response of the materials (see image 2). Shock propagation in 3D virtual structures will be computed using the Eulerian solver Ouranos from CEA (see image 3).

Among É. Kaeshammer’s PhD goals  are the understanding of the evolution of damage in microstructures, the transition between shock and detonation, and the identification of the relevant morphological parameters for a given solicitation. Currently, emphasis is being put on the numerical aspects. In a following step, material tests will be carried out on energetic samples with varying microstructures, to study the connection between dynamical loadings and local damage. Also, numerical tools are being developed at the mesoscopic scale to study damage, using virtual and image-segmented microstructures.

Reference: É. Kaeshammer, B. Erzar, S. Belon, F. Willot, P. Dokladal, J. Corbel, L. Borne (2018). Étude expérimentale et numérique de la sensibilité de compositions énergétiques: influence de la microstructure et rôle de l’endommagement, Colloque National Mécamat, Aussois,

If you are interested in further information, contact François Willot (, Benjamin Erzar (, Steve Belon (, Lionel Borne (, Petr Dokladal (


Figure 3

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