A Mixture Theory Approach for the Shock Response of Composite Materials

A fiber-reinforced composite material is composed of a fiber embedded within a matrix or binder material. The shock response of these two materials is, in gen eral, quite different; typically, the matrix material is considerably more compliant than the fiber. Therefore, the passage and unloading from a shock will result in different thermo dynamic states for the two materials. Mixture theory provides the basis for the develop ment of a methodology to treat the individual thermodynamic responses of a composite material within the context of a macroscopic continuum computer code. The equations for the mixture theory are presented and then applied to a finite-difference representation. The treatments of equations of state, distortional (plastic work) energy, and viscous dissipation (artificial viscosity) are explicitly discussed. The paper concludes with some examples of shocking and unloading, both for isothermal and adiabatic mixing between the two con stituents, of an epoxy and glass composite material.