Test Results and Discussions

A total of 83 tests were performed from different wave source locations. Because the data acquisition system was limited to 16 channels, several unload-reload cycles were required for each load condition. Unfortunately this load cycling resulted in excessive deformation of the test specimen. Although some accelerometer response was lost due to excessive deformation, useful data were obtained for the first three load cases. The in-plane Young's modulus ( $E_{11}=E_{22}=E$) and the out-of-plane Young's modulus ($E_{33}=E'$) were calculated from Eq. (5) and Eq. (6). The in-plane Poisson's ratio ( $\nu_{12}=\nu_{21}$) was calculated from the in-plane shear modulus Eq.( 7) and in-plane Young's modulus as,

$$\nu_{12}=\frac{E_{11}}{2G_{12}}-1$$ (19)

The out-of-plane Poisson's ratios ($\nu_{31}$ and $\nu_{13}$) were calculated from the in-plane Young's modulus ($E_{11}$), out-of-plane Young's modulus ($E_{33}$), and out-of-plane shear moduli, $G'' = G_{13}$ (Eq. 9) and $G' = G_{31}$ (Eq. 8) as

$$\nu_{31}=\frac{E_{33}}{2G_{31}}-1 \;\;\;\;\;\; \;\;\;\;\;\; \nu_{13}=\frac{E_{11}}{2G_{13}}-1$$ (20)

To describe the behavior of a cross-anisotropic material, five independent elastic constants are required. All other constants can be defined from these five independent constants. In this study the redundant constants are calculated either for use in the elastic-plastic material model Eq. (22) or to cross-check with published data [4]. The test results are tabulated in Table 3.

Table 3: Elastic Constants

load	$\sigma_v$	$\sigma_h$	$G_{31}$	$G_{13}$	$E_{33}$	$E_{11,22}$	$E_{11}/E_{33}$	$\nu_{12}$	$\nu_{13}$	$\nu_{31}$
1	23.9	11.3	1500	1820	3330	5000	1.5	0.11	0.37	0.11
2	47.9	13.4	2550	5320	3825	9000	2.35	0.22	-0.15	-0.25
3	65.8	18.4	4890	19440	3835	13000	3.39	0.33	-0.67	-0.6

The current testing program shows that the computed $G_{31}$ is equal to the computed $G_{32}$, as would be expected for a cross-anisotropic material. The testing also shows that $E_{11}$ was greater than $E_{33}$, and that the ratio appears to increase with increased loading. Thus the data appears to confirm the cross-anisotropic assumption proposed for the layered tire shred model. Indeed, the results indicate a stress-induced anisotropy, i.e., the anisotropy increases with increased stress. It is also noted that the measured negative Poisson's ratio, while physically possible, may be open for discussion. This will be investigated in the next set of tests that are forthcoming in early 2004. It is suspected that the increase of confinement from the stretched latex membrane may have added some error to calculating Poisson's ratios.