Central force networks arise naturally in the study of granular and fibrous materials with implications for the mechanical behavior of hierarchical materials such as nano-composites, cytoskeleton mechanics and tissue engineering. Using simulations based on a damped molecular
dynamics approach, we study the soft and stiff modes of deformation in both Gaussian and Poissonian networks of random linear springs with the goal of understanding the onset of elasticity, and the eventual strain-stiffening in these networks. Although the individual springs are linear, we see that collectively the systems are nonlinear due to the effects of rotation and alignment. We observe a strong dependence of the above quantities on the
coordination number in systems, which effect may be rationalized using some classical arguments going back to the work of Maxwell. Floppy (almost zero energy) modes play a central role in the deformation process, and are responsible for both the softening and stiffening behavior of these networks; in fact strain stiffening is due to the annihilation of these floppy modes. Some implications of these results for the behavior of hierarchical materials will be outlined.