Energy absorption of graded foam subjected to blast: A theoretical approach Hongyuan Zhou a , Yonghui Wang b , Xiaojuan Wang b, ⁎, Zhiye Zhao a, ⁎, Guowei Ma c a School of Civil and Environmental Engineering, Nanyang Technological University, 639798, Singapore b Department of Civil and Environmental Engineering, National University of Singapore, 117576, Singapore c School of Civil, Environmental and Mining Engineering, The University of Western Australia, Crawley WA6009, Australia abstract article info Article history: Received 26 January 2015 Received in revised form 5 May 2015 Accepted 18 June 2015 Available online 28 June 2015 Keywords: Energy absorption Blast Cladding Foam Graded foam Density gradient Energy absorption of graded foam subjected to blast is investigated, in which the high velocity crushing of foam is modeled with shock theory and rigid-perfectly-plastic-locking idealization. The characteristics of a typical blast are taken into account when determining the foam density profile. Different from the homogeneous foam, the graded foam density variation is designed largest at the loading end and smallest at the supporting end, with an exponential decay in between. It is found that, subjected to the same blast load, the total input energy, in fact the energy to be dissipated by the cladding, decreases with increasing density gradient. The final foam deformation with larger density gradient is smaller. © 2015 Elsevier Ltd. All rights reserved. 1. Introduction With an increasing number of man-made blast hazards and industri- al accidental explosions, blast mitigation manifests itself as a multi- disciplinary field requiring great attention. The conventional method for structural damage alleviation against blast is strengthening the potentially threatened structural members with higher strength and rigidity. However, if damaged, retrofit of such strengthening is not only labor and cost intensive, but also time-consuming which greatly reduces the resilience of the structure. Cellular materials and structures exist widely in nature, such as certain grass stems and trabecular bones [1,2]. It is the natural selection that balances the weight and mechanical properties, i.e. bending and buckling resistances. These foam-like or honeycomb-like materials and structures are light and sufficiently strong to survive typical external loads from the environment. The merits of cellular material have been realized and this bio-inspired material finds its applications in various fields and industries due to the advantages over its solid counterpart, in aerospace, automobile, nuclear and defense. Specifically, with the exceptional energy absorp- tion capacity, a blast mitigation philosophy of attaching sandwich cladding with cellular solid core to the exterior of protected structure emerged. When subjected to a blast load, the cladding itself absorbs a large amount of energy and lowers down the incident load to the protected structure, by undergoing large plastic deformation (thereafter shortened as “deformation”, referring to plastic deformation unless otherwise stated). After the blast, the damaged/sacrificed cladding can be replaced with a new one to quickly recover its protection capacity, which greatly improves the resilience of the structure. In particular, the cellular solid core (for instance, foams) plays a major role in the cladding and was investigated experimentally, numerically and analytically [e.g. 3–12]. Different crushing modes were observed. To understand the observation, some analytical models were proposed. Amongst, one-dimensional shock theory with rigid-perfectly-plastic- locking (RPPL) idealization effectively delineates the crushing process of low density cellular solid (relative density, defined as the density ratio of the cellular solid to base material, smaller than 0.2) under high velocity dynamic load [13]. Not only single layer cladding, but also double layer cladding subjected to a blast load was investigated [14]. Further, the protection efficiency of a system consisting of a blast mitigation cladding with metal foam core and protected structure sub- jected to a blast load was examined [15,16]. Full scale tests of aluminum foam cladding protected concrete structures subjected to blast were conducted and reported [17,18]. It is worth noting that with metal foam claddings attached to the protected structure under a blast load, the load exerted on the protected structure is not necessarily reduced; in some cases, the stress level on the protected structure is even higher than that in the case without a cladding [19], called negative mitigation effect. Following the observation of the effect, one believed major cause is that subjected to the blast load, the face plate preventing the foam Materials and Design 84 (2015) 351–358 ⁎ Corresponding authors. E-mail addresses: ceewang@nus.edu.sg (X. Wang), czzhao@ntu.edu.sg (Z. Zhao). http://dx.doi.org/10.1016/j.matdes.2015.06.124 0264-1275/© 2015 Elsevier Ltd. All rights reserved. Contents lists available at ScienceDirect Materials and Design journal homepage: www.elsevier.com/locate/jmad