Technical report | CTH Implementation of a Two-Phase Material Model With Strength: Application to Porous Materials

Abstract 

A material model accounting for strength developed earlier for two-phase materials is implemented in the CTH hydrocode. The strain response to load in the model is decoupled into shear and volumetric contributions in order to satisfy the model implementation requirements for CTH. Multi-phase description is realised via constitutive equations complementing the conservation laws for a material represented as a mixture of several phases. Such a formulation agrees well with the CTH code structure and is suitable for conventional user implementation. The implementation has been applied to a generic material representing sand at various porosities. The constitutive equations and equations of state have been fitted in order to describe literature data. Numerical illustrations in the report demonstrate agreement of the calculation results with the anomalous behaviour observed in the literature for a highly porous sand at shock compression and a good description of the experiments available in the literature on the explosion of a sand-buried charge.

Executive Summary

Involvement of the Australian Defence Forces (ADF) in various operational theatres requires improvement of protective capability against buried mines and Improvised Explosive Devices (IEDs). The threat to a target (e.g., a vehicle) due to a detonating buried device is twofold: i) the structural threat due to mainly gaseous detonation products that are loading the target quite slowly in the millisecond range of time and over a wide area of the target; and ii) the impact threat due to the soil ejecta colliding with the target and transferring momentum to the target rather quickly within the microsecond range of time and localised over a compact area of the target. The impact threat is the most immediate and important one before the structural effects take place.

To develop a protection capability against this impact threat, an enhanced assessment of the response of porous geological materials blanketing a detonating device and transferring momentum to the target via the ejecta impact needs to be undertaken. Such an assessment can be performed with the physics modelling tools, hydrocodes, such as LS-DYNA and CTH available in DSTO. However, even with the use of these powerful modelling techniques, behaviour of the porous geological materials, commonly sand or soil, is not easy to describe in the conditions of shock loading. Complexity in the behaviour of porous materials, demonstrated for example in [1], is manifested by highly non-linear response of those materials due to their multi-phase structure with drastically different compressibilities of constituents. In turn, the solid constituents of these porous mixtures are strength resistant and strain rate sensitive. This behaviour, specifically evaluation of the parameters responsible for the momentum transfer, is not well predicted within the traditional approaches using established material models available in the hydrocodes.

In order to improve the hydrocode modelling capability, the present report describes an implementation of an advanced two-phase material model [2] that takes into account the multi-phase nature of the geological materials (sand, soil, etc). Along with the air contained in the pores, the condensed constituents of the materials are also compressible at this level of loads. In addition, the solid constituents are strength and strain rate sensitive. In the present report, the two-phase model [2] is implemented in the CTH hydrocode [3] and the implementation flowchart is briefly outlined. Sand is considered as a model material in the test calculations. Mechanical characteristics of the material are fitted in order to correlate with available literature data for the constituents, namely, the air and quartz. The numerical illustrations demonstrate a good description of physical features that are typical for the porous materials at shock compression and are difficult to describe with material models available in the hydrocode. The first numerical example demonstrates the anomalous behaviour observed in experiments for highly porous sand, but this behaviour is not customarily predicted by available material models within the physics-modelling framework of the hydrocode. The second example illustrates formation of the soil ejecta due to explosion of a buried charge. Comparison of the numerical results with available literature experiments shows good agreement. The illustrations demonstrate the importance of the physics modelling for the description of parameters responsible for the momentum transfer from the soil ejecta to a target.

The present model development and CTH implementation activity is also performed as a part of the joint efforts within the Modelling and Simulation Focus Area of the Conventional Weapons Technology Group (Terminal Effects) of The Technical Cooperation Program (TTCP).