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Thermodynamically Consistent Decoupled Shear-Volumetric Strain Model and CTH Implementation.

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Abstract

Many hydrocodes, such as LS-DYNA and CTH, require the decoupling of the shear from volumetric response in a material model used. A constitutive model is formulated, which decouples the responses of a rate sensitive material. Basis of the model is a general Maxwell-type viscoelastic model, which, however, is not originally decoupled and, thus, not suitable for implementation in the hydrocodes. The formulation provides the thermodynamic consistency for the case of small deviatoric elastic deformations and unrestricted volumetric response. A schematic of implementation in CTH is briefly described. Numerical illustrations demonstrate agreement of the CTH calculations with calculations available in the literature.

Executive Summary

The development of advanced weaponry demands science and industry pay attention to novel energetic materials and materials with enhanced protective properties, including composite materials, porous and multi-phase mitigants, advanced materials manufactured with nanotechnology, etc. The response of these materials needs to be predicted and this raises new challenges for the area of computer modelling of the material response to extreme pressure and temperature. Advanced shock physics codes are a solid basis for modelling efforts. Among them hydrocodes are the most relevant to the level of loads and temperatures because they are able to deal both with the material behaviour in conditions of hydrodynamic flow and with the elastic-plastic deformation at moderate loads when the material strength is important. Hydrodynamic (strength negligible) flows due to extreme loads are typical for materials subject to the hyper-velocity impact by shaped charge jets and for materials in direct contact with detonating energetic materials. The effect of these conditions on enhanced materials requires consideration of multi-phase behaviour with phase transitions, however, such models are yet to be developed. The elastic-plastic (strength relevant) deformations prevail in materials at the load levels typical of high-velocity fragmentation impact or of blast effects from charges in a certain proximity to the target. The elastic-plastic response under these conditions is of the constitutive type, i.e., the materials manifest rate sensitivity and require advanced modelling approaches. In summary, the development and use of advanced models in commercially available hydrocodes is a great challenge. The modelling capability in DSTO is supported by several hydrocodes. The LS-DYNA3D hydrocode (originally a Lagrangian code) has been employed for a number of years in DSTO. It has proved its efficiency for modelling the weapon and terminal effects in problems involving moderate deformations and requiring a good resolution of contact material interfaces. A user-defined material model is relatively simple to incorporate within the DYNA interface though no well-documented implementation procedures are established. A number of material models have been implemented in this code in DSTO exploring the constitutive model capabilities for: i)conventional materials subject to high-velocity fragment impact [1] and materials involved in the shaped charge jet formation, when studying the weapon effects of the two-stage follow-through grenade weapon [2], ii)composite materials subject to ballistic impact for the Army Reconnaissance Helicopter project [3],iii)concretes subject to hyper-velocity impact, when studying the target effects against the multi-stage weapon threats [2, 4], and iv)materials manifesting multi-phase features, when simulating the underwater explosion in a Navy project [5]. However, for the problems such as counter-IED (Improvised Explosive Devices) dealing with large deformations, intensive flows and high multi-phase/multi-material mixing a Eulerian code is more suitable. Therefore, the present work is attempting to gather the implementation experience for the CTH hydrocode developed by Sandia National Laboratories in the US. Implementation procedures for the code are quite well documented. The implementation difficulties are mainly associated with the necessity for the user to intervene in a number of entry points of the code, the number of which and the places of entry depend on the nature of the model to be incorporated. Due to the release features of the code not all necessary points of entry may be easily accessible, this is another challenge for the user. The present work adapts a rate sensitive strength model for conventional materials, which has been published earlier in the literature, to a form decoupling the shear and volumetric responses. The present formulation is in agreement with the CTH implementation requirements and it preserves the thermodynamic consistency of the model. In addition, this formulation suggests a general thermodynamically consistent way of decoupling between the shear and volumetric responses of a material, which might be useful for the development of advanced strength models requiring this decoupling. The model along with its implementation is tested with a number of impact and shaped charge problems. The CTH calculations are compared with numerical solutions and experiments available in the literature and a good agreement is observed. Thus, the present work establishes the model implementation capability in DSTO for the CTH hydrocode.

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