Toward four-dimensional materials: The true nature of undamageable materials and bimodal self-regenerating materials

Abstract

The development of the theories of undamageable materials and bimodal self-regenerating materials leads directly to four-dimensional materials. Both are types of sought after materials. The authors have established that undamageable materials are the limit of Voyiadjis-Kattan materials of order n as n approaches infinity. Similarly, the authors established also that so called bimodal materials are the limit of self-regenerating materials of order n as n approaches infinity. In this work, a solid link is established between these theories that were developed recently and the new four-dimensional materials to come. It is concluded that both undamageable materials and bimodal materials are prime examples of four-dimensional materials. The conclusion is based on sound mathematical and mechanical principles.