Core (filler) materials are key components of the sandwich panel and box-beams that are used in the design of lightweight structures. They perform a variety of elastic-range functions such as transferring and supporting working stresses and energy and collapse management. There is an increasing demand, however, for post-yield performance characteristics such as buckling control, impact toughness, and maintenance of component strength after damage. Low density is also an important consideration, as overall component mass is critical in most applications. These cellular solids need to perform well under normal working stress conditions, yet still resist damage from simple and unavoidable low velocity impacts. A new design approach is suggested by biological systems that have evolved for toughness and damage tolerance (bones, trees, plants, corals, etc.). These systems share the relatively low density cellular arrangements of common synthetic core materials, but also exhibit variable density gradients within the core. (Figures 1 and 2) This paper describes engineering design methods that are inspired by such biology. The result is that a design's failure modes can be more effectively “designed-in”, controlling locations and amounts of failure.