A one-dimensional model for designing functionally graded materials to manage stress waves

The development of Functionally Graded Materials (FGMs) for energy-absorbing applications requires understanding of stress wave propagation in these structures in order to optimize their resistance to failure. A simple, one-dimensional model is proposed to develop insight into stress wave management issues. This model is initially applied to FGMs with discrete layering, then extended to continuously graded architectures. From this model, it is determined that the peak stress of waves re¯ected from the FGM interface is slightly greater than for materials with sharp interfaces. The bene®t of the FGM over the sharp interface is to introduce a time delay to the re¯ected wave propagation when stresses approach peak levels. This time delay is highly dependent on the composition gradient and the di€erences in base material properties, consequently the optimal choice of FGM architecture will depend signi®cantly on the critical design conditions for speci®c applications. Time-history pro®les of re¯ected stress waves are presented for two speci®c cases of interest in armor applications: (1) porous FGMs, and (2) Alumina±Aluminum FGMs