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Technical report | CTH Implementation of a Two-Phase Material Model With Damage


A material model taking strength and damage accumulation into acccount is implemented in the CTH hydrocode. The model is based on a two-phase approach with the phases representing virgin and fully crushed material states with individual strength and elastic characteristics. Multi-phase description is realised via a homogenisation procedure representing a damaging material as a mixture of the phases, which results in an equation of state, constitutive equations, and conservation laws. The implementation has been used for numerical modelling of high velocity impact against targets made of generic materials representing glass and concrete. The calculations illustrate the dominating effect of the damage mode specified by material.

Executive Summary

Critical materials used in civilian and military applications (high-speed vehicles, warheads, and military protection) are often brittle materials such as structural materials (concretes), glasses, and ceramics. The rate sensitivity of conventional and advanced materials is one of the driving factors in the development of novel constitutive models. At the same time, geological brittle materials are extremely sensitive to the loading modes resulting in dramatically different response to compression, tension, or shear. 

For enhancement of the DST Group modelling capability against impact threats in structural and other brittle materials, an advanced model analysing material damage response to different strain rates and modes of loading has been developed [1] and implemented in a hydrocode. In the present work, this model is reformulated to decouple the bulk and shear response of materials, which is convenient for implementation in the CTH hydrocode. This shock physics modelling code is available in DST Group and has an extended material model database enabling the user to evaluate a number of weapons and protection systems. Numerical examples considered with the present implementation demonstrate that the model is capable of describing both the fracture waves associated with the compression mode of loading in glasses and the damage characterised by frontal scabbing and rear spallation associated with the shear mode of loading in concretes.

[1] A.D. Resnyansky, E.I. Romensky, and N.K. Bourne, Constitutive Modeling of Fracture Waves, J. App. Physics, 2003, 93 (3), pp. 1537-1545.

Key information


Anatoly D. Resnyansky

Publication number


Publication type

Technical report

Publish Date

October 2018


Unclassified - public release


CTH hydrocode, Multi-phase constitutive modelling, Brittle materials, Damage, High-velocity Impact