In this work, both the concepts of Voyiadjis–Kattan materials and undamageable materials are introduced. The Voyiadjis–Kattan material of order n is defined as a nonlinear elastic material that has a higher-order strain energy form in terms of n. The undamageable material is obtained as the limit of the Voyiadjis–Kattan material of order n as n goes to infinity. The relations of these types of materials to other nonlinear elastic materials from the literature are outlined. Also, comparisons of these types of materials with rubber materials are presented. Finally, a proof is given to show that the value of the damage variable remains zero in an undamageable material throughout the deformation process. It is hoped that these proposed new types of materials will open the way to new areas of research in both damage mechanics and materials science.

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