Instability of a fiber-reinforced thick slab under axial loading

Equations for small deformations superimposed on a finite deformation of an arbitrary isotropic and compressible, non-linearly elastic solid constrained by inextensible fibers are reviewed. The instability of a thick slab of infinite extent reinforced by strong fibers oriented through its thickness normal to the loading axis is then examined by application of Euler's criterion for dead loading. Solutions are obtained which suggest that special results in the literature on the tension instability of an ideal reinforced Blatz-Ko foamed rubber slab are questionable. It is proved that if the non-linearly elastic matrix material of the ideal reinforced slab satisfies the empirical inequalities and the tension-extension principle, the only mode of instability consistent with plane strain conditions occurs for compression loading, never for tension loading. The class of generalized Blatz-Ko materials that respect these rules is described; the foamed rubber model is not in this class.