## 6.2. Equation of State Parameters

Figure 6.4: Kevlar/Epoxy IFPT, Influence of Shock Effects. (Experimental Result Courtesy of EMI [1]) compares the results of simulations of inverse flyer plate tests on a Kevlar-epoxy composite material to experiment. The blue velocity trace is recorded in a simulation that used an orthotropic model with a linear equation of state. It is obvious that the initial Hugoniot states are under predicted. However a much improved correspondence with experiment is achieved when using the orthotropic material model a polynomial equation of state.

Figure 6.4: Kevlar/Epoxy IFPT, Influence of Shock Effects. (Experimental Result Courtesy of EMI [1])

Based on the results of Figure 6.4: Kevlar/Epoxy IFPT, Influence of Shock Effects. (Experimental Result Courtesy of EMI [1]) a plot of the derived Hugoniot impact states is given in terms of shock- versus particle-velocity points in Figure 6.5: Shock Velocity versus Particle Velocity Relationship for Kevlar-epoxy Inverse Flyer Plate Tests. (Data courtesy of EMI [1]). Further details of this can be found in [1][2]. Kevlar-epoxy exhibits typical solid behavior with shock velocity approximately increasing linearly with particle velocity.

Figure 6.5: Shock Velocity versus Particle Velocity Relationship for Kevlar-epoxy Inverse Flyer Plate Tests. (Data courtesy of EMI [1])

If the application being modelled requires use of a nonlinear equation of state in conjunction with an orthotropic material model then the gradient and intercept of the line in Figure 6.5: Shock Velocity versus Particle Velocity Relationship for Kevlar-epoxy Inverse Flyer Plate Tests. (Data courtesy of EMI [1]) can be directly input as the S1 and C1 inputs, respectively, for a shock equation of state.

Alternatively, a polynomial equation of state may be used. In this case the A1 term is calculated as the effective bulk modulus. The A2 and A3 terms may then be calibrated by simulation to give best agreement with experiment. This is indeed the approach used to obtain the results of Figure 6.4: Kevlar/Epoxy IFPT, Influence of Shock Effects. (Experimental Result Courtesy of EMI [1]).

Assuming that the 11-direction is defined as being through the thickness of the composite material it is possible to calculate the C11 stiffness matrix coefficient. Since the flyer plate tests are approximately uniaxial in strain the following expression applies,

| (6–14)

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