3D finite element simulation of sandwich panels with a functionally graded core subjected to low velocity impact E. Etemadi, A. Afaghi Khatibi * , M. Takaffoli Faculty of Mechanical Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran article info Article history: Available online 25 June 2008 Keywords: Functionally graded materials Sandwich materials Low velocity impact Contact Finite element Indentation abstract Three-dimensional finite element simulations were conducted for analyzing low velocity impact behav- ior of sandwich beams with a functionally graded (FG) core. After validating the finite element model using available analytical data, the effects of projectile initial velocity and kinetic energy, as well as the beam’s dimensions on the impact behavior and indentation and displacement history were studied. It was concluded from these observations that for sandwich beams having functionally graded cores, the maximum contact force increases and the maximum strain decreases compared to those of sandwich beams with a homogenous core. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Sandwich structures usually are made of two thin and stiff face sheets that are separated with a thick and low density core. One of the important problems in sandwich structures is the damage due to discontinuity of mechanical properties at the boundary of face sheets and core. When these structures are exposed to impact loading, for example, shear stresses can cause the debonding of face sheets from core. Wu and Sun [1] and Shipsha et al. [2] inves- tigated different failure modes of sandwich beams and suggested that these structures can be upgraded using new materials. Utilizing a functionally graded (FG) core in sandwich panels is increasing because of their capabilities in reducing thermal- and residual-stresses induced between the face sheets and core materials in comparison to conventional sandwich panels. Venkataraman and Sankar [3] indicated that a graded core expres- sively could reduce the face sheet–core interfacial shear stresses while Nakamura and Wang [4] demonstrated the possibility of reducing impact damage in FGMs using finite element method. FGMs, a group of advanced nonhomogenous composites, usually are consisting of ceramic and metal phases. Mechanical properties such as young modulus of these materials vary continuously throughout the thickness direction. The variations of Poisson’s ratio are negligible and in most cases it’s assumed to be constant [5]. Suresh and Mortensen [6] and Miyamoto et al. [7] have reviewed the history of FGM and Butcher and Rousseau [8] and Parameswa- ran and Shukla [9] have described the manufacturing methods of these materials. Conventional models for two phase composites, such as rule of mixture, modified rule of mixture [10] and microme- chanical based models [11] together with appropriate volume frac- tion functions are used to determine mechanical properties of FGMs. Researchers often use exponential [12] or power low [13] volume fraction functions. Considering sudden changes at the inter- faces and consequently stress concentrations in these functions, Chung and Chi [14] suggested a sigmoid function for defining mechanical properties. Chi and Chung [15] also investigated FGM plates under transverse loading using sigmoid functions for mechanical properties. On the other hand, the distribution of con- stituents in a functionally graded material is not uniform; therefore, several models such as matricity [16], aM model and bM [17] have been developed to describe the microstructure of FGMs. For a sandwich structure subjected to impact loading by a pro- jectile, the main parameters to be investigated through developing of dynamic models are (i) projectile motion, (ii) local and global deformation, (iii) contact area and (iv) the behavior of sandwich structure. Several types of mathematical models are used to study the impact of a structure. The classical method decouples the local and global responses and ignores any interaction between the two. The first order shear deformation theory (FSDT) and higher-order shear deformation theories (HSDT) and Bernoulli–Euler beam the- ory and Timoshenko beam theory [18,19] do not consider the flex- ibility of the core in transverse direction. In addition, the interaction between face sheets and soft and flexible core is also neglected. Most recently, the higher-order sandwich plate theory (HSAPT) [20] and improved higher-order sandwich plate theory (IHSAPT) [21] has been introduced. 0263-8223/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.compstruct.2008.06.013 * Corresponding author. Tel.: +98 21 61114041; fax: +98 21 88013029. E-mail address: aafaghi@ut.ac.ir (A.A. Khatibi). URL: http://www.ut.ac.ir (A.A. Khatibi). Composite Structures 89 (2009) 28–34 Contents lists available at ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct